1 Introduction
Coral sands, a distinctive type of marine soil, are abundant in tropical and subtropical coral reefs worldwide, encompassing roughly 40% of the land-ocean boundary on Earth [1-5]. Unlike terrigenous silica sand, coral sands originate from the remains of marine organisms [6-8]. Consequently, the coral sands possess distinctive particle soil properties, such as high porosity, high calcium carbonate content, and susceptibility to particle breakage [9-12]. With the progress of marine construction engineering in recent years, numerous buildings and structures have been constructed on natural and artificial islands covered with coral sand. However, the stability of coral sand slope foundations under the footing loads exerted by these buildings and structures remains unclear. When subjected to the loads, the coral sand particles under the footings may break or interlock, causing the mechanical behavior of coral sand slope foundations to differ significantly from those of common silica sand slope foundations [13-15]. Therefore, relying solely on classical slope foundation theories without considering the unique particle breakage and interlocking behaviors may lead to inaccurate estimations of bearing capacity and incorrect assessments of slope stability. Hence, it is crucial to examine and understand the effect of breakable particle corners on the bearing characteristics and stability of coral sand slope foundations under footings.
Extensive studies have been focused on the bearing capacity of granular soil slope foundations under footings [16-18]. Experimental studies have demonstrated that the bearing capacity of footings on granular soil slopes is highly influenced by factors such as slope angle, slope height, footing types, setback distance of footings to the slope surface, and mechanical characteristics of the granular soil [19, 20]. Among these factors, the characteristics of the granular soil, including particle friction and particle breakage, are particularly important for determining the deformation and failure of the soil slope foundations [13, 21, 22]. Moreover, recent investigations have shown that the primary particle breakage pattern of coral sand is particle corner breakage under footing loads, which differs significantly from the classical fracture breakage observed in previous studies on common particles [13, 23-25]. Although these experimental studies have improved our understanding of soil slope foundations in coral sand areas, there is still a lack of comprehensive investigations into the detailed deformation and failure mechanisms of coral sand slope foundations under footings. This deficiency in experimental studies can be attributed to the challenges associated with analyzing progressive underground soil deformation and obtaining detailed information on the amount and location of particle corner breakage in the slope soil. In terms of numerical investigations, it has been common practice in recent decades to model the deformation and failure of granular soil slope foundations utilizing diverse constitutive models that neglect the effects of particle breakage [26-29]. Although some constitutive models have started to consider the effect of particle breakage in recent years [22, 30, 31], accurately reproducing specific behaviors of coral sand slope foundations in numerical simulations remains challenging due to the inherent use of the traditional particle fracture pattern [13, 22, 32]. Therefore, it is essential to consider the true particle breakage pattern (corner breakage) of coral sand in the mechanical analysis of coral sand slope foundations.
On the other hand, compared with the widely mentioned particle breakage effect, the particle interlocking effect of coral sands has received little attention in previous research. Early studies have indicated that the internal friction angle of coral sand is usually much larger than that of silica sand. However, it was only in recent years that compression tests have shown that coral sand can easily interlock into a block under compressive pressures, leading to significant changes in soil properties [33, 34]. Field tests have also revealed that highly compacted coral sand foundations can exhibit considerably high bearing capacity due to particle corner interlocking [35, 36]. Therefore, apart from the corner breakage effect, the particle interlocking effect also should be considered in the analysis of coral sand slope foundations. In fact, breakable particle corners in coral sand have dual effects: corner interlocking and corner breakage. In other words, breakable particle corners have the potential to improve the bearing capacity of granular foundations by corner interlocking, and also have the potential to reduce the bearing capacity through corner breakage. The combined effects of these opposing factors on the bearing and deformation behaviors of slope foundations remain unexplored. Currently, the discrete element method (DEM) can model both particle corner interlocking and particle breakage of granular soil at both macro-scale and particle-scale [37-39]. Thus, the DEM method should be proper for examining the coupled corner interlocking and breakage effects on the deformation and failure of coral sand slope foundations under strip footings.
