Abstract
Localized beam-bottom support loss can alter deformation compatibility within reinforced concrete lattice beams and reduce their load-carrying capacity, yet the associated spatial response remains insufficiently quantified. This study conducted staged central-node loading tests on 1:10 square-grid lattice-beam models under complete support and three prescribed support-loss conditions (η = 0.2, 0.4, and 0.6). Optical-frequency-domain-reflectometry distributed sensing provided continuous longitudinal strain fields on the upper and lower beam surfaces. Response evolution was evaluated from strain-field patterns, signed longitudinal-profile correlation, and the recorded system-level peak load. Increasing η produced progressively stronger strain localization around Horizontal Beam 2 and the orthogonally connected vertical beams, accompanied by relative unloading of peripheral parallel beams. At η = 0.6, the upper-surface correlation coefficient of Horizontal Beam 2 decreased to −0.59 to −0.77 at 200–400 kg, indicating substantial reorganization of the longitudinal strain distribution. The recorded peak load decreased from 1235 kg under complete support to 978, 782, and 604 kg, corresponding to reductions of 20.8%, 36.7%, and 51.1%, respectively. The observations demonstrate that localized support loss changes grid-level deformation sharing while progressively degrading the model-scale peak load. These results provide an experimental basis for identifying support-loss-sensitive regions and designing distributed monitoring layouts for lattice-beam slope-protection systems.
1 Introduction
Reinforced concrete lattice beams offer good construction adaptability, broad load-dispersion capacity, and effective interaction with anchors or prestressed cables, and are therefore widely used for slope protection, landslide stabilization, and tunnel-portal reinforcement (; ; ; ; ). Their longitudinal and transverse beams are connected at nodes to form a spatial grid, while the underlying soil provides continuous support. Rainfall-induced erosion, differential settlement, and construction disturbance may locally separate the beam soffit from the supporting soil (Yang, 2024; ), converting a supported beam segment into a locally unsupported span and redistributing forces to adjacent members through the nodes.
Previous studies have mainly examined tunnel-segment joints, composite columns, and arch members, with emphasis on the effects of contact gaps, axial-force levels, interface behavior, and local stiffness variations on compression--bending capacity and deformation (; ; Ye et al., 2025; ; Zhang et al., 2023; ; ; Yang et al., 2025; ; ; ; ; ; ). These studies have shown that changes in support or restraint conditions can cause internal-force redistribution and transitions in the load-carrying mode. However, most investigations have focused on individual members or single joints and therefore cannot directly explain multi-path load transfer in orthogonal grid structures. Unlike these individual members and joints, a slope lattice beam behaves as an orthogonally connected grillage whose response is additionally governed by beam–soil support and nodal deformation compatibility. Winkler-based lattice-beam analyses show that nodal load distribution and internal-force response depend on member stiffness and subgrade reaction (; ), while grillage studies demonstrate that local support degradation can alter system-level deformation and reaction patterns as a function of support stiffness ().
Distributed fiber-optic sensing, digital image correlation, acoustic emission, and discrete lattice models can continuously identify local strain gradients, damage propagation, and changes in spatial structural response (; ; ; ; ; ). In a lattice beam, the influence of support loss is not confined to the affected beam segment but can propagate through the nodes to orthogonal and peripheral members. A unified monitoring scheme that simultaneously compares the horizontal beam crossing the voided region, the orthogonal vertical beam, and the peripheral parallel beams is therefore required to identify the spatial response redistribution induced by local support loss.
This study conducted staged loading tests at the central node of a scaled square-grid lattice-beam model under four support conditions, with void coefficients η = 0, 0.2, 0.4, and 0.6. Distributed fiber-optic sensing was used to continuously measure longitudinal strains along the monitored beam surfaces. The spatial evolution of the strain field and changes in longitudinal-profile correlation were evaluated together with the recorded model-scale peak load. The study thereby examines how localized beam-bottom support loss modifies the response of the directly affected, orthogonally connected, and peripheral members, and how this response evolves with increasing void extent.
