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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Built Environ.</journal-id>
<journal-title>Frontiers in Built Environment</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Built Environ.</abbrev-journal-title>
<issn pub-type="epub">2297-3362</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1386803</article-id>
<article-id pub-id-type="doi">10.3389/fbuil.2024.1386803</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Built Environment</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Investigation of piezocone dissipation test interpretation in clay accounting for vertical and horizontal porewater pressure dissipation with a large deformation axisymmetric penetration model</article-title>
<alt-title alt-title-type="left-running-head">Moug et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fbuil.2024.1386803">10.3389/fbuil.2024.1386803</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Moug</surname>
<given-names>Diane</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2598229/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/methodology/"/>
<role content-type="https://credit.niso.org/contributor-roles/supervision/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Huffman</surname>
<given-names>Andrew</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
<role content-type="https://credit.niso.org/contributor-roles/investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>DeJong</surname>
<given-names>Jason T.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Civil and Environmental Engineering</institution>, <institution>Portland State University</institution>, <addr-line>Portland</addr-line>, <addr-line>OR</addr-line>, <country>United States</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Civil and Environmental Engineering, University of California, Davis</institution>, <addr-line>Davis</addr-line>, <addr-line>CA</addr-line>, <country>United States</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1549747/overview">Krishna Kumar</ext-link>, The University of Texas at Austin, United States</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/191415/overview">Christos Vrettos</ext-link>, University of Kaiserslautern, Germany</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/869049/overview">Rui Chen</ext-link>, Harbin Institute of Technology, Shenzhen, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Diane Moug, <email>dmoug@pdx.edu</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>31</day>
<month>05</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="collection">
<year>2024</year>
</pub-date>
<volume>10</volume>
<elocation-id>1386803</elocation-id>
<history>
<date date-type="received">
<day>16</day>
<month>02</month>
<year>2024</year>
</date>
<date date-type="accepted">
<day>24</day>
<month>04</month>
<year>2024</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2024 Moug, Huffman and DeJong.</copyright-statement>
<copyright-year>2024</copyright-year>
<copyright-holder>Moug, Huffman and DeJong</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>The piezocone (CPTu) dissipation test is used to characterize how the applied load from the penetrating cone is distributed between the soil and pore fluid during both penetrometer advancement and when penetration is paused. The coefficient of consolidation is often estimated from CPTu dissipation tests by interpreting the rate of excess porewater pressure (<inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
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</inline-formula>) decay to static conditions during a pause in cone penetration. Most CPTu dissipation test interpretation methods are based on Terzaghi consolidation theory for <inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
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</inline-formula> dissipation at the cone shoulder (<inline-formula id="inf3">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position) or cone face (<inline-formula id="inf4">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position) and assume that radial <inline-formula id="inf5">
<mml:math id="m5">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dissipation dominates the response. However, several recent studies show that vertical <inline-formula id="inf6">
<mml:math id="m6">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration does contribute to the response. This study uses a large deformation direct axisymmetric cone penetration model to characterize the soil-water mechanical response during CPTu dissipation tests, and in particular, the role of vertical <inline-formula id="inf7">
<mml:math id="m7">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
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</inline-formula> dissipation on the response at the <inline-formula id="inf8">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf9">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> positions. Large deformations around the penetrating cone are accommodated with an Arbitrary Lagrangian Eulerian approach. Soil behavior is modeled with the MIT-S1 constitutive model calibrated for Boston blue clay (BBC) soil behavior. <inline-formula id="inf10">
<mml:math id="m10">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dissipation following undrained cone penetration is simulated with coupled consolidation for BBC with over-consolidation ratios (OCR) of 1, 2, and 4 and a range of hydraulic conductivity anisotropy. The simulated <inline-formula id="inf11">
<mml:math id="m11">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf12">
<mml:math id="m12">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation responses are presented to study how they are affected by OCR and hydraulic conductivity anisotropy. A correction factor is recommended to account for hydraulic conductivity anisotropy when interpreting the horizontal coefficient of consolidation from CPTu dissipation tests.</p>
</abstract>
<kwd-group>
<kwd>cone penetration testing</kwd>
<kwd>dissipation testing</kwd>
<kwd>ALE</kwd>
<kwd>large deformations</kwd>
<kwd>finite deformation</kwd>
<kwd>overconsolidated clay</kwd>
<kwd>coefficient of consolidation</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Geotechnical Engineering</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>The piezocone (CPTu) dissipation test is used in geotechnical engineering and environmental engineering to characterize how the applied load from the penetrating cone is distributed between the soil and pore fluid during both penetrometer advancement and when penetration is paused. The test is performed by pausing cone penetration and monitoring excess porewater pressure (<inline-formula id="inf13">
<mml:math id="m13">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>) dissipation with time at discrete locations on the cone penetrometer. The soil coefficient of consolidation and hydraulic conductivity, which the CPTu dissipation test interprets, control the rate at which the porewater pressure enables stress transfer from the pore fluid to the soil skeleton.</p>
<p>Many commonly used CPTu dissipation interpretation methods assume that radial <inline-formula id="inf14">
<mml:math id="m14">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dissipation dominates the measured response (e.g., <xref ref-type="bibr" rid="B29">Teh and Houlsby, 1991</xref>; <xref ref-type="bibr" rid="B4">Burns and Mayne, 1998</xref>), and therefore, interpretation yields estimates for the horizontal coefficient of consolidation (<inline-formula id="inf15">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) and the horizontal soil permeability (<inline-formula id="inf16">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>). However, subsequent studies note that vertical <inline-formula id="inf17">
<mml:math id="m17">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration contributes to the CPTu <inline-formula id="inf18">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation test response, including <xref ref-type="bibr" rid="B7">Chai et al. (2014)</xref>, <xref ref-type="bibr" rid="B1">Agaiby and Mayne (2018)</xref>, and <xref ref-type="bibr" rid="B30">Tsegaye (2021)</xref>. In particular, <xref ref-type="bibr" rid="B1">Agaiby and Mayne (2018)</xref> note that the interpreted coefficient of consolidation reflects hydraulic properties in both vertical and horizontal directions and, therefore, term the interpreted value to be <inline-formula id="inf19">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> Therefore, <inline-formula id="inf20">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> may be over or underestimated depending on the soil&#x2019;s vertical hydraulic conductivity (<inline-formula id="inf21">
<mml:math id="m21">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) and hydraulic conductivity anisotropy (i.e., <inline-formula id="inf22">
<mml:math id="m22">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>). Although the influence of <inline-formula id="inf23">
<mml:math id="m23">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and vertical <inline-formula id="inf24">
<mml:math id="m24">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration is recognized, no current methods for CPTu dissipation test interpretation explicitly account for these properties when interpreting CPTu dissipation tests.</p>
<p>Numerical investigations into porewater pressure dissipation following undrained penetration are one of the primary tools for understanding the mechanics of the CPTu dissipation test and developing and validating methods to interpret the test results. These investigations include indirect and direct approaches to simulate cone penetration. Indirect methods capture cone penetration loading as a cylindrical or spherical cavity expansion problem (e.g., <xref ref-type="bibr" rid="B4">Burns and Mayne, 1998</xref>; <xref ref-type="bibr" rid="B14">Imre et al., 2010</xref>). These are relatively simple approaches that can often capture <inline-formula id="inf25">
<mml:math id="m25">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distributions around the cone with closed-form equations; however, the full loading condition from the penetrating cone is not captured, and porewater pressure migration is limited to the radial direction only. Direct penetration models simulate the full penetration loading condition on the surrounding soil and allow porewater pressure migration to occur vertically and radially. However, continuum methods (i.e., finite element or finite difference models) must accommodate large soil deformations around the penetrating cone, or mesh entanglement and other numerical errors will occur before reaching steady-state penetration conditions. Therefore, numerical techniques must be implemented to accommodate these large deformations. Continuum direct penetration models to study CPTu dissipation tests have been performed with the strain path method (<xref ref-type="bibr" rid="B29">Teh and Houlsby, 1991</xref>), a smooth cone-soil interface (<xref ref-type="bibr" rid="B31">Abu-Farskah et al., 2003</xref>), the press-replace method (<xref ref-type="bibr" rid="B19">Lim et al., 2019</xref>), the ABAQUS non-linear geometry option (<xref ref-type="bibr" rid="B2">Ansari et al., 2014</xref>; <xref ref-type="bibr" rid="B10">Deng et al., 2023</xref>), arbitrary Lagrangian Eulerian (ALE) techniques (<xref ref-type="bibr" rid="B6">Chai et al., 2012</xref>; <xref ref-type="bibr" rid="B22">Mahmoodzadeh et al., 2014</xref>; <xref ref-type="bibr" rid="B20">Liu et al., 2022</xref>), and material point methods (<xref ref-type="bibr" rid="B5">Ceccato and Simonini, 2016</xref>). These previous numerical dissipation studies used simple soil models such as Mohr Coulomb or modified Cam clay that do not fully capture the response of undrained clay to cone penetration loading, as shown in <xref ref-type="bibr" rid="B24">Moug et al. (2019)</xref>.</p>
<p>Of the above studies, only <xref ref-type="bibr" rid="B31">Abu-Farskah et al. (2003)</xref> and <xref ref-type="bibr" rid="B19">Lim et al. (2019)</xref> studied the role of <inline-formula id="inf26">
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<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
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</inline-formula> during CPTu dissipation; the two studies yielded conflicting results. <xref ref-type="bibr" rid="B31">Abu-Farskah et al. (2003)</xref> found that <inline-formula id="inf27">
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</inline-formula> dissipation responses comparing simulations of <inline-formula id="inf30">
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</inline-formula>; while <xref ref-type="bibr" rid="B19">Lim et al. (2019)</xref> found no effect of <inline-formula id="inf32">
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</inline-formula> on the <inline-formula id="inf33">
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</inline-formula> dissipation curve. This study addresses the knowledge gap regarding the contribution of vertical porewater pressure dissipation when interpreting <inline-formula id="inf34">
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</mml:math>
</inline-formula> interpretation.</p>
<p>This study uses a direct, axisymmetric cone penetration model, ALE techniques, and an advanced constitutive model to investigate soil-water interactions during CPTu dissipation. The direct axisymmetric cone penetration model is implemented in the finite difference program FLAC and accommodates large deformations around the penetrating cone with a user-implemented ALE algorithm. An advanced elastoplastic bounding surface constitutive model, MIT-S1 (<xref ref-type="bibr" rid="B25">Pestana and Whittle, 1999</xref>), is calibrated for Boston blue clay (BBC) to capture anisotropic saturated clay behavior. This numerical model, specifically the combination of a large deformation direct penetration simulation and the use of a complex anisotropic soil model, differs from previous numerical studies of CPTu dissipation since it uses a direct penetration model that can capture the full loading condition around the penetrating cone, and can capture the anisotropic shear strength behavior and shear-induced <inline-formula id="inf38">
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<mml:math id="m40">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
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<mml:msub>
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<mml:mi>v</mml:mi>
</mml:msub>