This research aims to analyze the underlying mechanism of the unique behaviors displayed by coral sand slope foundations, by investigating the effect of breakable particle corners on macro-to-micro soil behaviors using DEM simulations. The study consists of comparing the bearing capacity of slope foundations in model tests and numerical simulations and preliminarily explaining the unique bearing capacity of coral sand soil by particle contact behaviors. Additionally, the dual effects of breakable particle corners on stress transmission and distribution in slope foundations are explored. Moreover, detailed comparisons and analyses of the deformations of slope foundations under footings are performed. Finally, the failure patterns of granular soil slope foundations are established and their relationships to particle corner interlocking and breakage effects are elucidated. This study provides a new perspective to clarify the behaviors of slope foundations composed of breakable corner particle materials.
2 Granular materials and DEM method
2.1 Coral sand in experiment tests and clusters in numerical simulations
Coral sand belongs to a kind of unique type of marine sediment commonly found in tropical marine regions [40-42], and it is fragments of coral rock (Figure 1(a)) primarily derived from reef-building corals, coral algae, and bone fragments of other marine organisms [10, 33, 43, 44]. The coral sand collected from the South China Sea exhibits a high calcium carbonate (CaCO3) content, accounting for over 94% of its weight. Due to the short transportation distance during the geological sedimentation process, the sand particles have low roundness and numerous corners [41, 45-47]. The specific gravity of the sand is approximately 2.78. Its irregular morphology (Figure 1(b)) and rough surface (Figure 1(c)) contribute to a significantly larger internal friction angle compared to common silica sand. Ordinarily, common silica sand possesses high strength and is relatively hard to break under a confining pressure less than 2.0 MPa [48, 49]. In contrast, coral sand is breakable even under low-pressure conditions [23, 50, 51], distinguishing it from common silica sand. Besides, current studies have proven that the primary pattern of particle breakage in coral sand is particle corner breakage [24, 52]. Further information regarding the characteristics of coral sand can be seen in the model tests conducted by LUO et al [13].
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The mechanical analysis capabilities of the discrete element method (DEM) at a microscopic level are widely acknowledged, which motivated its adoption in this study. Consistent with previous research [53, 54], the particle size distribution of the slope soil in DEM simulations is identical to that used in model tests, with the particle size scaled up to ensure computational efficiency (Figure 2). As shown in Figure 3(a), previous studies have proven that the primary pattern of particle breakage in coral sand is particle corner breakage [24, 32, 52]. Currently, the cluster method in DEM simulations can model both particle corner interlocking and particle breakage of granular soils [37-39, 55, 56]. However, the computational efficiency of the cluster method is low when the particle number is large [56-58]. To simulate corner particles efficiently, the construction of irregular particles using the fewest spheres possible is crucial. Thus, in this study, the detailed inner pores of grains in coral sand were not constructed in numerical simulations. Typically, this involves using large spheres for the main body and a minimal number of smaller spheres arranged symmetrically around the main body to represent the corners [32, 57, 59]. The same as in previous DEM studies [58, 60], one large central ball and three smaller balls were used to create three-corner particles, aiming to simulate the corner effect of coral sand. In contrast, two-corner particles were employed to represent particles with fewer corners. Firstly, two types of clump templates (Figure 3(b)) were created, each consisting of a large central ball and two or three smaller balls symmetrically attached to the central ball. Based on statistical data in tests, the ratio of radius between attaching small spheres and the primary sphere is stochastic, with a reasonable range from 1:3 to 1:7 to model real corner breakage [40]. Consistent with previous studies on pile-soil interaction in calcareous sand [53, 54], the radius ratio between small spheres and primary spheres is chosen to be 1:3.85 in this numerical study. These templates were used to determine the shape of the clusters. In accordance with prior research [58, 61], breakable corner particles were constructed by converting clumps into clusters one by one, where the corners (small balls) were bonded at the contact points (upper part of Figure 3(c)). In the cluster method, the particle corners (represented by small balls) will detach from the cluster (lower part of Figure 3(c)) when the contact force exceeds the bond strength [62, 63]. The number of particle corner breakages in the DEM simulations corresponded to the number of destroyed bonds. Detailed information regarding the linear parallel bond model can be found in Ref. [39].
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2.2 Adopted model tests and numerical model in DEM simulations
This numerical study followed the model tests conducted by LUO et al [13] (Figure 4). The model tests were performed in a model tank with a depth of 800 mm. The internal friction angle of the coral sand was about 35°. The sand pluviation (raining) technique [64] was employed to fill the coral sand slope foundation with a relative density of 70%±1%. Subsequently, a long strip footing (steel plate) measuring 80 mm in width (B=80 mm) was installed on top of the slope, oriented parallel to the slope crest in the longitudinal direction. The horizontal setback distance (b) between the footing edge and the slope crest varied in different test cases. The settlement of the footing was controlled using a high-precision hydraulic jack with a slow loading rate. Pressure measurements under the footings and corresponding settlements were recorded using an acquisition system. More detailed information on the model tests can be found in the study conducted by LUO et al [13].