2 Study object and experimental model
2.1 Study object and problem definition
The study object was a reinforced concrete lattice beam used in a slope-protection system. Under intact conditions, the soil beneath the beams provides continuous or nearly continuous support, and the longitudinal and transverse beams jointly distribute slope loads through their intersections. Local loss of support increases the flexural response of the affected beam segment and may alter the internal-force distribution in adjacent members.
The technical records describe separate specimen groups for the four support conditions, with one reported destructive test result for each condition and no replicate series. S0–S3 are used as condition codes. Model geometry, material batch, loading position, monitoring layout, model box, and staged loading protocol were kept consistent across the series. The available records do not specify a separate chronological execution sequence; accordingly, no sequence-dependent interpretation is made.
2.2 Geometric and reinforcement parameters of the scaled model
The test model was a square planar lattice consisting of three horizontal and three vertical beams connected orthogonally to form 4 cells. The overall dimensions were 64 cm × 64 cm, the clear span of each beam was 30 cm, and each beam had a 4 cm × 4 cm cross-section with a nominal concrete cover of 0.5 cm. Longitudinal reinforcement consisted of Φ4 bars and Φ1 wire stirrups at 5 cm spacing. The model geometry (a), reinforcement section (b), and monitored-fiber locations (c) are illustrated in Figure 1. The beams were cast with C35 fine-aggregate concrete using 42.5-grade cement. These fabrication specifications are those documented in the project report. Because independent material-test results for the test batch were not recorded with the lattice-beam dataset, elastic-modulus-based moment reconstruction is not used in the revised analysis.
The model was geometrically scaled at 1:10. All support conditions used the same model geometry, material batches, reinforcement arrangement, supporting-soil preparation, and loading protocol. Stiffness, strength, reinforcement, fracture, and soil-support similarity were not independently scaled; the experiment was therefore designed for comparative model-scale assessment rather than direct prototype conversion. Table 1 summarizes the implemented controls and the corresponding interpretation scope.
TABLE 1
| Item | Implemented control | Degree of similitude | Interpretive consequence |
|---|---|---|---|
| Geometry | Cl = 0.10 for span, section, and prescribed support-loss length | Controlled | Supports model-scale comparison of support-loss extent |
| Gravity/density | Normal gravity; similar material density across conditions | Partial | Used consistently within the test series |
| Elastic/strength properties | Same material types and batches; not scaled to theoretical ratios | Incomplete | No direct prototype stiffness or strength conversion |
| Reinforcement/cracking | Geometrically scaled arrangement with model-specific bars and cover | Incomplete | Model-scale cracking and size effects are retained |
| Soil support | Same prepared soil and model box across conditions; stiffness not independently calibrated | Controlled within series | Supports within-series comparison of boundary-condition changes |
| Loading | Same staged central-node loading protocol | Controlled within series | Peak loads interpreted as model-scale system responses |
Similitude relations and applicable scope of the model.
Cl denotes the geometric similarity ratio; all reported responses are interpreted at model scale.
2.3 Loading system and model boundaries
The loading system comprised a rigid model box, a portal reaction frame, a servo-controlled hydraulic jack, and a data-acquisition system (Figure 2). The supporting soil was prepared from clayey soil sampled in the Zhuhai area at an approximate depth of 5 m. Tests conducted in accordance with GB/T 50,123–2019 gave a natural density of 2.00 g/cm3, specific gravity of 2.71, water content of 25.3%, plastic limit of 18.3%, liquid limit of 37.3%, plasticity index of 19, cohesion of 20 kPa, friction angle of 20°, and maximum dry density of 1.74 g/cm3. Percent passing was 99.8%, 99.1%, 85.0%, 65.4%, 40.5%, 16.0%, and 7.4% at sieve sizes of 2, 1, 0.5, 0.2, 0.1, 0.075, and 0.063 mm, respectively. The soil was placed in layers to the intended test density and leveled before placement of the lattice beam. A deformation modulus for the supporting soil was not measured in this test series; soil stiffness is therefore treated as a controlled boundary characteristic rather than a calibrated experimental variable.