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</inline-formula> during piezocone dissipation tests. Specifically, this study examines how <inline-formula id="inf41">
<mml:math id="m41">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
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<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
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<mml:mrow>
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</inline-formula> position) and the cone shoulder (<inline-formula id="inf43">
<mml:math id="m43">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
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</mml:math>
</inline-formula> position) to suggest an approach to estimate <inline-formula id="inf44">
<mml:math id="m44">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
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</inline-formula> and <inline-formula id="inf45">
<mml:math id="m45">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>v</mml:mi>
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</inline-formula> that accounts for vertical <inline-formula id="inf46">
<mml:math id="m46">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration. CPTu dissipation following undrained penetration is examined for BBC with <inline-formula id="inf47">
<mml:math id="m47">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
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</inline-formula> ranging from 1 to 10. Simulations are performed for undrained penetration in saturated clay with OCR of 1, 2, and 4 to investigate if stress history affects the role of <inline-formula id="inf48">
<mml:math id="m48">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
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</inline-formula> during CPTu dissipation tests.</p>
</sec>
<sec id="s2">
<title>2 Axisymmetric piezocone penetration and dissipation model</title>
<p>A direct axisymmetric cone penetration model with ALE to accommodate large deformations was used to simulate CPTu dissipation following steady-state undrained penetration in clay. The simulations were performed using the explicit finite difference program FLAC 8.0 (Fast Lagrangian Analysis of Continua; Itasca 2016) with the MIT-S1 constitutive model (<xref ref-type="bibr" rid="B25">Pestana and Whittle, 1999</xref>; <xref ref-type="bibr" rid="B26">Pestana et al., 2002</xref>) calibrated for BBC. Penetration was simulated with initial OCR of 1, 2, and 4.</p>
<sec id="s2-1">
<title>2.1 Piezocone dissipation model</title>
<p>The axisymmetric model geometry simulates steady-state penetration at one depth in the soil column for a standard 10&#xa0;cm<sup>2</sup> cone as shown in <xref ref-type="fig" rid="F1">Figure 1</xref>. The model is initialized with stress and material properties for the &#x201c;wished-in-place&#x201d; condition at the depth of interest in the soil column. Cone geometry and conditions between the cone and soil are captured with Mohr-Coulomb interface elements that obey the Mohr-Coulomb friction condition. The interface coefficient of friction (<inline-formula id="inf49">
<mml:math id="m49">
<mml:mrow>
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<mml:mi>&#x3d5;</mml:mi>
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<mml:mi>c</mml:mi>
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<mml:mi>n</mml:mi>
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</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>&#x3d5;</mml:mi>
<mml:mrow>
<mml:mi>c</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>s</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) was set at 0.8, where 0.0 would represent a perfectly smooth cone and 1.0 would represent a perfectly rough cone. The stiffnesses of the shear and normal springs in these interface elements were set large enough that they had negligible effects on the solution (<xref ref-type="bibr" rid="B15">Itasca, 2016</xref>).</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Penetration model geometry and boundary conditions.</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g001.tif"/>
</fig>
<p>The penetration boundary conditions are specified for soil flowing upwards relative to a stationary cone; soil conceptually flows into the bottom of the model and exits at the top of the model. The <italic>in-situ</italic> vertical stress is applied across the bottom boundary, where this boundary is sufficiently far from the penetrating cone&#x2019;s zone of influence that the <italic>in-situ</italic> stress condition prevails. The right radial boundary is represented with an infinite elastic boundary condition and is sufficiently far from the penetrating cone to avoid boundary effects (<xref ref-type="bibr" rid="B23">Moug, 2017</xref>). The model dimensions are 37 cone diameters in the radial direction, 37 cone diameters below the cone tip, and 5 cone diameters above the cone shoulder. The cone penetration velocity is applied to all gridpoints across the top boundary, with adjustments made to the gridpoint adjacent to the cone shaft to accommodate friction at the soil-shaft interface. Penetration is then simulated until steady-state penetration resistance, and steady-state stress and <inline-formula id="inf50">
<mml:math id="m50">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
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</inline-formula> conditions around the penetrating cone are reached; for this work, steady-state stress and <inline-formula id="inf51">
<mml:math id="m51">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distributions were considered to be achieved after 30 cone diameters of simulated penetration, which is consistent with <xref ref-type="bibr" rid="B21">Lu et al. (2004)</xref>. Piezocone dissipation is simulated by first bringing the simulated penetration velocity to zero, then re-assigning hydraulic properties and monitoring <inline-formula id="inf52">
<mml:math id="m52">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
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</inline-formula> over the simulated time.</p>
<p>Groundwater seepage boundary conditions for simulated dissipation were a combination of no-flow, fixed porewater pressure, and leaky boundaries. A no-flow condition was assigned at the axisymmetric boundary (x &#x3d; 0). <italic>In-situ</italic> static porewater pressures were fixed at the far radial boundary and the bottom horizontal boundary; these boundaries were far enough from the penetrating cone that <inline-formula id="inf53">
<mml:math id="m53">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
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</inline-formula> conditions prevailed. A leaky boundary was implemented at the top of the model to allow seepage flow across the boundary. The leaky boundary is assigned by assuming that the distance to <inline-formula id="inf54">
<mml:math id="m54">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
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<mml:mo>&#x3d;</mml:mo>
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</inline-formula> was the distance to the top of the water table and assuming a constant <inline-formula id="inf55">
<mml:math id="m55">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
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</inline-formula> over this distance.</p>
</sec>
<sec id="s2-2">
<title>2.2 ALE for large deformations cone penetration</title>
<p>Large deformations during simulated penetration are addressed with a user-implemented ALE algorithm that performs rezoning and remapping operations throughout simulated penetration (<xref ref-type="bibr" rid="B24">Moug et al., 2019</xref>). The user-defined ALE algorithm is coupled with FLAC&#x2019;s large deformation Lagrangian formulation to allow full penetration simulations and implementation with the MIT-S1 constitutive model. The ALE algorithm is implemented by simulating penetration for a time interval with FLAC&#x2019;s standard Lagrangian deformation formulation. The rezoning step takes place before significant deformation of the model zones occurs; the rezoning step resets the model geometry to the &#x201c;undeformed&#x201d; or original condition. The Eulerian remapping step then maps the model properties from the deformed model zones onto the undeformed model zones; this step is implemented in FLAC through a user-defined language according to the approach in <xref ref-type="bibr" rid="B32">Pember and Anderson (2001)</xref> and adapted for FLAC as described in <xref ref-type="bibr" rid="B23">Moug (2017)</xref>. The Lagrangian, rezoning, and Eulerian remapping steps are continued in succession until steady-state cone penetration conditions are reached.</p>
</sec>
<sec id="s2-3">
<title>2.3 MIT-S1 Boston Blue clay calibration</title>
<p>The MIT-S1 constitutive model is a bounding surface plasticity model that can capture soil behavior from sedimentary clays to clean sands (<xref ref-type="bibr" rid="B25">Pestana and Whittle, 1999</xref>; <xref ref-type="bibr" rid="B26">Pestana et al., 2002</xref>). <xref ref-type="bibr" rid="B16">Jaeger (2012)</xref> initially implemented the version of MIT-S1 used in this study, with some minor modifications to the model. Additional modifications to the MIT-S1 implementation for the penetration model in FLAC are described in <xref ref-type="bibr" rid="B23">Moug (2017)</xref>. Cone penetration and piezocone dissipation are simulated using the MIT-S1 model to accurately capture the effects of anisotropic <inline-formula id="inf56">
<mml:math id="m56">
<mml:mrow>
<mml:msub>
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</inline-formula> on the cone penetration problem, including the <inline-formula id="inf57">
<mml:math id="m57">
<mml:mrow>
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</inline-formula> distribution; <xref ref-type="bibr" rid="B24">Moug et al. (2019)</xref> demonstrated the role of <inline-formula id="inf58">
<mml:math id="m58">
<mml:mrow>
<mml:msub>
<mml:mi>s</mml:mi>
<mml:mi>u</mml:mi>
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</inline-formula> anisotropy on cone penetration tip resistance, stress distribution, and <inline-formula id="inf59">
<mml:math id="m59">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
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</inline-formula> distribution.</p>
</sec>
<sec id="s2-4">
<title>2.4 Hydraulic properties</title>
<p>The soil-water properties assigned to the FLAC model aimed to capture CPTu dissipation following undrained penetration. The fluid bulk modulus (<inline-formula id="inf60">
<mml:math id="m60">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
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</inline-formula>) was assigned to be at least 10 times larger than the soil skeleton bulk modulus or equal to <inline-formula id="inf61">
<mml:math id="m61">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>x</mml:mi>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mn>6</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> kPa, whichever was smaller. This was numerically advantageous since it results in an incompressible <inline-formula id="inf62">
<mml:math id="m62">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> relative to the soil skeleton without compromising numerical efficiency as a large <inline-formula id="inf63">
<mml:math id="m63">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> can result in a small dynamic timestep and long simulation times. The model remained completely saturated throughout penetration and dissipation simulations.</p>
<p>The <inline-formula id="inf64">
<mml:math id="m64">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf65">
<mml:math id="m65">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values during cone penetration were assigned to capture a completely undrained penetration response according to the normalized penetration velocity (<xref ref-type="bibr" rid="B9">DeJong and Randolph, 2012</xref>). <inline-formula id="inf66">
<mml:math id="m66">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf67">
<mml:math id="m67">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values during CPTu dissipation were coupled to the mechanical response through the <xref ref-type="bibr" rid="B13">House (2012)</xref> relationship:<disp-formula id="e1">
<mml:math id="m68">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">k</mml:mi>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">k</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn mathvariant="bold">10</mml:mn>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">e</mml:mi>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">e</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mn mathvariant="bold">0.44</mml:mn>
</mml:mfrac>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where this log-linear relationship between <inline-formula id="inf68">
<mml:math id="m69">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and void ratio (<inline-formula id="inf69">
<mml:math id="m70">
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>) was estimated with constant rate of strain consolidation tests on reconstituted BBC. <inline-formula id="inf70">
<mml:math id="m71">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the hydraulic conductivity at the void ratio <inline-formula id="inf71">
<mml:math id="m72">
<mml:mrow>
<mml:msub>
<mml:mi>e</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf72">
<mml:math id="m73">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the hydraulic conductivity at the void ratio <inline-formula id="inf73">
<mml:math id="m74">
<mml:mrow>
<mml:msub>
<mml:mi>e</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Similar relationships between <inline-formula id="inf74">
<mml:math id="m75">
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf75">
<mml:math id="m76">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> have been characterized by other researchers (e.g., <xref ref-type="bibr" rid="B28">Taylor, 1948</xref>; <xref ref-type="bibr" rid="B11">Dunn and Mitchell, 1984</xref>), however, the relationship in Eq. <xref ref-type="disp-formula" rid="e1">1</xref> was used for this study since it is specific to BBC. This relationship was incorporated into the CPTu dissipation simulations where <inline-formula id="inf76">
<mml:math id="m77">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf77">
<mml:math id="m78">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> were updated throughout the simulations in response to simulated changes in <inline-formula id="inf78">
<mml:math id="m79">