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The DEM simulations were employed to further investigate the slope foundation behaviors. In the adopted model tests, the length of the footing was roughly 10 times of its width, allowing for numerical simulations to be efficiently conducted under plane strain conditions. Under these circumstances, a two-dimensional numerical simulation, in contrast to a three-dimensional approach, is not only viable but also significantly enhances computational efficiency [38, 39]. To facilitate comparative numerical research, several types of clusters were utilized in the numerical cases, including unbreakable 2-corner particles, unbreakable 3-corner particles, and breakable 3-corner particles, as depicted in Figure 5(a). The slope height, slope angle, and width (B=80 mm) of the model footing were consistent between the DEM numerical simulations and model tests, as illustrated in Figure 5(b). In the numerical simulations, the horizontal setback distance (b) between the footing edge and the slope crest varied from 1B to 4B. The particle median diameter (d50) was 6.4 mm, resulting in a ratio of the footing width (B) to d50 of 12.5. This ratio was deemed sufficient to disregard the particle scale effect based on earlier research [65-67]. The normal and shear stiffness in ball-ball contacts were set at kn=6.0×106 N/m and ks=4.0×106 N/m, respectively, based on previous research on structure-soil interaction in coral sand [32, 68]. To compare the effects of breakable and unbreakable particles, the parallel bond tensile strength was set at 5.0×106 and 5.0×1060 N/m2 for breakable and unbreakable clusters, respectively, based on previous research on structure-soil interaction in coral sand [32, 58]. Similarly, the parallel band cohesion was set at 5.0×106 and 5.0×1060 N/m2 for breakable and unbreakable clusters, respectively. The relative compaction of soil (70%) in the DEM models was controlled by the commonly used approach proposed by DELUZARCHE et al [38], which was consistent with the relative compaction of soil in model tests. This method involves obtaining the maximum porosity from friction samples placed under gravity and obtaining the minimum porosity by successively decreasing the friction coefficient (f) of the particles until f=0, along with isotropic compression and cycles of compaction by the walls [38]. Thus, by using the porosity in DEM simulations, the maximum and minimum porosities obtained by the approach proposed by DELUZARCHE et al [38], the relative density in DEM can be calculated.
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Similar to previous studies on structure-soil interaction using DEM simulations [32, 69, 70], particle parameters in this research were calibrated based on pressure-settlement curves obtained from model tests. Unlike other calibration methods that rely on parameters from individual soil property tests, direct calibration using pressure-settlement curves offers a comprehensive understanding of soil-structure interactions at a physical level [32, 69, 71]. The pressure-settlement curves of the footings on breakable 3-corner particle slope foundations were calibrated based on the footing bottom pressure-settlement curves in coral sands. The simulation and test results in Figure 6 exhibit similar peak pressures, curve shapes, and relationship between peak position and normalized setback distance (b/B), indicating that the bearing characteristics of footings on coral sand slopes in model tests could be effectively captured by using breakable corner particles in DEM simulations. Then, the bearing capacity of slope foundations constructed with unbreakable 2-corner particles, unbreakable 3-corner particles, and breakable 3-corner particles is compared. Detailed parameters adopted in the numerical simulations are displayed in Table 1. The case design for the research on footing load on granular soil slopes is displayed in Table 2.
