Effects of Salt Thickness on the Structural Deformation of Foreland Fold-and-Thrust Belt in the Kuqa Depression, Tarim Basin: Insights From Discrete Element Models

The salt layer is critical for the structural deformation in the salt-bearing fold-and-thrust system, which not only acts as the efficient décollement layer but also flows to form salt tectonics. Kuqa Depression has a well-preserved thin-skinned fold-and-thrust system with the salt layer as the décollement. To investigate the effects of salt thickness on the structural deformation in the Kuqa Depression, three discrete element models with different salt thicknesses were constructed. The experiment without salt was controlled by several basal décollement dominant faults, forming several imbricate sheets. The experiments with salt developed the decoupled deformation with the salt layer as the upper décollement (subsalt, intrasalt, and suprasalt), significantly similar to the Kuqa Depression along the northern margin of Tarim Basin. Basal décollement dominant imbricated thrusts formed at the subsalt units, while the monoclinal structure formed at the suprasalt units. The decoupled deformation was also observed in the tectonic deformation graphics, distortional strain fields, and max shear stress fields. However, the salt layer was thickened in the thick salt model, and the salt thickness of the thin salt model varied slightly because the thin salt weakened the flowability of the salt. The lower max shear stress zone was easily formed in the distribution region of salt under the action of compression stress, which is conducive to the flow convergence of salt and the crumpled deformation of interlayer in salt. The results are well consistent with the natural characteristics of structural deformation in the Kuqa Depression. Our modeling result concerns the structural characteristics and evolution of salt-related structures and the effects of salt thickness on the structural deformation in the compressional stress field, which might be helpful for the investigations of salt-related structures in other salt-bearing fold-and-thrust belts.


INTRODUCTION
The Kuqa Depression is a peripheral foreland basin placed at the southern piedmont of Tianshan Orogen, Northwest China ( Figure 1). It develops from the Late Permian to Quaternary with strong compressional deformation since the late Cenozoic (Nishidai and Berry (1990); (Lu et al., 1994;Yin et al., 1998;Lu et al., 1999;Liu et al., 2000)). Bounded by the Kuqa River, the depression can be divided into the eastern Kuqa Depression and the western Kuqa Depression (Xin et al., 2002). From the north to south, five main structural belts are divided according to the different structural features in the western Kuqa Depression: the North structural belt (NSB), Kelasu structural belt (KLSSB), Baicheng sag (BCS), Qiulitage structural belt (QLTGSB), and the South basement slope belt (SBSB) (Figure 1) (Yin et al., 1998;Xin et al., 2002). As one of the most important hydrocarbonbearing evaporite basins in China (Yu et al., 2014;Feng et al., 2018;Song et al., 2019), numerous salt-related structures were widely developed in the Kuqa Depression, especially in the Kelasu structural belt with obvious topographic relief features and obvious structural deformation features Wu et al., 2014;Yu et al., 2014;Wu et al., 2015a;Zhao and Wang, 2016;Wang et al., 2017;Neng et al., 2018).
In recent years, based on structural analysis of seismic profiles with the application of several structural analysis techniques, such as the interpretation or balanced analysis of seismic profiles (Li and Qi, 2012;Neng et al., 2012;Neng et al., 2013;Yu et al., 2015;Hou et al., 2019), the area-depth-strain method (Xie et al., 2015;Wang et al., 2017), and the Coulomb wedge theory (Suppe, 2007;Lin et al., 2017), and structural simulated techniques, such as the sandbox physical simulation (Wang et al., 2010;Yin et al., 2011;Li and Qi, 2012;Xu et al., 2012;Wu et al., 2014) and numerical simulation (Wang et al., 2010;Xu et al., 2012;Li W. et al., 2017;Duan et al., 2017;Li, 2019;Li et al., 2020), further understanding has been obtained on the research of structures in the Kelasu structural belt. In many compressional salt-bearing basins around the world, the rock salt, as the important décollement layer, has been demonstrated to have important impact on regional structural evolution (Cotton and Koyi, 2000;Wu et al., 2014;Wu et al., 2015b). Meanwhile, much attention has been paid on the differential thickness distribution of Kumugeliemu salt and Jidike salt in the western and eastern Kuqa Depression Tang et al., 2004;Yu et al., 2014;Tang et al., 2015;Zhao and Wang, 2016;Wang et al., 2017). How did differential thickness distribution of these two salt layers influence the structural deformation in the western and eastern depression? It is worthy of further research to explore the influence of the differential thickness of rock salt on the structural evolution, especially from the perspective of experimental simulation.
In this study, two seismic profiles were presented to reveal the differential structural deformation caused by the difference in the thickness of the salt layers. Besides, three two-dimensional discrete element models with different salt thicknesses were constructed to investigate the characteristics of the differential structural deformation in the western Kuqa Depression. The experimental setup, the model construction technique, the material, and the wall properties were prescribed. Based on three simulation experiments, we focused on the internal relationship between the experimental results and structural deformation characteristics in the northern margin of the Kuqa area, e.g., the formation of the "accommodative space" in the salt strata and the crumpled deformation of the dolomite interbed in the Kelasu structural belt.