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>Simulated dissipation tests were performed for a range of <inline-formula id="inf79">
<mml:math id="m80">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values where the lowest assigned hydraulic conductivities were <inline-formula id="inf80">
<mml:math id="m81">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>m</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and the highest assigned hydraulic conductivities were <inline-formula id="inf81">
<mml:math id="m82">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>m</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. These values of <inline-formula id="inf82">
<mml:math id="m83">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf83">
<mml:math id="m84">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are at least an order of magnitude higher than typical values for clayey soils (<xref ref-type="bibr" rid="B18">Kulhawy and Mayne, 1990</xref>). These higher-than-typical <inline-formula id="inf84">
<mml:math id="m85">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> values allowed this study to be performed without having exceedingly long simulation times due to low <inline-formula id="inf85">
<mml:math id="m86">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> values. The <inline-formula id="inf86">
<mml:math id="m87">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> values were found not to compromise the objectives of this study, as discussed in the following section.</p>
</sec>
<sec id="s2-5">
<title>2.5 Model validation</title>
<p>Dissipation was simulated with different <inline-formula id="inf87">
<mml:math id="m88">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf88">
<mml:math id="m89">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values from the same steady-state undrained penetration simulation for each OCR. This approach assumes that simulated <inline-formula id="inf89">
<mml:math id="m90">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dissipation patterns depend on the initial <inline-formula id="inf90">
<mml:math id="m91">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distribution and <inline-formula id="inf91">
<mml:math id="m92">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> anisotropy during dissipation. Additionally, the approach assumes that dissipation is not affected by <inline-formula id="inf92">
<mml:math id="m93">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values during penetration if undrained conditions prevail. Therefore, CPTu dissipation curves shift in time proportionally to changes to <inline-formula id="inf93">
<mml:math id="m94">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> when dissipation is simulated from the same initial state and with the same <inline-formula id="inf94">
<mml:math id="m95">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. This assumption is validated in <xref ref-type="fig" rid="F2">Figures 2A, B</xref>. <xref ref-type="fig" rid="F2">Figure 2A</xref> compares the resulting dissipation curves for <inline-formula id="inf95">
<mml:math id="m96">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>m</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf96">
<mml:math id="m97">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>m</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> as <inline-formula id="inf97">
<mml:math id="m98">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation versus simulated time. <xref ref-type="fig" rid="F2">Figure 2B</xref> compares the same curves as dissipation versus simulated time normalized by the time to 50% <inline-formula id="inf98">
<mml:math id="m99">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dissipation (<inline-formula id="inf99">
<mml:math id="m100">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) and shows that the curves normalize to an identical curve. Therefore, the assumption that <inline-formula id="inf100">
<mml:math id="m101">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> patterns during CPTu dissipation tests and the shape of CPTu curves are not affected by <inline-formula id="inf101">
<mml:math id="m102">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> magnitude during dissipation is reasonable for this study.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Simulated <inline-formula id="inf102">
<mml:math id="m103">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation for OCR &#x3d; 1: <bold>(A)</bold> <inline-formula id="inf103">
<mml:math id="m104">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> versus simulated dissipation time for isotropic hydraulic conductivities, <bold>(B)</bold> <inline-formula id="inf104">
<mml:math id="m105">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> versus simulated dissipation time normalized by <inline-formula id="inf105">
<mml:math id="m106">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for isotropic hydraulic conductivities, and <bold>(C)</bold> <inline-formula id="inf106">
<mml:math id="m107">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> versus simulated dissipation time from initial conditions for penetration in <inline-formula id="inf107">
<mml:math id="m108">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>8</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> m/s and <inline-formula id="inf108">
<mml:math id="m109">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>8</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>m</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> clay.</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g002.tif"/>
</fig>
<p>The assumption that the initial <inline-formula id="inf109">
<mml:math id="m110">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distribution is unaffected if undrained penetration is simulated is further examined in <xref ref-type="fig" rid="F2">Figure 2C</xref>. The figure shows two dissipation curves. One dissipation curve was simulated following steady-state penetration in soil with <inline-formula id="inf110">
<mml:math id="m111">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>8</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> m/s, and the other following steady-state penetration in soil with <inline-formula id="inf111">
<mml:math id="m112">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>8</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> m/s. Dissipation for both cases was simulated with <inline-formula id="inf112">
<mml:math id="m113">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> m/s. The resulting <inline-formula id="inf113">
<mml:math id="m114">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation curves in <xref ref-type="fig" rid="F2">Figure 2C</xref> are identical and validate the assumption that <inline-formula id="inf114">
<mml:math id="m115">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dissipation patterns are unaffected by <inline-formula id="inf115">
<mml:math id="m116">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>/<inline-formula id="inf116">
<mml:math id="m117">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> during penetration provided <inline-formula id="inf117">
<mml:math id="m118">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf118">
<mml:math id="m119">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are small enough for undrained conditions to exist.</p>
<p>The CPTu simulations are further validated by comparing simulated results against a CPTu dissipation test performed in a BBC deposit. <xref ref-type="fig" rid="F3">Figure 3</xref> includes the published CPTu <inline-formula id="inf119">
<mml:math id="m120">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation data from <xref ref-type="bibr" rid="B3">Baligh and Levadoux (1986)</xref> for BBC with an OCR less than 2 compared with simulated CPTu <inline-formula id="inf120">
<mml:math id="m121">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation in BBC with OCR &#x3d; 1. The tests are plotted as <inline-formula id="inf121">
<mml:math id="m122">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> versus <inline-formula id="inf122">
<mml:math id="m123">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> to normalize the curves for stress conditions and <inline-formula id="inf123">
<mml:math id="m124">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values. The close agreement indicates that the simulated CPTu dissipation tests in BBC can be used to study CPTu dissipation tests in normal clay.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Comparison of simulated CPTu <inline-formula id="inf124">
<mml:math id="m125">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation test in OCR &#x3d; 1 BBC with <xref ref-type="bibr" rid="B3">Baligh and Levadoux (1986)</xref> CPTu field test in BBC.</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g003.tif"/>
</fig>
</sec>
</sec>
<sec id="s3">
<title>3 Results of simulated piezocone dissipation</title>
<p>Dissipation following undrained steady-state cone penetration was simulated for BBC with OCR &#x3d; 1, 2, and 4. The initial total vertical stress (<inline-formula id="inf125">
<mml:math id="m126">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) and porewater pressure (<inline-formula id="inf126">
<mml:math id="m127">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mi>o</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) for each case were 200&#xa0;kPa and 100&#xa0;kPa, respectively. Initial horizontal effective stress (<inline-formula id="inf127">
<mml:math id="m128">
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>h</mml:mi>
<mml:mi>o</mml:mi>
</mml:mrow>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>) was established based on OCR and lateral at rest coefficient of effective stress (<inline-formula id="inf128">
<mml:math id="m129">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mi>&#x3d;</mml:mi>
<mml:msub>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>h</mml:mi>
<mml:mi>o</mml:mi>
</mml:mrow>
<mml:mi>&#x2032;</mml:mi>
</mml:msubsup>
<mml:mo>/</mml:mo>
</mml:msub>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>o</mml:mi>
</mml:mrow>
<mml:mi>&#x2032;</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>) for the MIT-S1 BBC calibration; <inline-formula id="inf129">
<mml:math id="m130">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values were 0.50, 0.60, and 0.80, for OCR &#x3d; 1, 2, and 4, respectively. Dissipation was simulated for the initial <inline-formula id="inf130">
<mml:math id="m131">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> conditions: <inline-formula id="inf131">
<mml:math id="m132">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> m/s, <inline-formula id="inf132">
<mml:math id="m133">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>k</mml:mi>
</mml:mrow>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mi>x</mml:mi>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> m/s, <inline-formula id="inf133">
<mml:math id="m134">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mi>k</mml:mi>
</mml:mrow>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>5</mml:mn>
<mml:mi>x</mml:mi>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> m/s, <inline-formula id="inf134">
<mml:math id="m135">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mn>10</mml:mn>
<mml:mi>k</mml:mi>
</mml:mrow>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> m/s, and <inline-formula id="inf135">
<mml:math id="m136">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> m/s. As discussed above, <inline-formula id="inf136">
<mml:math id="m137">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf137">
<mml:math id="m138">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> were updated throughout dissipation and coupled to the mechanical soil response.</p>
<sec id="s3-1">
<title>3.1 Simulated dissipation at u<sub>1</sub> and u<sub>2</sub> positions</title>
<p>Dissipation over time was examined at the <inline-formula id="inf138">
<mml:math id="m139">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf139">
<mml:math id="m140">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> positions. The <inline-formula id="inf140">
<mml:math id="m141">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation curves show monotonic responses for all OCR conditions (<xref ref-type="fig" rid="F4">Figures 4A&#x2013;C</xref>), while the simulated <inline-formula id="inf141">
<mml:math id="m142">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation curves result in monotonic or non-monotonic responses depending on initial OCR (<xref ref-type="fig" rid="F4">Figures 4D&#x2013;F</xref>). This is consistent with published CPTu tests where monotonic responses prevail at the <inline-formula id="inf142">
<mml:math id="m143">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position regardless of whether a monotonic or non-monotonic response is observed at the <inline-formula id="inf143">
<mml:math id="m144">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position (e.g., <xref ref-type="bibr" rid="B8">Chen and Mayne, 1994</xref>; <xref ref-type="bibr" rid="B27">Sully et al., 1999</xref>; <xref ref-type="bibr" rid="B12">Finke et al., 2001</xref>). The simulated <inline-formula id="inf144">
<mml:math id="m145">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> results show a monotonic dissipation response for OCR &#x3d; 1, which is consistent with most piezocone dissipation tests following undrained penetration in normally consolidated soils (e.g., <xref ref-type="bibr" rid="B4">Burns and Mayne, 1998</xref>). The simulated results for OCR &#x3d; 2 show a slightly non-monotonic <inline-formula id="inf145">
<mml:math id="m146">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> response where the difference between <inline-formula id="inf146">
<mml:math id="m147">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf147">
<mml:math id="m148">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is about 5&#xa0;kPa for all simulated dissipation scenarios. The results for OCR &#x3d; 4 show a strongly non-monotonic <inline-formula id="inf148">
<mml:math id="m149">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> response where the difference between <inline-formula id="inf149">
<mml:math id="m150">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf150">
<mml:math id="m151">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is about 130&#x2013;150&#xa0;kPa. This is consistent with published <inline-formula id="inf151">