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| Structure-soil interaction | Parameter | Value |
|---|---|---|
| Footing | Wide/mm | 80 |
| Density/(kg‧m-3) | 7850 | |
| Elastic modulus, E/(N‧m-2) | 2.0×1011 | |
| Poisson ratio | 0.20 | |
| Particles | Particle density/(kg‧m-3) | 2700 |
| Porosity | 0.15 | |
| Particle median diameter, d50/mm | 6.4 | |
| Particle-footing contacts | Normal stiffness, kn/(N‧m-1) | 6.0×107 |
| Shear stiffness, ks/(N‧m-1) | 4.0×107 | |
| Friction coefficient, f | 0.4 | |
| Particle-particle contacts | Normal stiffness, kn/(N‧m-1) | 6.0×106 |
| Shear stiffness, ks/(N‧m-1) | 4.0×106 | |
| Friction coefficient, f | 0.4 | |
| Contacts in clusters | Parallel bond normal stiffness, _Xml/alternativeImage/91068826-D865-4fdc-AC4E-B019A9DD958C-M003c.jpg) | 3.0×1010 |
Parallel bond shear stiffness, _Xml/alternativeImage/91068826-D865-4fdc-AC4E-B019A9DD958C-M004c.jpg) | 2.0×1010 | |
| Parallel bond tensile strength/(N‧m-2) | 5×106, 5×1060 | |
| Parallel bond cohesion/(N‧m-2) | 5×106, 5×1060 | |
Friction angle, _Xml/alternativeImage/91068826-D865-4fdc-AC4E-B019A9DD958C-M005c.jpg) | 22.0 |
| Case | Type | Particle breakage | Bond strength in clusters/(N·m-2) | Data source |
|---|---|---|---|---|
| In silica sand | Model tests | — | — | SALIH KESKIN and LAMAN [14] |
| In coral sand | Model tests | Yes | — | LUO et al [13] |
| In unbreakable 2-corner particles | DEM simulations | No | 5×1060 | This study |
| In unbreakable 3-corner particles | DEM simulations | No | 5×1060 | This study |
| In breakable 3-corner particles | DEM simulations | Yes | 5×106 | This study |
It is noteworthy that in numerical research based on DEM, various particle factors (i.e., particle size, shape, and void ratio) can be greatly simplified and therefore different from the model tests to achieve acceptable computational efficiency [32, 72, 73]. Therefore, the value difference between the results obtained from DEM-based research and model tests was inevitable [74, 75]. Instead of solely focusing on precise numerical results, it is worthwhile to emphasize the qualitative mechanisms.
3 Results and analysis
3.1 Effects of breakable particle corners on bearing capacity of granular soil slope foundations
The ultimate bearing capacity (Pu) is a fundamental parameter for footing design in granular soil [76]. Figure 7 presents a comparison of Pu for footings on different granular soil slope foundations, while Figure 8 illustrates the schematic diagram of particle corner contact and breakage behaviors in granular soil. It is evident that in all cases, Pu increased with the normalized setback distance of b/B. Interestingly, Pu of footings on coral sand slope foundations was larger than the bearing capacity on silica sand slope foundations at large setback distances of b/B_Xml/alternativeImage/91068826-D865-4fdc-AC4E-B019A9DD958C-M001c.jpg)
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In fact, the intriguing bearing capacity of footings on breakable corner particle slope foundations can be primarily explained by the particle contact and breakage behaviors depicted in Figure 8. In classical corner-less particles (Figure 8(a)), particle interaction is primarily influenced by the surface friction of particles, and large soil stress is required for particle fracture breakage [32, 77-79]. After particle fracture breakage, the soil loosening effect is limited as the fragments continue to act as soil skeletons, and the volume of the soil skeleton does not significantly decrease. However, in breakable corner particles such as coral sand (Figure 8(b)), the particle contacts and breakage behaviors differ significantly. Under low loads, soil particles experience limited movement (less relative particle sliding) due to particle interlocking (corner-friction effect), which corresponds to the higher bearing capacity of footings on coral sand slope foundations at large setback distances. However, as the relative slide among particles increases, particle corners are prone to breakage owing to stress concentration around corners. Unlike particle fracture breakage, this particle corner breakage effect results in notable soil loosening by weakening the supporting points in soil skeletons (tiny broken corners tend to migrate into inter-particle voids) and decreasing the internal friction angle of the soil (φsoil). This particle corner breakage effect contributes to the lower bearing capacity of footings on slope foundations at small setback distances. In essence, breakable corner particles, which exhibit both corner interlock and breakage effects, appear to be a key underlying factor contributing to the unique bearing capacity characteristics of coral sand slope foundations. Further analysis of this phenomenon will be provided in subsequent sections.
3.2 Effects of breakable particle corners on stress transmission in slope foundations
The stress transmission under footings provides valuable insights into the bearing mechanism of soil slope foundations [67, 80-82]. However, there is a lack of studies in the existing literature that have specifically examined the effects of breakable particle corners on stress transmission in slope foundations. The analysis of contact force chains proves to be effective in understanding the pattern of stress transmission beneath footings [58, 83].