GEOLOGICAL SETTING
The Kelasu structural belt is a strong structural deformation belt placed at the northern part of the western Kuqa Depression (Figure 1). The stratigraphy of the Kuqa Depression has been   Figure 1 for location) of the western Kelasu structure in the western Kuqa Depression; data revised from Wang et al. (2017). (B) The thin salt model. Interpreted seismic section Line 2 (see Figure 1 for location) of the eastern Kelasu structure in the western Kuqa Depression; data revised from Wu et al. (2014). The prekinematic strata (syn, isopachous layer) interval whose initial stratigraphic thickness is constant above a salt structure. It records sedimentation before salt movement. The synkinematic layer accumulated during salt flow and may include internal onlap or truncation. The subsalt strata were sedimentary units immediately underlying salt.
Frontiers in Earth Science | www.frontiersin.org August 2021 | Volume 9 | Article 655173 3 summarized regionally (Yin et al., 1998;Chen et al., 2004;Wang et al., 2011). Isolated by the evaporative rock salt, the stratigraphic column could be subdivided into three parts ( Figure 2): (1) Palaeozoic and Mesozoic subsalt basement; (2) the Palaeocene-Eocene Kumugeliemu (E 1-2 km) evaporative rock salt; and (3) Eocene-Quaternary overburden which is composed of old strata to young strata by Suweiyi formation (E 2-3 s), Jidike formation (N 1 j), Kangcun formation (N 1 k), Kuqa formation (N 2 k), and Xiyu formation (Q 1 x). The strata E 2-3 s to N 1 k were interpreted as prekinematic strata ( Figure 3A) which were deposited before salt flow began. The prekinematic strata (syn, isopachous layer) interval's initial stratigraphic thickness is constant above a salt structure (Jackson and Talbot, 1991). These record sedimentation before salt movement. The strata N 2 k to the Quaternary (Q) were interpreted as synkinematic strata ( Figure 3A) which accumulated during salt flow and may include internal onlap or truncation (Jackson and Talbot, 1991;Wu et al., 2014). The thickness of the synkinematic sedimentation is about 6-8 km in the western Kuqa Depression . According to the interpreted seismic profiles (Figure 3), the differential thickness and the vertical distribution of the salt layer were presented, i.e., the thick salt model with ca. 1,000 m salt in the western Kelasu structural belt (Wu et al., 2014) and the thin salt model with ca. 200 m salt in the eastern Kelasu structural belt . Several typical structural characteristics were summarized as follows based on the comprehensive comparison and analysis of typical seismic profiles.

The Western Kelasu Structural Belt
The salt layer was thickened in the thick salt model ( Figure 3A) because the flowability of the salt could be enhanced. The fault F1 ( Figure 3A) pinched out on the salt layer. Two major décollement levels exist in Kuqa Depression, i.e., an upper décollement with salt-gypsum lithologies (the Paleogene-Miocene Kumgeliem and Jidike strata) and the lower décollement mostly within Jurassic coal and mudstone strata . Imbricate thrust faults and duplex structures linking the two décollements developed with salt that flowed into the cores of the duplex structure (F1, Figure 3A). The differences in the geometries of salt structures in different regions show that the thickness of the salt sequences has an important influence on the development of salt-cored décollement folds and related thrust faults in the Tarim Basin (Wu et al., 2014).

The Eastern Kelasu Structural Belt
The fault F2 ( Figure 3B) in the piedmont thrust fold belt of the Kuqa Depression directly cuts through all the layers and nappes to the shallow strata from the deep of orogenic belts. The thin salt between the salt substratum and the slat superstratum shows no obvious rheological properties, so the salt thickness shows little variation ( Figure 3B).