<mml:math id="m152">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation traces in varying OCR conditions, including those published by <xref ref-type="bibr" rid="B7">Chai et al. (2014)</xref>, that show a stronger non-monotonic response as OCR increases.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Simulated dissipation curves for OCR &#x3d; 1, 2 and 4 with varying <inline-formula id="inf152">
<mml:math id="m153">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> at the <inline-formula id="inf153">
<mml:math id="m154">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(A&#x2013;C)</bold> and <inline-formula id="inf154">
<mml:math id="m155">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(D&#x2013;F)</bold> positions.</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g004.tif"/>
</fig>
<p>The non-monotonic <inline-formula id="inf155">
<mml:math id="m156">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> response for OCR &#x3d; 4 is affected by <inline-formula id="inf156">
<mml:math id="m157">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf157">
<mml:math id="m158">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> decreases as the <inline-formula id="inf158">
<mml:math id="m159">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> ratio increases. Specifically, <inline-formula id="inf159">
<mml:math id="m160">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> with <inline-formula id="inf160">
<mml:math id="m161">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> is about 10% larger than <inline-formula id="inf161">
<mml:math id="m162">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for <inline-formula id="inf162">
<mml:math id="m163">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>. These results indicate that vertical <inline-formula id="inf163">
<mml:math id="m164">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration does affect the <inline-formula id="inf164">
<mml:math id="m165">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> response, however, vertical <inline-formula id="inf165">
<mml:math id="m166">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration is likely not the driving mechanism of non-monotonic <inline-formula id="inf166">
<mml:math id="m167">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation responses since vertical <inline-formula id="inf167">
<mml:math id="m168">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration is slightly suppressed for the <inline-formula id="inf168">
<mml:math id="m169">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> case compared to the isotropic case.</p>
<p>Dissipation rates do increase as <inline-formula id="inf169">
<mml:math id="m170">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> increases and <inline-formula id="inf170">
<mml:math id="m171">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is kept constant, as is expected. However, increases in dissipation rate, represented by <inline-formula id="inf171">
<mml:math id="m172">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, are less than the increase in <inline-formula id="inf172">
<mml:math id="m173">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. <inline-formula id="inf173">
<mml:math id="m174">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the time to 50% dissipation from the <inline-formula id="inf174">
<mml:math id="m175">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> or <inline-formula id="inf175">
<mml:math id="m176">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values at the start of the dissipation test and are directly related to the coefficient to consolidation in many common CPTu test interpretation methods (e.g., <xref ref-type="bibr" rid="B29">Teh and Houlsby, 1991</xref>; <xref ref-type="bibr" rid="B1">Agaiby and Mayne, 2018</xref>). <xref ref-type="fig" rid="F5">Figure 5</xref> plots the <inline-formula id="inf176">
<mml:math id="m177">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values for both <inline-formula id="inf177">
<mml:math id="m178">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf178">
<mml:math id="m179">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation from the results in <xref ref-type="fig" rid="F4">Figure 4</xref> versus model-assigned <inline-formula id="inf179">
<mml:math id="m180">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values. For the non-monotonic <inline-formula id="inf180">
<mml:math id="m181">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> responses for OCR &#x3d; 4, the <inline-formula id="inf181">
<mml:math id="m182">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the time to reach 50% of the peak <inline-formula id="inf182">
<mml:math id="m183">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> from the time that the dissipation curve reaches its peak according to the <xref ref-type="bibr" rid="B27">Sully et al. (1999)</xref> correction. This <inline-formula id="inf183">
<mml:math id="m184">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> correction for the non-monotonic tests results in a very small change to <inline-formula id="inf184">
<mml:math id="m185">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> due to dissipation trends occurring over a log-time scale, and the results of this study are insensitive to this correction. The <inline-formula id="inf185">
<mml:math id="m186">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> results show that increases of <inline-formula id="inf186">
<mml:math id="m187">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> from <inline-formula id="inf187">
<mml:math id="m188">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> conditions do not result in directly proportional changes to <inline-formula id="inf188">
<mml:math id="m189">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> at either the <inline-formula id="inf189">
<mml:math id="m190">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> or <inline-formula id="inf190">
<mml:math id="m191">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> positions, indicating that <inline-formula id="inf191">
<mml:math id="m192">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf192">
<mml:math id="m193">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation tests respond to both <inline-formula id="inf193">
<mml:math id="m194">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf194">
<mml:math id="m195">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Simulated time to 50% of the maximum excess pore pressure at the <inline-formula id="inf195">
<mml:math id="m196">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf196">
<mml:math id="m197">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> positions for <bold>(A)</bold> OCR &#x3d; 1, <bold>(B)</bold> OCR &#x3d; 2, and <bold>(C)</bold> OCR &#x3d; 4.</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g005.tif"/>
</fig>
<p>The contribution of vertical <inline-formula id="inf197">
<mml:math id="m198">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> to reach <inline-formula id="inf198">
<mml:math id="m199">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for isotropic conditions (<inline-formula id="inf199">
<mml:math id="m200">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) is about 40%&#x2013;44% for the <inline-formula id="inf200">
<mml:math id="m201">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> response and 43%&#x2013;51% for the <inline-formula id="inf201">
<mml:math id="m202">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> response. These values are interpreted from <xref ref-type="fig" rid="F6">Figure 6</xref>, which plots the ratio of <inline-formula id="inf202">
<mml:math id="m203">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> from <inline-formula id="inf203">
<mml:math id="m204">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mi>m</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (<inline-formula id="inf204">
<mml:math id="m205">
<mml:mrow>
<mml:mfenced open="" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mn>50</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>s</mml:mi>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
</inline-formula> to the <inline-formula id="inf205">
<mml:math id="m206">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for anisotropic conditions (<inline-formula id="inf206">
<mml:math id="m207">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mn>50</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>s</mml:mi>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) against <inline-formula id="inf207">
<mml:math id="m208">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. The 1:1 line on <xref ref-type="fig" rid="F6">Figure 6</xref> represents where <inline-formula id="inf208">
<mml:math id="m209">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mn>50</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>s</mml:mi>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> would plot if <inline-formula id="inf209">
<mml:math id="m210">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf210">
<mml:math id="m211">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> increased isotropically. The values of vertical <inline-formula id="inf211">
<mml:math id="m212">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> contribution are approximated by assuming that <inline-formula id="inf212">
<mml:math id="m213">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is dominated by horizontal migration for the <inline-formula id="inf213">
<mml:math id="m214">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> conditions. For example, with OCR &#x3d; 1 the <inline-formula id="inf214">
<mml:math id="m215">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for <inline-formula id="inf215">
<mml:math id="m216">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> m/s is 40% smaller than the <inline-formula id="inf216">
<mml:math id="m217">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> would be for <inline-formula id="inf217">
<mml:math id="m218">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> conditions at the <inline-formula id="inf218">
<mml:math id="m219">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position, and 44% at the <inline-formula id="inf219">
<mml:math id="m220">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position. The contribution of vertical <inline-formula id="inf220">
<mml:math id="m221">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> increases as OCR increases; these increases are addressed in detail in the discussion section below. The slightly greater contribution of vertical <inline-formula id="inf221">
<mml:math id="m222">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> at the <inline-formula id="inf222">
<mml:math id="m223">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position is attributed to the gradients in the initial <inline-formula id="inf223">
<mml:math id="m224">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distribution during undrained cone penetration, which are discussed in the next section.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Change in t<sub>50</sub> from CPTu dissipation as k<sub>h</sub>/k<sub>v</sub> changes showing that t<sub>50</sub> is a response to both k<sub>h</sub> and k<sub>v</sub>.</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g006.tif"/>
</fig>
</sec>
<sec id="s3-2">
<title>3.2 Excess porewater pressure distribution during piezocone dissipation</title>
<p>The <inline-formula id="inf224">
<mml:math id="m225">
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distribution during undrained cone penetration and during dissipation is examined in this section. The distributions provide additional evidence that vertical <inline-formula id="inf225">
<mml:math id="m226">
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration contributes to <inline-formula id="inf226">
<mml:math id="m227">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf227">
<mml:math id="m228">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation responses and should be considered for dissipation test interpretation, and that non-monotonic test responses are primarily due to horizontal <inline-formula id="inf228">
<mml:math id="m229">
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration.</p>
<p>The <inline-formula id="inf229">
<mml:math id="m230">
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> field during undrained penetration is induced by a combination of changes in normal and shear stresses from initial static conditions that are dependent on OCR (e.g., <xref ref-type="bibr" rid="B4">Burns and Mayne, 1998</xref>; <xref ref-type="bibr" rid="B17">Krage and DeJong, 2016</xref>). This section examines how changes in octahedral normal total stress (<inline-formula id="inf230">
<mml:math id="m231">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) and octahedral shear stress (<inline-formula id="inf231">
<mml:math id="m232">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c4;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) relate to <inline-formula id="inf232">
<mml:math id="m233">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> for the three initial conditions with OCR &#x3d; 1, 2, and 4.</p>
<p>
<xref ref-type="fig" rid="F7">Figure 7</xref> plots the steady-state undrained penetration profiles of <inline-formula id="inf233">
<mml:math id="m234">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf234">
<mml:math id="m235">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c4;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf235">
<mml:math id="m236">
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> as soil transitions from initial conditions ahead of the penetrating cone, to the penetrating cone face, and then to the cone shaft. These profiles show that <inline-formula id="inf236">
<mml:math id="m237">
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> strongly relates to <inline-formula id="inf237">
<mml:math id="m238">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and that large <inline-formula id="inf238">
<mml:math id="m239">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> unloading from the cone face to the cone shoulder corresponds to differences between <inline-formula id="inf239">
<mml:math id="m240">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf240">
<mml:math id="m241">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. There is some contribution to <inline-formula id="inf241">
<mml:math id="m242">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> from <inline-formula id="inf242">
<mml:math id="m243">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c4;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> depending on OCR, though it is less than the contribution of <inline-formula id="inf243">