Modern footing design has shifted from load-based design to displacement-based design [84]. Figure 9 compares the distributions of contact force chains under the same footing settlements. The thickness of the red lines, representing force chains, is directly proportional to the magnitude of particle contact forces. Regarding the slope effect, when the setback distance (b/B) is small, such as b/B=1, the contact force on the left side of the footings was significantly larger than that on the right side (Figure 9) due to stress release near the slope surface. However, the stress transmission was much deeper on the side close to the slope surface at the small setback distance of b/B=1. This deeper stress transmission is a result of soil block sliding near the slope surface, which will be further explored in subsequent sections. Under a larger setback distance of b/B=3, the contact force chains under footings were relatively symmetrical (only slightly smaller on the side close to the slope surface). In unbreakable 2-corner particles, the area of stress diffusion and the corresponding stress diffusion angle beneath the footings were relatively small, as shown in Figure 9(a). As the number of particle corners increased, the area of stress diffusion and the corresponding stress diffusion angle notably increased (Figure 9(b)) due to the enhanced corner interlocking. When considering the corner breakage effect, the contact force chains undergo further changes, as illustrated in Figure 9(c). Under a small settlement of S=6.5 mm, the distributed area of contact force chains remained unchanged, while the magnitude of contact forces decreased significantly owing to the shrinkage of the soil skeleton caused by particle corner breakage. Under a large settlement of S=10 mm, the decrease in the magnitude of contact forces became more pronounced, and the distributed area of contact force chains also decreased with a much smaller stress diffusion angle, owing to the substantial increase in corner breakage beneath the footings.
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The deformation and failure of soil slope foundations are primarily influenced by the shear stress within the soil [85, 86]. Therefore, the distribution of shear stress within slope soils is depicted in Figure 10. Consistent with the distribution of contact force chains, a small setback distance of b/B=1 resulted in a deeper and wider distribution of shear stress on the side close to the slope surfaces. Furthermore, the effect of breakable particle corners has a noticeable impact on the width and depth of the shear stress distribution. As presented in Figure 10(a), the shear stress distribution was relatively narrow and deep in unbreakable 2-corner particles. As the number of corners increased, as shown in Figure 10(b), the width of the shear stress distribution significantly increased, which is attributed to the enhanced corner interlock effect in the granular soil. However, when the corner breakage effect was taken into account, the distributed area of shear stress decreased notably (Figure 10(c)) due to the damage to the corner interlocking. Moreover, the locations of corner breakages correspond well to the high-pressure zone at the bottom and the shear stress zones (shear bands), which will be further analyzed in subsequent sections.
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3.3 Effects of breakable particle corners on deformation of slope foundations
The effect of breakable particle corners on stress transmission in granular soil further affects the deformation of granular soil slope foundations. According to Figure 6, the bearing capacity of footings under small setback distances was much smaller than that under large setback distances. Besides, the results shown in Figures 9 and 10 indicated that corner breakage under small setback distances has a significantly larger impact on the stress transmission beneath footings. Thus, for the stability and safety of footings, the analysis of corner breakage under small setback distances deserves more attention. As a result, the following parts are mainly focused on corner breakage effects under small setback distances. The slope deformations under two different footing settlements, S=10 mm and S=35 mm are shown in Figure 11. As depicted in Figure 11(a), the deepest slope deformation occurred in the unbreakable 2-corner particle soil. This is attributed to the small stress diffusion angle resulting from relatively weak particle interlock (Figure 9(a)). With an increase in the number of particle corners, the depth of soil deformation noticeably decreased due to the larger stress diffusion angle under the footings. Consequently, significant horizontal movement of particles was observed in unbreakable 3-corner particles, as shown in Figure 11(b). Additionally, compared to the 2-corner particle slopes, noticeable soil upheaval was observed on both sides of the footings in 3-corner particle slopes due to stronger horizontal squeezing movement of particles. When taking the corner breakage into consideration under a settlement of S=10 mm, the depth of slope deformation further decreased notably owing to the decrease in soil-squeezing intensity caused by the soil shrinkage effect of particle corner breakage. Under conditions without corner breakage (Figures 11(a) and (b)), or with limited corner breakage (the left of Figure 11(c)), particle displacement decreased from the upper-right to the lower-left, perpendicular to slip bands. However, under the strong particle corner breakage condition with a large footing settlement of S=35 mm (the right of Figure 11(c)), the slip band transformed into a slip surface, with soil blocks moving as a unit. This phenomenon will be further elucidated by the corner breakage in the subsequent sections.