EXPERIMENTAL METHOD AND MODEL SETUP
The discrete element method (DEM) has been applied to the study of geological and geophysical problems in recent decades (Hardy et al., 2009;Yin et al., 2009;Liu et al., 2015;Morgan, 2015;Botter et al., 2016;Buiter et al., 2016;Morgan and Bangs, 2017;Li, 2019;Li et al., 2020;Xu et al., 2021). A full, detailed description of the theory behind this modeling approach and its application to geological problems is given by Morgan (2015) and Li C. et al. (2017Li C. et al. ( , 2018Li C. et al. ( , 2021, Li (2019). A geological body is simplified into an assemblage of ball elements which obey Newton's equations of motion and can move under the action of the forces which are generated by interaction with pairs by elastic springs. Our implementation of DEM in the discrete element software ZDEM was summarized by Li (2019).
Three experiments presented here were all initialized by randomly generating particles within a 40 km wide × 14 km-tall domain. Particles were allowed to settle under gravity, bound by two vertical walls and a basal row of fixed particles. The resulting particle assembly was 40 km wide and 5 km thick, and values were chosen to allow typical sedimentary covers to be modeled, large absolute values of convergence to be achieved, and model boundaries to be far from the locus of deformation (Figure 4). The particle packing consisted of 12,234 particles, with uniform distribution radii of 60.0 and 80.0 m. To examine the influence of salt thickness on the structural deformation, three experiments were carried out on initially identical homogeneous packings and boundary and initial conditions and dimensions but using different sets of the salt thickness ( Figure 4). As a reference experiment, there is no salt layer in Exp. 1. The salt thickness of Exp. 2 was set to ca. 300 m tall, and the salt thickness of Exp. 3 was set to ca. 1,000 m tall. Frontiers in Earth Science | www.frontiersin.org August 2021 | Volume 9 | Article 655173 4 The particle properties of experiments are presented in Table 1. Upon settling, bonds of assigned strengths ( Table 2) were introduced at all interparticle contacts, except salt layers. Interparticle friction was set to 0.3 throughout the bonded domain (i.e., rock layer). There are two major décollement levels existing in the Kuqa Depression, i.e., an upper décollement in the salt layer and the lower décollement mostly within Jurassic coal and mudstone strata . As the low décollement, the interparticle friction of the foot wall was set to 0.15. As the upper décollement, the interparticle friction of the salt layers was set to 0.0 to ensure its lower strength.
The bulk mechanical properties of the numerical materials used in these experiments were prescribed by particle properties and bond parameters in Tables 1 and 2. These parameters in Tables 1 and 2 were consistent with previous studies (Morgan, 2015;Li, 2019). They were calibrated through a series of repose angles and two-dimensional biaxial tests based on the method presented by Li, (2019; and Morgan (2015). In numerical simulations, a local damping coefficient, which was the one most commonly used (Potyondy and Cundall, 2004;Itasca Consulting Group 2008;Kozicki and Donzé, 2008;O'Sullivan, 2011;Scholtès and Donzé, 2013;Weatherley et al., 2014;Zhao, 2015;Li, 2019;Xu et al., 2021), was added to damp the reflected waves from the boundary of the particle and to avoid buildup of kinetic energy in the closed system (Itasca Consulting Group 2008;Li, 2019). The meaning of the other parameters in Tables 1 and 2 was given by Morgan (2015) and Li (2019). The value of cohesion of rock layer and salt layer is, respectively, ca. 10.5 MPa and ca. 1.8 MPa (Li, 2019). The values of friction angles of rock layer and salt layer are ca. 18.6°and ca. 4.3°, respectively (Li, 2019). The value of cohesion is consistent with the strength of shallow crustal sediments (Camac et al., 2009;Jaeger et al., 2009;Schumann et al., 2014). Note that the values of friction angle are significantly lower than the typical value of friction angle, 30° (Jaeger et al., 2009;Wu et al., 2014), which is a common characteristic of these numerical materials (Morgan, 1999;Aharonov and Sparks, 2004;Morgan, 2004;Vidal and Bonneville, 2004;Dean et al., 2013;Gray et al., 2014;Morgan, 2015;Li, 2019), and consistent with shear experiments on smooth glass rods (Frye and Marone, 2002;Sun et al., 2016;Li, 2019).
The horizontal contraction was initiated by capturing particles along the right sidewall and applying a constant velocity of 2.0 m/ s to the left. The time step per cycle was 0.05 s, producing 0.1 m of wall displacement per cycle. The synkinematic sedimentation played an important role in structural deformation in Kuqa Depression (Yin et al., 2011;Wu et al., 2014). After the first thrust was formed (ca. 2 km of shortening), ca. 0.5 km-thick synkinematic layer was deposited for every 1 km of shortening. The final thickness of the synkinematic layer was ca. 5 km.