<mml:math id="m244">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. For OCR &#x3d; 1, <inline-formula id="inf244">
<mml:math id="m245">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 159&#xa0;kPa and <inline-formula id="inf245">
<mml:math id="m246">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 111&#xa0;kPa at the <inline-formula id="inf246">
<mml:math id="m247">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position and <inline-formula id="inf247">
<mml:math id="m248">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 172&#xa0;kPa and <inline-formula id="inf248">
<mml:math id="m249">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 132 at the <inline-formula id="inf249">
<mml:math id="m250">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position; therefore, <inline-formula id="inf250">
<mml:math id="m251">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c4;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> causes an overall increase in <inline-formula id="inf251">
<mml:math id="m252">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. With OCR &#x3d; 2, <inline-formula id="inf252">
<mml:math id="m253">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 172&#xa0;kPa and <inline-formula id="inf253">
<mml:math id="m254">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 165&#xa0;kPa at the <inline-formula id="inf254">
<mml:math id="m255">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position and <inline-formula id="inf255">
<mml:math id="m256">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 262&#xa0;kPa and <inline-formula id="inf256">
<mml:math id="m257">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 261&#xa0;kPa; therefore, there is minimal change in <inline-formula id="inf257">
<mml:math id="m258">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> due to <inline-formula id="inf258">
<mml:math id="m259">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c4;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, which is consistent with constitutive behavior of OCR &#x3d; 2 clay in shear loading. For OCR &#x3d; 4, <inline-formula id="inf259">
<mml:math id="m260">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 81&#xa0;kPa and <inline-formula id="inf260">
<mml:math id="m261">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 148&#xa0;kPa at with <inline-formula id="inf261">
<mml:math id="m262">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position and <inline-formula id="inf262">
<mml:math id="m263">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 407&#xa0;kPa and <inline-formula id="inf263">
<mml:math id="m264">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 422&#xa0;kPa; there is a reduction in <inline-formula id="inf264">
<mml:math id="m265">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> due to <inline-formula id="inf265">
<mml:math id="m266">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c4;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> up to 2.5 cone diameters ahead of the cone tip, but the reduction is small compared to <inline-formula id="inf266">
<mml:math id="m267">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> induced by <inline-formula id="inf267">
<mml:math id="m268">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. <xref ref-type="fig" rid="F7">Figure 7</xref> also shows that the <inline-formula id="inf268">
<mml:math id="m269">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position is in a transition area between the cone face and cone shaft; therefore, <inline-formula id="inf269">
<mml:math id="m270">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> may not fully reflect loading conditions on either the cone face or cone shaft. This effect of this transition between the cone tip and cone shaft on the <inline-formula id="inf270">
<mml:math id="m271">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation response is examined in <xref ref-type="bibr" rid="B19">Lim et al. (2019)</xref>.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Change in octahedral stresses, shear stresses, and pore pressures relative to initial conditions along the penetrating cone path for steady state undrained penetration in <bold>(A)</bold> OCR &#x3d; 1, <bold>(B)</bold> OCR &#x3d; 2, and <bold>(C)</bold> OCR &#x3d; 4 clay.</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g007.tif"/>
</fig>
<p>The decrease in <inline-formula id="inf271">
<mml:math id="m272">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> from the cone face to the cone shoulder in <xref ref-type="fig" rid="F7">Figure 7</xref> possibly drives some vertical <inline-formula id="inf272">
<mml:math id="m273">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration during dissipation from the cone tip to the cone shoulder. As OCR increases, the difference between <inline-formula id="inf273">
<mml:math id="m274">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf274">
<mml:math id="m275">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> increases which causes a larger <inline-formula id="inf275">
<mml:math id="m276">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> gradient between the cone face and cone shoulder. Between the <inline-formula id="inf276">
<mml:math id="m277">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf277">
<mml:math id="m278">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> positions, <inline-formula id="inf278">
<mml:math id="m279">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> reduces by about 8% for OCR &#x3d; 1 from 172&#xa0;kPa at <inline-formula id="inf279">
<mml:math id="m280">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> to 159&#xa0;kPa at <inline-formula id="inf280">
<mml:math id="m281">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>; 34% for OCR &#x3d; 2 from 262&#xa0;kPa at <inline-formula id="inf281">
<mml:math id="m282">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> to 172&#xa0;kPa at <inline-formula id="inf282">
<mml:math id="m283">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>; and 80% for OCR &#x3d; 4 from 407&#xa0;kPa at <inline-formula id="inf283">
<mml:math id="m284">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> to 81&#xa0;kPa at <inline-formula id="inf284">
<mml:math id="m285">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. This may relate to a more strongly non-monotonic <inline-formula id="inf285">
<mml:math id="m286">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation response as OCR increases. Similarly, the <inline-formula id="inf286">
<mml:math id="m287">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> gradient downward from the cone tip increases as OCR increases, which is consistent with the larger role of vertical <inline-formula id="inf287">
<mml:math id="m288">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration at the <inline-formula id="inf288">
<mml:math id="m289">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position and as OCR increases.</p>
<p>Radial <inline-formula id="inf289">
<mml:math id="m290">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distributions at steady state penetration conditions (<inline-formula id="inf290">
<mml:math id="m291">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>) and during simulated dissipation from <inline-formula id="inf291">
<mml:math id="m292">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf292">
<mml:math id="m293">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> positions are plotted in <xref ref-type="fig" rid="F8">Figure 8</xref>. Distributions for <inline-formula id="inf293">
<mml:math id="m294">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>m</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf294">
<mml:math id="m295">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> m/s are presented to compare the soil response with isotropic and strongly anisotropic <inline-formula id="inf295">
<mml:math id="m296">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. Distributions are plotted for times relative to <inline-formula id="inf296">
<mml:math id="m297">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> determined at the <inline-formula id="inf297">
<mml:math id="m298">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position for OCR &#x3d; 1 and 2 and <inline-formula id="inf298">
<mml:math id="m299">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for the strongly non-monotonic response of OCR &#x3d; 4. This provides insight into how soil response differs between monotonic and non-monotonic dissipation tests. Since the response of OCR &#x3d; 2 is slightly non-monotonic, the distributions at <inline-formula id="inf299">
<mml:math id="m300">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are not considered for radial distributions. Distributions are plotted over a radial distance of 10 cone diameters from the simulated penetrometer, which is smaller than the influence zone but allowed examination of conditions near the penetrometer. For all OCR values, the initial distributions from the <inline-formula id="inf300">
<mml:math id="m301">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position are monotonic and remain so throughout dissipation (<xref ref-type="fig" rid="F8">Figures 8A, C, E</xref>). The radial distribution from the <inline-formula id="inf301">
<mml:math id="m302">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position is initially monotonic and remains so throughout dissipation for OCR &#x3d; 1 (<xref ref-type="fig" rid="F8">Figure 8B</xref>). The radial <inline-formula id="inf302">
<mml:math id="m303">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distribution from <inline-formula id="inf303">
<mml:math id="m304">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for OCR is initially slightly non-monotonic with <inline-formula id="inf304">
<mml:math id="m305">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 172&#xa0;kPa and the maximum <inline-formula id="inf305">
<mml:math id="m306">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>u in the distribution equal to 192&#xa0;kPa; the distribution becomes monotonic by <inline-formula id="inf306">
<mml:math id="m307">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.1</mml:mn>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for OCR &#x3d; 2 (<xref ref-type="fig" rid="F8">Figure 8D</xref>) with <inline-formula id="inf307">
<mml:math id="m308">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 167&#xa0;kPa for both <inline-formula id="inf308">
<mml:math id="m309">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 1 and 10. The radial <inline-formula id="inf309">
<mml:math id="m310">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> u distribution from <inline-formula id="inf310">
<mml:math id="m311">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is initially non-monotonic for OCR &#x3d; 4 with <inline-formula id="inf311">
<mml:math id="m312">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 81&#xa0;kPa and the maximum <inline-formula id="inf312">
<mml:math id="m313">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>u equal to 235&#xa0;kPa (<xref ref-type="fig" rid="F8">Figure 8F</xref>); the distribution becomes monotonic by <inline-formula id="inf313">
<mml:math id="m314">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> at which time <inline-formula id="inf314">
<mml:math id="m315">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 232&#xa0;kPa for <inline-formula id="inf315">
<mml:math id="m316">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and 216&#xa0;kPa for <inline-formula id="inf316">
<mml:math id="m317">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Radial distributions of <inline-formula id="inf317">
<mml:math id="m318">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> from <inline-formula id="inf318">
<mml:math id="m319">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(A&#x2013;C)</bold> and <inline-formula id="inf319">
<mml:math id="m320">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(D&#x2013;F)</bold> during simulated dissipation for <inline-formula id="inf320">
<mml:math id="m321">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 1 and 10.</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g008.tif"/>
</fig>
<p>The results in <xref ref-type="fig" rid="F8">Figure 8</xref> show that there are small differences in radial <inline-formula id="inf321">
<mml:math id="m322">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distributions between the <inline-formula id="inf322">
<mml:math id="m323">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf323">
<mml:math id="m324">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> cases that are attributable to different contributions of vertical and horizontal <inline-formula id="inf324">
<mml:math id="m325">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration. For OCR &#x3d; 1 and 2, <inline-formula id="inf325">
<mml:math id="m326">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> at <inline-formula id="inf326">
<mml:math id="m327">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is slightly larger at the cone face for the <inline-formula id="inf327">
<mml:math id="m328">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> case (<inline-formula id="inf328">
<mml:math id="m329">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 74&#xa0;kPa and 86&#xa0;kPa for OCR &#x3d; 1 and 2, respectively) than the <inline-formula id="inf329">
<mml:math id="m330">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> case (<inline-formula id="inf330">
<mml:math id="m331">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 72&#xa0;kPa and 82&#xa0;kPa for OCR &#x3d; 1 and 2, respectively); this is likely due to more vertical <inline-formula id="inf331">
<mml:math id="m332">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dissipation leading to lower <inline-formula id="inf332">
<mml:math id="m333">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for the isotropic <inline-formula id="inf333">
<mml:math id="m334">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> case.</p>
<p>The OCR &#x3d; 4 radial <inline-formula id="inf334">
<mml:math id="m335">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distributions for <inline-formula id="inf335">
<mml:math id="m336">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mn>0.1</mml:mn>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf336">
<mml:math id="m337">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf337">