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To provide a comprehensive analysis of the effect of breakable particle corners on soil deformation, slope surface deformations relative to the initial slope surface are displayed in Figure 12. Regardless of particle breakability, the magnitude of deformation on 3-corner particle slopes decreased with increasing distance from the slope crest on the slope surface. Under identical footing settlements, the downward movement of 3-corner particles was hindered by strong particle interlock from surrounding particles (consistent with a large stress diffusion angle). As a result, the soil relatively horizontally moved towards the free surface of the slopes. Besides, corner breakage reduced the squeezing effect around the footing in breakable 3-corner particles, leading to slightly smaller deformations on slope surfaces. In contrast, significant soil deformation occurred in the middle position of slope surfaces in 2-corner particle soils. This can be explained by the weak corner interlock that allows particles to move downward, which aligns with the analysis of the small stress diffusion angle presented in Figure 9(a).
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3.4 Effects of breakable particle corners on failure mode of slope foundations
Particle-scale behaviors, such as particle rotation velocity and particle breakage distributions, play a crucial role in understanding the detailed mechanisms of granular soil deformation and failure [52, 67, 87, 88]. Previous studies [89, 90] have demonstrated the usefulness of particle rotation velocity distributions in identifying slip bands in granular soil. Figure 13 compares the variability of particle rotation velocity distributions in different slopes to explore the effect of corner breakage on slip and failure behaviors of granular soil slope foundations. In Figure 13, the positions with high rotation velocity corresponded to the slip bands or slip surfaces in granular soils. Therefore, the trigonal compression zones under footings were clearly indicated by the surrounding particle rotation distributions. In the unbreakable 3-corner particle slopes (Figure 13(a)), the different locations of strong particle rotation areas under different but adjacent settlements indicated the presence of an variable slip band in the slope foundation, consistent with the findings of a previous study by WANG et al [22]. However, when taking the particle corner breakage into consideration in Figure 13(b), the location of the slip band became stable under different footing settlements; this is because the particle corner breakage promotes the extension of the slip band to the slope surface, which is consistent with stable bulk slip observed in the right figure of Figure 11(c).
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In fact, the stable slip band in breakable corner particle slope foundations is attributed to the extension of particle corner breakage within the slip bands, as shown in Figure 14. As demonstrated in the recent study [58], corner breakage, unlike classical particle fracture breakage, is highly influenced by the relative particle slide among corners. As shown in the diagram of Figure 14(a), corner breakage occurs due to stress concentration caused by the sliding of particles relative to each other [32]. Consequently, significant corner breakage occurs within the slip band. After the breakage of particles at the corner within the slip band, the friction resistance caused by corner interlocks decreases around the broken particles. This results in the formation of a stable slip surface (Figure 14(b)) with reduced friction resistance. Moreover, the decrease in friction resistance on the slip surface also contributes to the lower bearing capacity of the footing on breakable corner particle slope foundations under small setback distances, as shown in Figure 7.
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After a sequence of macro- and micro-scale analyses, the mechanical failure patterns of different granular soil slope foundations under strip footings are summarized in this section. The effect of breakable particle corners on slope performance under strip footings is a combined outcome of corner interlocking and corner breakage, which significantly affects the bearing and failure behaviors of slope foundations. Under large setback distances of footings to slope surfaces, corner interlocking noticeably improves the bearing capacity of footings on coral sand slope foundations. However, under small setback distances, the breakage of corners results in a decreased bearing capacity and altered failure pattern of slope foundations, as shown in Figure 15. In the case of slope foundations with common corner-less particles (e.g., silica sand) as shown in Figure 15(a), the soil beneath the footings exhibits a typical shear failure mode, characterized by deep and unstable slip bands, the strongest slope deformation at the mid-position of slope surfaces, and weak soil upheaval on both sides of the footings. In contrast, for slope foundations with breakable corner particles (e.g., coral sand), shear failure of the slope foundations tends to occur in a stable slip surface (Figure 15(b)) due to slide-induced corner breakage on the slip surface. In this scenario, slope failure is characterized by a shallow and stable slip surface, the strongest deformation of the slope foundation around the slope crest, and pronounced soil upheaval on both sides of the footings. Therefore, it is reasonable to conclude that neglecting the effect of breakable particle corners and merely relying on classical design theories may lead to misjudgments regarding the bearing characteristics and failure patterns of coral sand slope foundations, posing a potential engineering risk in coral sand areas.