Distribution Deformation
Comparative plots of the final particle configurations (12 km wall displacement) of the three experiments with different salt thicknesses are shown in Figure 5. Three experiments have the same initial model but use different sets of salt thickness. As the reference experiment, Exp. 1 is without salt ( Figure 5A). The salt thickness is ca. 300 m in Exp. 2 with thin salt ( Figure 5B), while salt thickness is ca. 1,000 m in Exp. 3 with thick salt ( Figure 5C). Two faults form in Exp. 1 without salt layer, and the growth strata show the features of fault-propagation fold in accordance with the fault activity ( Figure 5A). But, the deformation was apparently divided into two parts in Exp. 2 (ca. 300 m salt, Figure 5B) and Exp. 3 (ca. 1,000 m salt, Figure 5C) containing the salt layer. Deformation above and below the salt layer was decoupled, with the imbricate structure formed in the subsalt units and back-thrust fault formed in suprasalt units.
In Figure 3B, continuous progradation from the southern Tianshan piedmont until the end of the late Miocene-early Pliocene made Kumugeliemu salt flow basinward and F2 developed . Accelerated crustal shortening since the end of the late Pliocene-early Pleistocene amplified the Misikantake anticline and formed the Quele salt nappe, and several new forward subsalt structures developed and they do not extend to the surface . Previous studies have shown that frictional resistance increases with salt pinch-out (Dooley et al., 2007) and buttressing effects of a distal salt pinch-out can control the location and style of distal salt structures (Costa and Vendeville, 2002;Couzens-Schultz et al., 2003;Dooley et al., 2007). Faults can easily cut through rock layers without salt layers ( Figure 5A), but they rarely cut the thick salt layers; instead, they detach along with the salt layers ( Figure 3A, 5C).

Distortional Strain
The distortional strain was used to quantify the results for DEM and was calculated according to the study by Morgan (2015). Distortional strain, i.e., strain-induced distortion, can be quantified as the second invariant of the deviatoric finite strain tensor (Morgan, 2015). Throughout the experiments, particle positions and interparticle forces were output every 10,000 cycles (1 km wall displacement), an interval referred to as an "increment." Subsequent calculations of particle displacements are made at whole increments, and this unit is used for plotting purposes.  The results of the three experiments are shown in Figure 6 with plots of cumulative distortional strain after 12 km (the shortening rate 20%) of shortening. The experiments were accommodated by largely distributed shear deformation with occasional local zones of more intense top-to-the-left shearing (Figure 6, blue zones). Dip angles of the forward thrust ( Figure 6, blue zones) were ca. 45°in all three experiments. They were in the same range as the dip angles (ca. 30°-50°, Figures 3A,B) of the forward thrust in the subsalt units. Figure 6B,C, F3-F6 did not cut through the salt layer; instead, they detached along with the salt layer because of the flow of salt that contributes significantly to structural relief in this part of the Kuqa fold-and-thrust belt. On the contrary, F1 and F2 ( Figure 6A) could easily cut through the rock layer. The salt layer was obviously thickened near the right wall when the initial thickness of salt was ca. 1,000 m ( Figure 6C). The thickness of salt had a little change when the initial thickness of salt was ca. 300 m ( Figure 6B) because the flowability of thin salt is weaker. The salt could be one of the main factors leading to differential tectonics. The contour map of distortional strain ( Figures 6A-C) shows local strain concentration around the fault, indicating that faulting played an important role in the fracture development in the damage zone surrounding the fault. This mechanism explained the higher density of shear fractures that developed in the near-fault area and the salt layers.

Max Shear Stress
Stress invariants for all of the systems are calculated and plotted for 1 × 1 km elements (summing over ca. 25 particles), with colors scaled by stress magnitude. The final structure of each series (Figure 7) is superimposed by plotting regions of high distortional strain (i.e., the absolute value is greater than 4.8 in Figure 6) in black. Similar to the simulation results of Morgan (2015), there is a distinct variability within the wedges about the maximum shear stress, τ max (Figures  Frontiers in Earth Science | www.frontiersin.org August 2021 | Volume 9 | Article 655173 7A-C). τ max increased with depth due to the combined increase in both vertical and horizontal stresses with burial (Morgan, 2015). Moreover, τ max was relatively high near the moving wall and in the foot walls of major shear zones. The highest values of τ max usually appeared directly in front of the frontal thrusts, outlining regions of unfaulted material that still supported high shear stresses (Morgan, 2015). The frontal regions of high τ max expanded with decreasing salt thickness (Figure 7), demonstrating the flowability of salt layers to dissipate shear stresses. The stress also had obvious stratification characteristics in the experiments with the salt layer.