<mml:math id="m338">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>5</mml:mn>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf338">
<mml:math id="m339">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are shown in <xref ref-type="fig" rid="F8">Figures 8E, F</xref>. These distributions indicate that both radial <inline-formula id="inf339">
<mml:math id="m340">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration towards the <inline-formula id="inf340">
<mml:math id="m341">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position and vertical <inline-formula id="inf341">
<mml:math id="m342">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration from the cone face to the cone shoulder contribute to the simulated non-monotonic <inline-formula id="inf342">
<mml:math id="m343">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> responses. The initial <inline-formula id="inf343">
<mml:math id="m344">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distribution from the <inline-formula id="inf344">
<mml:math id="m345">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position is non-monotonic with the maximum <inline-formula id="inf345">
<mml:math id="m346">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> value of 235&#xa0;kPa generated at about 0.6 cone diameters from <inline-formula id="inf346">
<mml:math id="m347">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position. The distributions remain non-monotonic until <inline-formula id="inf347">
<mml:math id="m348">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, indicating that some radial <inline-formula id="inf348">
<mml:math id="m349">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> redistribution towards the <inline-formula id="inf349">
<mml:math id="m350">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position contributes to the non-monotonic response. At <inline-formula id="inf350">
<mml:math id="m351">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf351">
<mml:math id="m352">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>5</mml:mn>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> there are notable differences between the <inline-formula id="inf352">
<mml:math id="m353">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf353">
<mml:math id="m354">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> cases, specifically, <inline-formula id="inf354">
<mml:math id="m355">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> adjacent to the cone is larger at <inline-formula id="inf355">
<mml:math id="m356">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and smaller at <inline-formula id="inf356">
<mml:math id="m357">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for the <inline-formula id="inf357">
<mml:math id="m358">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> case (<inline-formula id="inf358">
<mml:math id="m359">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 232&#xa0;kPa and <inline-formula id="inf359">
<mml:math id="m360">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 287&#xa0;kPa at <inline-formula id="inf360">
<mml:math id="m361">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>;</mml:mo>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 181&#xa0;kPa and <inline-formula id="inf361">
<mml:math id="m362">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 179&#xa0;at <inline-formula id="inf362">
<mml:math id="m363">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) compared to the <inline-formula id="inf363">
<mml:math id="m364">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> case (<inline-formula id="inf364">
<mml:math id="m365">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 216&#xa0;kPa and <inline-formula id="inf365">
<mml:math id="m366">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 311&#xa0;kPa at <inline-formula id="inf366">
<mml:math id="m367">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>;</mml:mo>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 174&#xa0;kPa and <inline-formula id="inf367">
<mml:math id="m368">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 191&#xa0;at <inline-formula id="inf368">
<mml:math id="m369">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>), which may be due to a larger contribution of vertical <inline-formula id="inf369">
<mml:math id="m370">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration from the cone face to the cone shoulder for the isotropic case than for the anisotropic case.</p>
</sec>
<sec id="s3-3">
<title>3.3 Mean total and effective stress during piezocone dissipation</title>
<p>Radial distributions of change in mean total stress from initial conditions (<inline-formula id="inf370">
<mml:math id="m371">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>) (plotted in <xref ref-type="fig" rid="F9">Figure 9</xref>) show dependence on OCR and little dependence on <inline-formula id="inf371">
<mml:math id="m372">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Mean total stress (<inline-formula id="inf372">
<mml:math id="m373">
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>) unloading between the cone face and cone shoulder is evident in radial distributions and the magnitude of <inline-formula id="inf373">
<mml:math id="m374">
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> unloading increases as OCR increases, which is consistent with <inline-formula id="inf374">
<mml:math id="m375">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> distributions in <xref ref-type="fig" rid="F7">Figure 7</xref>. For OCR &#x3d; 1 and OCR &#x3d; 2, notable changes in <inline-formula id="inf375">
<mml:math id="m376">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distribution do not occur until <inline-formula id="inf376">
<mml:math id="m377">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>0.1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>; at <inline-formula id="inf377">
<mml:math id="m378">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf378">
<mml:math id="m379">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> there is an overall decrease in <inline-formula id="inf379">
<mml:math id="m380">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> as soil consolidates around the penetrometer. Between the initial conditions and <inline-formula id="inf380">
<mml:math id="m381">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for OCR &#x3d; 1, <inline-formula id="inf381">
<mml:math id="m382">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> adjacent to the cone decreases from 101&#xa0;kPa to 52&#xa0;kPa at <inline-formula id="inf382">
<mml:math id="m383">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and from 137&#xa0;kPa to 67&#xa0;kPa at <inline-formula id="inf383">
<mml:math id="m384">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Between the initial conditions and <inline-formula id="inf384">
<mml:math id="m385">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for OCR &#x3d; 2, <inline-formula id="inf385">
<mml:math id="m386">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> adjacent to the cone decreases from 176&#xa0;kPa to 114&#xa0;kPa at <inline-formula id="inf386">
<mml:math id="m387">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and from 272&#xa0;kPa to 141&#xa0;kPa at <inline-formula id="inf387">
<mml:math id="m388">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. For OCR &#x3d; 4, changes in <inline-formula id="inf388">
<mml:math id="m389">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distribution primarily occur when <inline-formula id="inf389">
<mml:math id="m390">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3e;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. The radial distributions from <inline-formula id="inf390">
<mml:math id="m391">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for OCR &#x3d; 4 (<xref ref-type="fig" rid="F9">Figure 9F</xref>) are non-monotonic throughout dissipation with the distribution becoming less non-monotonic during dissipation. The initial <inline-formula id="inf391">
<mml:math id="m392">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> at the <inline-formula id="inf392">
<mml:math id="m393">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position is 105&#xa0;kPa with a maximum value of 248 in the radial distribution, by <inline-formula id="inf393">
<mml:math id="m394">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <inline-formula id="inf394">
<mml:math id="m395">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> at the <inline-formula id="inf395">
<mml:math id="m396">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position is 148&#xa0;kPa with a maximum value of 184 in the radial distribution. The non-monotonic distribution may be due to combined unloading from the cone face to cone shoulder and friction at the cone-soil interface. At the <inline-formula id="inf396">
<mml:math id="m397">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position for OCR &#x3d; 1, the initial <inline-formula id="inf397">
<mml:math id="m398">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is 445&#xa0;kPa and decreases to 323&#xa0;kPa by <inline-formula id="inf398">
<mml:math id="m399">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Radial distributions of <inline-formula id="inf399">
<mml:math id="m400">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> from <inline-formula id="inf400">
<mml:math id="m401">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(A&#x2013;C)</bold> and <inline-formula id="inf401">
<mml:math id="m402">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(D&#x2013;F)</bold> during simulated dissipation for <inline-formula id="inf402">
<mml:math id="m403">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 1 and 10.</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g009.tif"/>
</fig>
<p>The radial distributions of change in mean effective stress from initial conditions (<inline-formula id="inf403">
<mml:math id="m404">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msup>
<mml:mi>p</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>) are plotted in <xref ref-type="fig" rid="F10">Figure 10</xref>; these distributions are directly related to the distributions in <inline-formula id="inf404">
<mml:math id="m405">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf405">
<mml:math id="m406">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> in <xref ref-type="fig" rid="F8">Figures 8</xref>, <xref ref-type="fig" rid="F9">9</xref>, respectively. Therefore, the <inline-formula id="inf406">
<mml:math id="m407">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> values during dissipation are affected by <inline-formula id="inf407">
<mml:math id="m408">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in the same way that <inline-formula id="inf408">
<mml:math id="m409">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distributions are affected by <inline-formula id="inf409">
<mml:math id="m410">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Overall, radial <inline-formula id="inf410">
<mml:math id="m411">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msup>
<mml:mi>p</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> distributions increase during consolidation around the piezocone and result in larger mean effective stress (<inline-formula id="inf411">
<mml:math id="m412">
<mml:mrow>
<mml:msup>
<mml:mi>p</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>) near the cone than the initial conditions, this is consistent with loading from the penetrometer transferring from the pore fluid to the soil skeleton during dissipation and consolidation. This effect is stronger with increasing OCR, which leads to larger <inline-formula id="inf412">
<mml:math id="m413">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msup>
<mml:mi>p</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> as OCR increases. For instance, the maximum <inline-formula id="inf413">
<mml:math id="m414">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msup>
<mml:mi>p</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> from the <inline-formula id="inf414">
<mml:math id="m415">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position at <inline-formula id="inf415">
<mml:math id="m416">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is 5.2&#xa0;kPa for OCR &#x3d; 1, 45&#xa0;kPa for OCR &#x3d; 2, and 70&#xa0;kPa for OCR &#x3d; 4; and the maximum <inline-formula id="inf416">
<mml:math id="m417">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msup>
<mml:mi>p</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> from the <inline-formula id="inf417">
<mml:math id="m418">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position at <inline-formula id="inf418">
<mml:math id="m419">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is 14&#xa0;kPa for OCR &#x3d; 1, 79&#xa0;kPa for OCR &#x3d; 2, and 213&#xa0;kPa for OCR &#x3d; 4. <inline-formula id="inf419">
<mml:math id="m420">
<mml:mrow>
<mml:msup>
<mml:mi>p</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> at some distances remains lower than the initial conditions for all OCRs; however, it is expected that <inline-formula id="inf420">
<mml:math id="m421">
<mml:mrow>
<mml:msup>
<mml:mi>p</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> continues to increase as dissipation continues past <inline-formula id="inf421">
<mml:math id="m422">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Radial distributions of <inline-formula id="inf422">
<mml:math id="m423">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msup>
<mml:mi>p</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> from <inline-formula id="inf423">
<mml:math id="m424">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(A&#x2013;C)</bold> <inline-formula id="inf424">
<mml:math id="m425">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(D&#x2013;F)</bold> during simulated dissipation for <inline-formula id="inf425">
<mml:math id="m426">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 1 and 10.</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g010.tif"/>
</fig>
</sec>
<sec id="s3-4">
<title>3.4 Volumetric strain during piezocone dissipation</title>
<p>The radial <inline-formula id="inf426">
<mml:math id="m427">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> distributions, plotted in <xref ref-type="fig" rid="F11">Figure 11</xref>, show responses that primarily depend on OCR, with little difference attributed to <inline-formula id="inf427">
<mml:math id="m428">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Since dissipation tests were simulated following undrained penetration conditions, the <inline-formula id="inf428">