FIGURE 2
Central-node loading activated the intersecting horizontal and vertical beams and induced compatible deformation in the surrounding grid. Comparisons among support conditions are based on the measured spatial strain response and recorded system load; the strain data are not used as a direct equilibrium reconstruction of member forces.
2.4 Beam-bottom void model and test conditions
The prescribed support-loss region was centered beneath node O and extended longitudinally along Horizontal Beam 2. The void coefficient η was defined as the ratio of the prescribed longitudinal void length LV to the single-span length LS (Equation 1):where LV is the prescribed longitudinal support-loss length and LS = 30 cm. Initial lengths of 0, 6, 12, and 18 cm corresponded to η = 0, 0.2, 0.4, and 0.6. The project record defines the longitudinal extent and location of the support-loss region but does not document a separate void depth, transverse width, or during-load gap measurement. Accordingly, η represents the initial prescribed longitudinal loss-of-support extent. The imposed condition combines reduced beam–soil contact with an increased local unsupported length, and these effects are interpreted jointly. The four prescribed support conditions (S0–S3) are summarized in Table 2.
TABLE 2
| Condition | Void location | Void length/cm | Void coefficient η | Support condition |
|---|---|---|---|---|
| S0 | Beneath node O | 0 | 0 | Complete support |
| S1 | Beneath node O | 6 | 0.2 | Slight local support loss |
| S2 | Beneath node O | 12 | 0.4 | Moderate void extent |
| S3 | Beneath node O | 18 | 0.6 | Large void extent |
Beam-bottom void conditions.
3 Research methods
3.1 Distributed fiber-optic strain monitoring
Beam strains were continuously monitored using a LUNA ODiSI-6104 optical frequency-domain reflectometry (OFDR) distributed fiber-optic sensing system. Single-mode fibers were bonded to the concrete surfaces with epoxy resin, and the same instrument and spatial layout were used for all conditions. The monitoring system and fiber-bonded installation on the lattice-beam model are shown in Figure 3. The laboratory labels “front” and “back” correspond to longitudinal fibers on opposite extreme surfaces through the beam depth (upper and lower surfaces in the horizontal test orientation), rather than the lateral faces across the beam width; Figure 1c clarifies this geometry.
FIGURE 1
FIGURE 3
The monitoring-point and beam-segment labels are shown in Figure 4. Horizontal Beams 1–3 and Vertical Beams 1–3 were identified by their positions in plan. The central node was O and the peripheral nodes were A–H. Upper-surface points (laboratory label “front”) were denoted O1 and A1–H1, and the corresponding lower-surface points (laboratory label “back”) were O2 and A2–H2. Horizontal Beam 2 crossed the prescribed support-loss region, whereas Vertical Beam 2 intersected it orthogonally at O. The remaining beam segments provided spatial reference responses for evaluating redistribution across the grid.
FIGURE 4
3.2 Staged loading protocol
A load-controlled quasi-static staged protocol was used for all conditions. Phase I comprised load readings of 20, 40, 60, and 80 kg. Phase II began at 100 kg and continued through 200, 300, and 400 kg, followed by further loading until the maximum recorded system load was reached. The complete staged loading program is summarized in Table 3. Data at each stage were taken after stabilization, and load readings were converted to force using 9.81 N/kg. The lattice-beam test record contains the applied load history and peak load but no independent displacement channel; consequently, the present analysis does not derive stiffness or ductility from load–displacement curves.