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4 Conclusions
This study aims to investigate the micromechanical mechanism underlying the distinctive performance of coral sand slope foundations under a strip footing. The focus is on analyzing the effects of breakable particle corners on the slope foundation soil behaviors at both macro and microscales through a sequence of numerical simulations using the discrete element method (DEM). The key findings can be summarized as follows.
1) Breakable particle corners have notable effects on the bearing characteristics of slope foundations. The bearing capacity of breakable corner particle slope foundations is lower than that of common corner-less particle slope foundations in both model tests and simulations when subjected to low footing setback distances. However, when subjected to large setback distances, the bearing capacity of breakable corner particle slope foundations exceeds that of the common slope foundations. A schematic diagram is provided to illustrate the bearing characteristics of breakable corner particle soil, in comparison to particle contact behaviors in corner-less granular soil. The diagram elucidates the phenomena of corner interlocking and corner breakage in the breakable corner particle soil.
2) The dual effects of corner interlocking and corner breakage alter the stress transmission in slope foundations. There is a positive correlation between the number of particle corners and the stress diffusion angle under footings, while a negative correlation between the number of corners and the depth of stress transmission is discovered. Besides, the occurrence of corner breakage resulted in a decrease in both the angle of stress diffusion and the depth of stress transmission. Additionally, the primary factor contributing to the wide shear stress zones in unbreakable corner particle slope foundations is the strong corner interlocking effect. On the other hand, the narrow shear stress zones observed in breakable corner particle slope foundations are attributed to the breakage of particle corners along these zones.
3) The effects of breakable corners heavily change the particle displacement and the slope deformation. Significant soil upheaval near the footings and notable soil horizontal squeezing movement in the soil slopes with corner-rich particles can be attributed to the strong interlocking effect among particle corners. Thus, the soil deformation is relatively shallow under footings in slope foundations with corner-rich particles. Additionally, the shrinkage in the soil skeleton caused by the breakage of particle corners is the underlying reason for the limited depth of soil deformation observed beneath strip footings. Moreover, this particle corner breakage effect also leads to the overall movement of granular soil on the bottom slip surface in granular soil slope foundations.
4) The correlation between the failure of slope foundations, slip band behaviors, and the development of particle corner breakage in slope foundations is established. The occurrence of particle corner breakage along slip bands plays a crucial role in the transformation of unstable slip bands into a stable slip surface in slope foundations. In contrast to classical particle fracture breakage, the presence of stress concentration around the corners of particles during particle sliding leads to the occurrence of particle corner breakage along the slip surface. Furthermore, a mechanism diagram is developed to illustrate the failure pattern of breakable corner particle slope foundations. This proposed diagram interpreted the distinctive bearing and deformation characteristics exhibited by coral sand slope foundations.
In summary, the research findings emphasize the significance of considering the effect of breakable particle corners when understanding the distinct behavior of coral sand slope foundations under strip footings. These effects not only have an impact on the bearing capacity but also modify the deformation and failure pattern of slope foundations. Consequently, this study offers insights for footing designs in slope foundations composed of breakable corner particle materials.