<mml:math id="m429">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> distribution at <inline-formula id="inf429">
<mml:math id="m430">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> is zero for all cases. Distributions from the <inline-formula id="inf430">
<mml:math id="m431">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position for all OCRs show similar contractive <inline-formula id="inf431">
<mml:math id="m432">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values adjacent to the cone face at <inline-formula id="inf432">
<mml:math id="m433">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. The similar values of <inline-formula id="inf433">
<mml:math id="m434">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> at <inline-formula id="inf434">
<mml:math id="m435">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> near the <inline-formula id="inf435">
<mml:math id="m436">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position for all OCRs (&#x2212;0.016 for OCR &#x3d; 1, &#x2212;0.014 for OCR &#x3d; 2, and &#x3d; 0.017 for OCR &#x3d; 4) is attributed to compensating effects of larger <inline-formula id="inf436">
<mml:math id="m437">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and greater soil stiffness as OCR increases. The simulated <inline-formula id="inf437">
<mml:math id="m438">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> response for OCR &#x3d; 1 is contractive from the <inline-formula id="inf438">
<mml:math id="m439">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position; there is little change in <inline-formula id="inf439">
<mml:math id="m440">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> at <inline-formula id="inf440">
<mml:math id="m441">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 0.01, and then <inline-formula id="inf441">
<mml:math id="m442">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> develops to &#x2212;0.003 adjacent to the cone by <inline-formula id="inf442">
<mml:math id="m443">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> and &#x2212;0.016 for <inline-formula id="inf443">
<mml:math id="m444">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. This is consistent with the <inline-formula id="inf444">
<mml:math id="m445">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> response for OCR &#x3d; 1 in <xref ref-type="fig" rid="F9">Figure 9</xref> where there is little change in <inline-formula id="inf445">
<mml:math id="m446">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distributions when <inline-formula id="inf446">
<mml:math id="m447">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is less than <inline-formula id="inf447">
<mml:math id="m448">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.1</mml:mn>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> For both the OCR &#x3d; 2 and OCR &#x3d; 4 simulations, the simulated <inline-formula id="inf448">
<mml:math id="m449">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> response close to the <inline-formula id="inf449">
<mml:math id="m450">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position is initially dilative with <inline-formula id="inf450">
<mml:math id="m451">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 0.0017 for OCR &#x3d; 2&#xa0;at <inline-formula id="inf451">
<mml:math id="m452">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.1</mml:mn>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf452">
<mml:math id="m453">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 0.011 for OCR &#x3d; 4&#xa0;at <inline-formula id="inf453">
<mml:math id="m454">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, which is consistent with the slightly non-monotonic response of OCR &#x3d; 2, the strongly non-monotonic response for OCR &#x3d; 4, and supports some radial <inline-formula id="inf454">
<mml:math id="m455">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> re-distribution towards the <inline-formula id="inf455">
<mml:math id="m456">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position at early times (<xref ref-type="fig" rid="F8">Figures 8D, F</xref>). Dilation dominates the response adjacent to the <inline-formula id="inf456">
<mml:math id="m457">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position for OCR &#x3d; 4 throughout dissipation, however the dilation response is limited to less than 0.5 cone diameters from the <inline-formula id="inf457">
<mml:math id="m458">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position and at further distances the response is compressive. The role of <inline-formula id="inf458">
<mml:math id="m459">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> anisotropy on the <inline-formula id="inf459">
<mml:math id="m460">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> response is small and is consistent with the small differences in <inline-formula id="inf460">
<mml:math id="m461">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distributions between the <inline-formula id="inf461">
<mml:math id="m462">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf462">
<mml:math id="m463">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> cases.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Radial distributions of <inline-formula id="inf463">
<mml:math id="m464">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> from <inline-formula id="inf464">
<mml:math id="m465">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(A&#x2013;C)</bold> and <inline-formula id="inf465">
<mml:math id="m466">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(D&#x2013;F)</bold> during simulated dissipation for <inline-formula id="inf466">
<mml:math id="m467">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 1 and 10.</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g011.tif"/>
</fig>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>4 Discussion</title>
<p>Numerical simulations of CPTu dissipation using large deformation methods allow investigation of <inline-formula id="inf467">
<mml:math id="m468">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> generation and dissipation as a system response to loading conditions imposed by the penetration cone, clay behavior, and hydraulic properties of the soil. This numerical study shows that at both the <inline-formula id="inf468">
<mml:math id="m469">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf469">
<mml:math id="m470">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> positions, and for OCR 1, 2, and 4, vertical <inline-formula id="inf470">
<mml:math id="m471">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> does have a contribution to the dissipation response for soils with isotropic or slightly anisotropic hydraulic conductivity. This finding is contrary to early CPTu dissipation test analysis, which assumed that due to natural soil anisotropy and induced gradients, <inline-formula id="inf471">
<mml:math id="m472">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> was dominant in the horizontal direction. However, this study supports the assertion by <xref ref-type="bibr" rid="B1">Agaiby and Mayne (2018)</xref> that the coefficient of consolidation estimated from CPTu tests should be represented as <inline-formula id="inf472">
<mml:math id="m473">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> to reflect dissipation in both the horizontal and vertical directions.</p>
<p>Based on the simulated <inline-formula id="inf473">
<mml:math id="m474">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values in <xref ref-type="fig" rid="F5">Figure 5</xref>, corrections to <inline-formula id="inf474">
<mml:math id="m475">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> to estimate <inline-formula id="inf475">
<mml:math id="m476">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are develop in <xref ref-type="fig" rid="F12">Figure 12</xref> and presented below, where:<disp-formula id="e2">
<mml:math id="m477">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x2248;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
<mml:mo>&#x2a;</mml:mo>
<mml:mi>c</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
<disp-formula id="e3">
<mml:math id="m478">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>ln</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>B</mml:mi>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
<inline-formula id="inf476">
<mml:math id="m479">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is a suggested correction factor to account for <inline-formula id="inf477">
<mml:math id="m480">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> when interpreting <inline-formula id="inf478">
<mml:math id="m481">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. The factors A and B are fit to the simulated results for <inline-formula id="inf479">
<mml:math id="m482">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf480">
<mml:math id="m483">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation and OCR &#x3d; 1, 2, and 4. The suggested values of A and B at these OCR values are summarized in <xref ref-type="table" rid="T1">Table 1</xref>. For OCR values between those listed in <xref ref-type="table" rid="T1">Table 1</xref>, it would be reasonable to interpolate between A and B values.</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Correction factor (<inline-formula id="inf481">
<mml:math id="m484">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) to estimate <inline-formula id="inf482">
<mml:math id="m485">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> from CPTu dissipation test interpreted <inline-formula id="inf483">
<mml:math id="m486">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g012.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Factors for use with Eq. <xref ref-type="disp-formula" rid="e3">3</xref> to estimate <inline-formula id="inf484">
<mml:math id="m487">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left"/>
<th colspan="3" align="center">u<sub>1</sub>
</th>
<th colspan="3" align="center">u<sub>2</sub>
</th>
</tr>
<tr>
<th align="left"/>
<th align="center">OCR &#x3d; 1</th>
<th align="center">OCR &#x3d; 2</th>
<th align="center">OCR &#x3d; 4</th>
<th align="center">OCR &#x3d; 1</th>
<th align="center">OCR &#x3d; 2</th>
<th align="center">OCR &#x3d; 4</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">A</td>
<td align="center">0.265</td>
<td align="center">0.316</td>
<td align="center">0.351</td>
<td align="center">0.225</td>
<td align="center">0.254</td>
<td align="center">0.282</td>
</tr>
<tr>
<td align="left">B</td>
<td align="center">0.805</td>
<td align="center">0.769</td>
<td align="center">0.750</td>
<td align="center">0.816</td>
<td align="center">0.819</td>
<td align="center">0.816</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The <inline-formula id="inf485">
<mml:math id="m488">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> approach is intended for use with CPTu interpretation methods that are based on estimation of <inline-formula id="inf486">
<mml:math id="m489">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (e.g., <xref ref-type="bibr" rid="B29">Teh and Houlsby, 1991</xref>; <xref ref-type="bibr" rid="B1">Agaiby and Mayne, 2018</xref>) and for normal clays with OCR 1 to 4. Use of this approach outside of these conditions and soil type requires further study and validation.</p>
<p>The <inline-formula id="inf487">
<mml:math id="m490">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values are based on <inline-formula id="inf488">
<mml:math id="m491">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, which would be estimated from either hydrogeologic studies, laboratory testing, or knowledge of the depositional environment (e.g., <xref ref-type="bibr" rid="B33">Leroueil and Jamiolkowski 1991</xref>). <inline-formula id="inf489">
<mml:math id="m492">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the assumed baseline anisotropy conditions from which CPTu dissipation test interpretation methods were initially developed and validated, and therefore little adjustment is needed (i.e., <inline-formula id="inf490">
<mml:math id="m493">
<mml:mrow>
<mml:mfenced open="" close=")" separators="&#x7c;">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#x2248;</mml:mo>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
</inline-formula>. This assumption is based on <xref ref-type="bibr" rid="B29">Teh and Houlsby (1991)</xref> who report little difference between dissipation curves once <inline-formula id="inf491">
<mml:math id="m494">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>; <xref ref-type="bibr" rid="B27">Sully et al. (1999)</xref> who evaluated the proposed non-monotonic <inline-formula id="inf492">
<mml:math id="m495">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> test correction to <inline-formula id="inf493">
<mml:math id="m496">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> with soils with <inline-formula id="inf494">
<mml:math id="m497">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> from 1 to 3 (i.e., isotropic to slightly anisotropic). As <inline-formula id="inf495">
<mml:math id="m498">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> increases, <inline-formula id="inf496">
<mml:math id="m499">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> at the <inline-formula id="inf497">
<mml:math id="m500">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf498">
<mml:math id="m501">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> positions will increase since there is limited <inline-formula id="inf499">
<mml:math id="m502">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dissipation in the vertical direction, and the interpreted <inline-formula id="inf500">
<mml:math id="m503">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> will decrease. Therefore, as the soil becomes more hydraulically anisotropic, <inline-formula id="inf501">
<mml:math id="m504">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> increases to reflect the decreasing contribution of vertical <inline-formula id="inf502">
<mml:math id="m505">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>
<inline-formula id="inf503">
<mml:math id="m506">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> differs slightly between <inline-formula id="inf504">
<mml:math id="m507">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf505">
<mml:math id="m508">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> CPTu dissipation curves, as shown in <xref ref-type="fig" rid="F12">Figures 12A, B</xref>, respectively, and OCR values. The <inline-formula id="inf506">