TABLE 3
| Loading phase | Load level | Load reading/kg | Primary analytical objective |
|---|---|---|---|
| Phase I | Level 1 | 20 | Initial contact and support adjustment |
| Phase I | Level 2 | 40 | Low-load strain response |
| Phase I | Level 3 | 60 | Evolution of low-load strain field |
| Phase I | Level 4 | 80 | Transition toward stable spatial response |
| Phase II | Level 1 | 100 | Establishment of intermediate-load response |
| Phase II | Level 2 | 200 | Intermediate-load spatial response |
| Phase II | Level 3 | 300 | Development of strain localization |
| Phase II | Level 4 | 400 | High-load spatial response |
| Phase II | Continued loading | To failure | Recorded system peak load and failure morphology |
Loading program for the lattice-beam model test.
3.3 Data processing and quality control
Data processing comprised spatial-coordinate alignment and signal-quality screening. Points showing pronounced backscatter-quality loss or isolated spikes in the loading-contact region were excluded, and no trend-based smoothing was applied to the remaining profiles. Heatmaps were generated from the processed strain data to visualize spatial distributions. Quantitative comparison focuses on the signed longitudinal-profile correlation and the recorded system peak load.
3.4 Signed strain-profile correlation and peak-load criterion
Pearson’s correlation coefficient r (Equation 2) was used to compare signed longitudinal strain profiles at matched spatial coordinates and load levels. A coefficient near 1 indicates preservation of the relative longitudinal strain pattern, whereas a negative coefficient indicates inverse covariance relative to the complete-support reference. Such a negative value may arise from migration of strain peaks and troughs and localized changes in strain sign; it does not imply a uniform reversal of tension and compression along the entire member. Correlation is therefore used as a descriptor of spatial-pattern change rather than as a direct measure of force transfer.where n is the number of valid matched monitoring points; εi and ε′i are signed strains at corresponding locations; and and are their respective means. The peak load is defined as the maximum recorded central-node load of the lattice-beam system during the staged test.
4 Results
4.1 Baseline strain response under complete support
Under complete support, the central-node load produced distributed strain responses in the intersecting and peripheral beams. At a load reading of 800 kg, visible cracking was documented on the specimen. The maximum strains measured along three side-face paths were 17.4, 17.9, and 35.5 με, respectively, and remained lower than the longitudinal strains on the monitored upper and lower surfaces. Continued loading produced the failure morphology shown in Figure 5, characterized by pronounced flexural deformation with local compressive damage around the central intersecting region.
FIGURE 5
During Phase I, longitudinal strain patterns along a given monitoring path were generally similar as the beam–soil contact response became established. During Phase II, differences between the central and peripheral beam responses became more persistent, providing the reference state for comparison with the prescribed support-loss conditions.
4.2 Low-load strain redistribution under prescribed support loss
The Phase I strain heatmaps are shown in Figure 6. Under complete support, the monitored strain fields were comparatively continuous. With prescribed support loss, localized changes appeared around Horizontal Beam 2 and the central node and became more pronounced as η increased. The spatial response also extended into the orthogonally connected vertical beams, whereas some peripheral parallel-beam regions showed reduced strain magnitudes. These patterns indicate an early redistribution of deformation within the connected grid.
FIGURE 6
Because absolute strains are small at low load, Phase I maps are used to identify spatial patterns rather than to define a quantitative defect threshold. Quantitative comparison is based on signed profile correlation and peak load.
4.3 Strain redistribution at intermediate and high loads
During Phase II, the spatial differences became more persistent, as shown in Figure 7. Horizontal Beam 2 exhibited stronger localization around the loading and support-loss region, while the orthogonally connected vertical beams showed increasingly distinct changes in their longitudinal strain distributions as η increased. Because the imposed support loss simultaneously reduces beam–soil contact and increases the local unsupported length, the measured response represents the combined effect of these boundary changes.
FIGURE 7
Horizontal Beams 1 and 3 showed relative unloading in several monitored profiles, whereas the vertical beams adjacent to the central node exhibited stronger response changes. The resulting pattern is consistent with a progressive change in deformation sharing within the orthogonal grid: response becomes more concentrated in the directly affected beam and its connected vertical members while peripheral parallel members contribute less strongly.