DISCUSSION
Both the regional geological structure analysis and the structural simulation experiments show that if there is a regional distribution of salt rock as an important décollement layer in the fold orogenic belt and its foreland basin, the strata will undergo obvious structural stratification deformation in the vertical direction ( Figures 5, 6) (Wang et al., 2010;Yin et al., 2011;Xu et al., 2012;Wu et al., 2014;Yang, 2017;Neng et al., 2018;Li, 2019;Li et al., 2020;Sun et al., 2021;Xu et al., 2021). The results of these experiments well reflect the regional structural characteristics of the northern margin of the western Kuqa Depression (Figure 8). In the northern margin of the western section of Kuqa Depression, the basement involved thrust faults into the salt with a large displacement. When the salt is thick, the thrust fault will make the overlying salt significantly thicken and create favorable "accommodative space," which is conducive to the formation of the salt anticline and salt diapir ( Figure 3A, 8A). When the salt is thin, it is easy to cut through by faults, which is not conducive to the formation of favorable "accommodative space" (Figure 3B, 8B).
The results of the three simulations also show that a lower max shear stress zone is easily formed in the distribution region of salt under the action of compression stress, which is conducive to the flow convergence of salt and the crumpled deformation of interlayer in salt (Figures 7, 9). When the thickness of salt decreases, the fluidity of salt decreases obviously which is not conducive to salt convergence to form salt-related structures ( Figure 8B). While the salt is thick enough, its fluidity is obviously enhanced which is conducive to the flow and convergence of salt from the high-stress area to the low-stress area and forms larger salt structures, such as salt anticline or salt diapir structures ( Figure 8A) There are a fewer imbricate faults of the subsalt units in three discrete element simulations ( Figure 5C) than in the interpreted seismic sections of the Kelasu structure in the Kuqa Depression ( Figure 3A, 8A). The displacement of shortening, the slope, and the thickness of substrate décollement may control the distribution range and the number of imbricate faults in the subsalt units. We would make further analysis in the later study.

CONCLUSION
Effects of salt thickness on the structural deformation were discussed using different seismic profiles in the foreland foldand-thrust belt of the Kuqa Depression, which indicated that the thickness of the salt had an important influence on the structural styles.
The experiment without salt was controlled by several basal décollement dominant faults, forming several imbricate sheets. The experiments with salt developed the decoupled deformation with the salt layer as the upper décollement (subsalt, intrasalt, and suprasalt), significantly similar to the Kuqa Depression in the northern margin of Tarim Basin. Basal décollement dominant imbricated thrusts formed at the subsalt units, while the monoclinal structure formed at the suprasalt units. The decoupled deformation was also observed in the tectonic deformation graphics, distortional strain fields, and max shear stress fields. However, the salt layer was thickened in the thick salt model and the salt thickness of the thin salt model varied slightly because the thin salt weakened the flowability of the salt evidently. The lower max shear stress zone was easily formed in the distribution region of salt under the action of compression stress, which is conducive to the flow convergence of salt and the crumpled deformation of interlayer in salt. These phenomena are well consistent with the natural characteristic of structural deformation in the Kuqa Depression, Tarim Basin.
The modeling results in this study concern the structural characteristics and evolution of salt-related structures and the effects of salt thickness on the structural deformation in the compressional stress field, which might be helpful for the investigations of salt-related structures in other salt-bearing fold-and-thrust belts.

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.

FUNDING
The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (grants 41972219, 41927802, 41572187, and 41602208), National S&T Major Project of China (grants 2016ZX05026-002-007, 2016ZX05003-001, and 2016ZX005008-001-005), the PhD Frontiers in Earth Science | www.frontiersin.org August 2021 | Volume 9 | Article 655173 8 Starting Foundation of East China University of Technology (grants DHBK2019024 and DHBK2019053), and Project of PetroChina Company Limited (grant 2018A-0101). CL was also supported by program B for being an outstanding PhD candidate of Nanjing University.