<mml:math id="m509">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> range is slightly larger for <inline-formula id="inf507">
<mml:math id="m510">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation, ranging from 0.75 to 1.55, compared to <inline-formula id="inf508">
<mml:math id="m511">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation, which ranges from 0.79 to 1.47. This is consistent with the previous observation that vertical <inline-formula id="inf509">
<mml:math id="m512">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dissipation is more dominant in the cone tip area due to hydraulic gradients vertically down from the cone tip and between the cone tip and the cone shaft. The range of <inline-formula id="inf510">
<mml:math id="m513">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> also increases as OCR increases, which indicates that vertical <inline-formula id="inf511">
<mml:math id="m514">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> becomes more important as OCR increases, potentially due to increasing <inline-formula id="inf512">
<mml:math id="m515">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> gradients.</p>
<p>The interpretation of <inline-formula id="inf513">
<mml:math id="m516">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf514">
<mml:math id="m517">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> from the simulated dissipation curves (termed <inline-formula id="inf515">
<mml:math id="m518">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf516">
<mml:math id="m519">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>h</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, respectively) are shown in <xref ref-type="fig" rid="F13">Figure 13</xref>. The <inline-formula id="inf517">
<mml:math id="m520">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values are found from the simulated <inline-formula id="inf518">
<mml:math id="m521">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="fig" rid="F5">Figure 5</xref>) using the <xref ref-type="bibr" rid="B29">Teh and Houlsby (1991)</xref> interpretation approach:<disp-formula id="e4">
<mml:math id="m522">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msubsup>
<mml:mi>T</mml:mi>
<mml:mn>50</mml:mn>
<mml:mi>&#x2a;</mml:mi>
</mml:msubsup>
<mml:msup>
<mml:mi>r</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:msubsup>
<mml:mi>I</mml:mi>
<mml:mi>r</mml:mi>
<mml:mn>0.5</mml:mn>
</mml:msubsup>
</mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
<inline-formula id="inf519">
<mml:math id="m523">
<mml:mrow>
<mml:msubsup>
<mml:mi>T</mml:mi>
<mml:mn>50</mml:mn>
<mml:mi>&#x2a;</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> is the time factor for 50% dissipation; at the <inline-formula id="inf520">
<mml:math id="m524">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position it is equal to 0.069 and at the <inline-formula id="inf521">
<mml:math id="m525">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position it is equal to 0.245. <inline-formula id="inf522">
<mml:math id="m526">
<mml:mrow>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the cone radius, which was 18&#xa0;cm in the model. <inline-formula id="inf523">
<mml:math id="m527">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the soil rigidity index, which is the ratio of soil shear modulus to undrained shear strength. The <inline-formula id="inf524">
<mml:math id="m528">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values are 115, 148, and 111 for OCR &#x3d; 1, 2, and 4, respectively. The <inline-formula id="inf525">
<mml:math id="m529">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values were determined from single element undrained isotropic consolidation triaxial compression simulations. Although <xref ref-type="bibr" rid="B29">Teh and Houlsby (1991)</xref> designate the interpretation to be <inline-formula id="inf526">
<mml:math id="m530">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, this study uses <inline-formula id="inf527">
<mml:math id="m531">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in Eq. <xref ref-type="disp-formula" rid="e4">4</xref> following the confirmation that vertical <inline-formula id="inf528">
<mml:math id="m532">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> contributes to the CPTu dissipation response.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Comparison of model assigned <inline-formula id="inf529">
<mml:math id="m533">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and interpretation of <inline-formula id="inf530">
<mml:math id="m534">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> or <inline-formula id="inf531">
<mml:math id="m535">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> from simulated CPTu dissipation tests: <bold>(A)</bold> <inline-formula id="inf532">
<mml:math id="m536">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>-interpreted <inline-formula id="inf533">
<mml:math id="m537">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <bold>(B)</bold> <inline-formula id="inf534">
<mml:math id="m538">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>-interpreted <inline-formula id="inf535">
<mml:math id="m539">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <bold>(C)</bold> <inline-formula id="inf536">
<mml:math id="m540">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>-interpreted <inline-formula id="inf537">
<mml:math id="m541">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> using <inline-formula id="inf538">
<mml:math id="m542">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <bold>(D)</bold> <inline-formula id="inf539">
<mml:math id="m543">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>-interpreted <inline-formula id="inf540">
<mml:math id="m544">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> using <inline-formula id="inf541">
<mml:math id="m545">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
</caption>
<graphic xlink:href="fbuil-10-1386803-g013.tif"/>
</fig>
<p>The <inline-formula id="inf542">
<mml:math id="m546">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values at the <inline-formula id="inf543">
<mml:math id="m547">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf544">
<mml:math id="m548">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> positions are compared to the model-assigned <inline-formula id="inf545">
<mml:math id="m549">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values (<inline-formula id="inf546">
<mml:math id="m550">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>h</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>m</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>l</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) in <xref ref-type="fig" rid="F13">Figures 13A, B</xref>, respectively. There is generally strong agreement between <inline-formula id="inf547">
<mml:math id="m551">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf548">
<mml:math id="m552">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>h</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>m</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>l</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> across OCR and <inline-formula id="inf549">
<mml:math id="m553">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values, providing further support that CPTu dissipation is reasonably captured by the cone penetration and dissipation model, with general scatter around the 1:1 lines. The <inline-formula id="inf550">
<mml:math id="m554">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values are applied to <inline-formula id="inf551">
<mml:math id="m555">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values in <xref ref-type="fig" rid="F13">Figures 13C, D</xref> with Eq. <xref ref-type="disp-formula" rid="e2">2</xref> to estimate <inline-formula id="inf552">
<mml:math id="m556">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>h</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. As expected, there is less scatter for <xref ref-type="fig" rid="F13">Figures 13C, D</xref> than in <xref ref-type="fig" rid="F13">Figures 13A, B</xref> when <inline-formula id="inf553">
<mml:math id="m557">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is not applied.</p>
</sec>
<sec sec-type="conclusion" id="s5">
<title>5 Conclusion</title>
<p>CPTu dissipation simulations were performed in saturated clay with a direct axisymmetric cone penetration model to examine test interpretation methods, and how dissipation is affected by OCR and <inline-formula id="inf554">
<mml:math id="m558">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Simulations were performed with the MIT-S1 constitutive model calibrated for BBC with OCR &#x3d; 1, 2, and 4. The simulated <inline-formula id="inf555">
<mml:math id="m559">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation tests showed monotonic responses for all OCR values. The simulated <inline-formula id="inf556">
<mml:math id="m560">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation tests showed a monotonic response for OCR &#x3d; 1, a slightly non-monotonic response for OCR &#x3d; 2, and a strongly non-monotonic response for OCR &#x3d; 4.</p>
<p>This study examined simulated <inline-formula id="inf557">
<mml:math id="m561">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration during dissipation. The results showed that <inline-formula id="inf558">
<mml:math id="m562">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration occurs in both the vertical and radial directions. Contribution of vertical <inline-formula id="inf559">
<mml:math id="m563">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration to CPTu dissipation tests is shown by 1) increased time to <inline-formula id="inf560">
<mml:math id="m564">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> at both the <inline-formula id="inf561">
<mml:math id="m565">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf562">
<mml:math id="m566">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position when <inline-formula id="inf563">
<mml:math id="m567">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is reduced but <inline-formula id="inf564">
<mml:math id="m568">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> remains the same and 2) reduced <inline-formula id="inf565">
<mml:math id="m569">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for non-monotonic dissipation tests as <inline-formula id="inf566">
<mml:math id="m570">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:mi>k</mml:mi>
</mml:mrow>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> increases. Vertical <inline-formula id="inf567">
<mml:math id="m571">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration may be driven by a gradient between the cone face and cone shaft that is induced by normal stress unloading and shear stress. This gradient was present for all OCR simulations and increased as OCR increased, which is notable since higher OCR is associated with stronger non-monotonic <inline-formula id="inf568">
<mml:math id="m572">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation responses. Non-monotonic <inline-formula id="inf569">
<mml:math id="m573">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> responses were also associated with initially non-monotonic radial <inline-formula id="inf570">
<mml:math id="m574">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distribution from the <inline-formula id="inf571">
<mml:math id="m575">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> position, indicating that radial <inline-formula id="inf572">
<mml:math id="m576">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration may also contribute to non-monotonic <inline-formula id="inf573">
<mml:math id="m577">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dissipation responses. Future research efforts will map <inline-formula id="inf574">
<mml:math id="m578">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration around the piezocone to relate migration to initial <inline-formula id="inf575">
<mml:math id="m579">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> distribution and recorded dissipation curves.</p>
<p>The role of hydraulic conductivity anisotropy and vertical <inline-formula id="inf576">
<mml:math id="m580">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> migration is incorporated into dissipation test interpretation with a correction factor, termed <inline-formula id="inf577">
<mml:math id="m581">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, based on prior knowledge of <inline-formula id="inf578">
<mml:math id="m582">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. The correction factor is applied to the <inline-formula id="inf579">
<mml:math id="m583">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> value interpreted from CPTu dissipation tests to estimate <inline-formula id="inf580">
<mml:math id="m584">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. The correction factor is based on changes in <inline-formula id="inf581">
<mml:math id="m585">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> with hydraulic conductivity anisotropy, and therefore, is appropriate for use with <inline-formula id="inf582">
<mml:math id="m586">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>50</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>-based <inline-formula id="inf583">
<mml:math id="m587">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> interpretation methods such as <xref ref-type="bibr" rid="B29">Teh and Houlsby (1991)</xref> or <xref ref-type="bibr" rid="B1">Agaiby and Mayne (2018)</xref> and for normal clays that are normally consolidated to moderately overconsolidated (i.e., OCR &#x3d; 1&#x2013;4).</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s6">
<title>Data availability statement</title>
<p>The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.</p>
</sec>
<sec id="s7">
<title>Author contributions</title>
<p>DM: Investigation, Methodology, Supervision, Writing&#x2013;original draft. AH: Data curation, Investigation, Writing&#x2013;review and editing. JD: Conceptualization, Writing&#x2013;review and editing.</p>
</sec>
<sec sec-type="funding-information" id="s8">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. Funding for this research was provided by the National Science Foundation (award CMMI-1927557). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the agency.</p>
</sec>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s10">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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