4.4 Evolution of strain-profile correlation
For η = 0.6, signed profiles were compared with the complete-support condition, as shown in Figure 8. For the upper surface of Horizontal Beam 2, the correlation coefficients at 40, 60, 80, 200, 300, and 400 kg were 0.01, −0.18, −0.08, −0.59, −0.73, and −0.77, respectively. The increasingly negative coefficients at 200–400 kg indicate a marked reordering of longitudinal strain peaks and troughs relative to the reference profile, rather than a uniform reversal of tension and compression. The corresponding coefficients for the upper surface of Vertical Beam 2 were 0.69, 0.70, 0.63, 0.27, 0.45, and 0.27, indicating partial preservation of the original pattern with substantially reduced correspondence.
FIGURE 8
Horizontal Beams 1 and 3 generally retained higher upper-surface similarity, whereas some lower-surface correlations decreased at intermediate and high loads. The different correlation trajectories across the six beams show that support loss does not produce a uniform grid-wide response. Instead, the directly affected and orthogonally connected members undergo the largest changes in spatial strain pattern, while peripheral parallel members retain more of the complete-support distribution. Representative coefficients are summarized in Figure 9.
FIGURE 9
4.5 Mechanical interpretation of strain redistribution
The prescribed support loss reduces beam–soil contact beneath the central region while increasing the local unsupported length of Horizontal Beam 2. This change increases local flexural deformation demand and modifies rotational compatibility at node O. The stronger strain changes observed in the orthogonally connected vertical beams, together with relative unloading of peripheral parallel beams, are consistent with redistribution of deformation demand through the connected grid. This interpretation agrees with elastic-foundation lattice-beam and grillage studies showing that member response depends jointly on nodal compatibility and support stiffness (; ; ).
As the support-loss extent increases, deformation becomes increasingly concentrated around the affected span and central intersection. Such concentration reduces the degree of distributed participation available from the surrounding grid and provides a mechanical basis for the concurrent reduction in system peak load. The measured strain fields establish this redistribution at the response level; they are not used to infer a unique set of member forces or support reactions.
4.6 Peak-load degradation and engineering implications
The maximum recorded central-node load was 1235 kg under complete support and 978, 782, and 604 kg for η = 0.2, 0.4, and 0.6, respectively, corresponding to reductions of 20.8%, 36.7%, and 51.1% (Figure 10; Table 4). Using 9.81 N/kg, the corresponding model-scale forces were approximately 12.11, 9.59, 7.67, and 5.92 kN. The peak load therefore decreased monotonically with increasing prescribed support-loss extent.
FIGURE 10
TABLE 4
| Void coefficient η | Peak load reading/kg | Converted peak force/kN | Reduction from complete support/% |
|---|---|---|---|
| 0 | 1235 | 12.11 | — |
| 0.2 | 978 | 9.59 | 20.8 |
| 0.4 | 782 | 7.67 | 36.7 |
| 0.6 | 604 | 5.92 | 51.1 |
Prescribed support-loss coefficient and recorded model-scale peak load.
The decline in peak load occurred concurrently with stronger strain localization and larger changes in longitudinal profile shape in the directly affected members. This co-evolution is mechanically consistent with reduced contact support, increased local unsupported length, and progressively concentrated deformation demand. The present data are used to establish this experimental trend rather than to formulate a predictive capacity equation.
For field monitoring, reference strain profiles can be established during commissioning or from a verified healthy-state record. Where a historical baseline is unavailable, symmetric or peripheral beam segments may provide contemporaneous spatial references, supplemented by temporal changes in strain gradients and crack observations. The test results indicate that monitoring should cover the beam crossing a suspected support-loss region, the intersecting node, and orthogonal members rather than relying on a single point or isolated beam segment.
4.7 Scope of applicability
The 1:10 model was designed for comparative evaluation of prescribed support conditions rather than direct prototype prediction. The reported series contains one test result for each condition and does not include independent support-reaction or load–displacement histories. Accordingly, the conclusions are limited to the observed strain-field evolution and model-scale peak-load trend for the tested geometry, materials, and support preparation. Quantitative prototype design requires project-specific structural analysis and verification of actual beam–soil support conditions.
5 Conclusion
Localized beam-bottom support loss produced a nonuniform redistribution of the measured strain field. With increasing η, the most pronounced changes occurred in Horizontal Beam 2 and the orthogonally connected vertical members, while several peripheral parallel-beam profiles showed relative unloading, indicating progressive concentration of deformation demand around the affected grid region.
For η = 0.6, the upper-surface correlation coefficient of Horizontal Beam 2 decreased from values close to zero at low load to −0.59 to −0.77 at 200–400 kg. The negative correlation reflects reordering and migration of longitudinal strain extrema relative to complete support, demonstrating a substantial change in spatial response pattern at intermediate and high loads.
The observed redistribution is mechanically consistent with the combined reduction in beam–soil contact and increase in local unsupported length. Enhanced local flexural demand at Horizontal Beam 2 modifies compatibility at the central node and increases the participation of the connected vertical beams, while deformation sharing by peripheral parallel beams is reduced.
The model-scale peak load decreased from 1235 kg under complete support to 978, 782, and 604 kg at η = 0.2, 0.4, and 0.6, corresponding to reductions of 20.8%, 36.7%, and 51.1%, respectively. The monotonic peak-load degradation and spatial strain redistribution jointly identify the central intersecting region as a critical monitoring zone under localized support loss.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
CW: Conceptualization, Writing – original draft. SH: Writing – original draft, Data curation. ZH: Writing – original draft, Investigation. SL: Resources, Writing – review and editing. CY: Writing – review and editing, Software. BN: Writing – review and editing, Validation. QZ: Writing – review and editing, Methodology. YW: Writing – review and editing, Supervision. QL: Writing – review and editing, Visualization. YG: Writing – review and editing, Project administration.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This study was supported by the General Research and Development Technology Project of Guangdong Provincial Transportation Group Co., Ltd. (No. JT2024YB06), the National Natural Science Foundation of China (No. 52578452), the Student Scientific Research Project of Hebei GEO University (No. KAG202606), and the Innovation Training Program for College Students of Hebei GEO University (No. Y202610077005). The author(s) declared that this work received funding from Guangdong Provincial Transportation Group Co., Ltd. (No. JT2024YB06). The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article, or the decision to submit it for publication.
Conflict of interest
Authors CW, SH, ZH, and ShL were employed by Guangdong Road and Bridge Construction Development Co., Ltd.
Authors CW, SH, ZH, and ShL were employed by Guangdong Guangfozhao Expressway Co., Ltd.
Authors CY, BN, QZ, YW, and QiL were employed by Guangdong Hualu Transportation Technology Co., Ltd.
The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Summary
Keywords
beam-bottom support loss, distributed fiber-optic sensing, peak-load degradation, reinforced concrete lattice beam, strain redistribution
Citation
Wei C, He S, Huang Z, Liu S, Yang C, Nie B, Zhang Q, Wu Y, Liu Q and Gu Y (2026) Experimental study on strain redistribution and peak-load degradation of reinforced concrete lattice beams under localized beam-bottom support loss. Front. Mater. 13:1964867. doi: 10.3389/fmats.2026.1964867
Received
11 August 2026
Revised
05 September 2026
Accepted
10 September 2026
Published
02 October 2026
Volume
13 - 2026
Edited by
Jue Li, Changsha University of Science and Technology, China
Reviewed by
Chunyang Su, Taiyuan University of Technology, China
Binglin Xie, Shenzhen University, China
Updates
Copyright
© 2026 Wei, He, Huang, Liu, Yang, Nie, Zhang, Wu, Liu and Gu.
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.
*Correspondence: Yashen Gu, yashengu77@163.com
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