Experimental investigation on mechanical behavior and particle crushing of calcareous sand retrieved from South China Sea
[J]. Engineering Geology, 2021, 280: 105932. DOI:10.1016/j.enggeo.2020.105932.Laboratory study on geotechnical characteristics of marine coral clay
[J]. Journal of Central South University, 2022, 29(2): 572-581. DOI:10.1007/s11771-022-4900-5.Analysis of influencing factors of penetration mechanism and vertical bearing characteristics of monopile in calcareous sand: Laboratory model testing and in situ testing
[J]. Soil Dynamics and Earthquake Engineering, 2024, 180: 108577. DOI:10.1016/j.soildyn.2024.108577.Constitutive relations of coral aggregate concrete under uniaxial and triaxial compression
[J]. Construction and Building Materials, 2020, 251: 118957. DOI:10.1016/j.conbuildmat.2020.118957.Foundation filling performance of calcareous soil on coral reefs in the South China Sea
[J]. Applied Ocean Research, 2022, 129: 103386. DOI:10.1016/j.apor.2022.103386.New perspective to improve the sulfate attack resistance of mortar by coral sand
[J]. Journal of Building Engineering, 2023, 71: 106483. DOI:10.1016/j.jobe.2023.106483.Cyclic failure mechanisms of saturated marine coral sand under various consolidations
[J]. Applied Ocean Research, 2023, 131: 103450. DOI:10.1016/j.apor.2022.103450.Effects of relative densities on particle breaking behaviour of non-uniform grading coral sand
[J]. Powder Technology, 2021, 382: 524-531. DOI:10.1016/j.powtec.2021.01.015.Morphology characterization and discrete element modeling of coral sand with intraparticle voids
[J]. Engineering Geology, 2023, 315: 107023. DOI:10.1016/j.enggeo.2023.107023.Effect of variable confining pressure on the long-term cyclic behaviour of calcareous sand: Experimental observation and microstructural interpretation
[J]. Canadian Geotechnical Journal, 2024, 61(2): 311-327. DOI:10.1139/cgj-2022-0492.Behavior of eccentrically loaded shallow foundations resting on composite soils
[J]. Journal of Building Engineering, 2019, 23: 220-230. DOI:10.1016/j.jobe.2019.01.036.Bearing capacity and deformation behavior of rigid strip footings on coral sand slopes
[J]. Ocean Engineering, 2023, 267: 113317. DOI:10.1016/j.oceaneng.2022.113317.Model studies of bearing capacity of strip footing on sand slope
[J]. KSCE Journal of Civil Engineering, 2013, 17(4): 699-711. DOI:10.1007/s12205-013-0406-x.Effects of particle size on the particle breakage of calcareous sands under impact loadings
[J]. Construction and Building Materials, 2022, 341: 127809. DOI:10.1016/j.conbuildmat.2022.127809.Stability analysis for footings on reinforced sand slopes
[J]. Soils and Foundations, 1994, 34(3): 21-37. DOI:10.3208/sandf1972.34.3_21.Limit load space of rigid strip footing on sand slope subjected to combined eccentric and inclined loading
[J]. Computers and Geotechnics, 2023, 162: 105652. DOI:10.1016/j.compgeo.2023.105652.Model tests for studying the failure mechanism of dry granular soil slopes
[J]. Engineering Geology, 2011, 119(1-2): 51-63. DOI:10.1016/j.enggeo.2011.02.001.The mechanics of surficial failure in soil slopes
[J]. Engineering Geology, 2010, 114(1-2): 57-64. DOI:10.1016/j.enggeo.2010.04.003.Effect of particle breakage-induced frictional weakening on the dynamics of landslides
[J]. Granular Matter, 2022, 24(3): 72. DOI:10.1007/s10035-022-01234-6.Particle breakage evolution of coral sand using triaxial compression tests
[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2021, 13(2): 321-334. DOI:10.1016/j.jrmge. 2020.06.010.Experimental study on the behavior of single pile foundation under vertical cyclic load in coral sand
[J]. Ocean Engineering, 2023, 280: 114672. DOI:10.1016/j.oceaneng.2023.114672.The creep characteristics and related evolution of particle morphology for calcareous sand
[J]. Powder Technology, 2024, 431: 119077. DOI:10.1016/j.powtec.2023.119077.Stability analysis of slope with building loads
[J]. Soil Dynamics and Earthquake Engineering, 1997, 16(6): 395-405. DOI:10.1016/S0267-7261(97)00008-0.Experimental and numerical study of strip footing supported on stabilized sand slope
[J]. Geotechnical and Geological Engineering, 2010, 28(4): 311-323. DOI:10.1007/s10706-009-9293-9.Undrained stability of footings on slopes
[J]. International Journal of Geomechanics, 2011, 11(5): 381-390. DOI:10.1061/(asce)gm.1943-5622.0000092.Undrained bearing capacity of strip footings on slopes
[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2010, 136(5): 677-685. DOI:10.1061/(asce)gt.1943-5606.0000269.Geohazard at volcanic soil slope in cold regions and its influencing factors
[J]. Japanese Geotechnical Society Special Publication, 2015, 1(1): 1-20. DOI:10.3208/jgssp.key-1.Slope failures/landslides over a wide area in the 2018 Hokkaido Eastern Iburi earthquake
[J]. Soils and Foundations, 2019, 59(6): 2376-2395. DOI:10.1016/j.sandf.2019.08.009.Analysis of particle corner-breakage effect on pile penetration in coral sand: Model tests and DEM simulations
[J]. Canadian Geotechnical Journal, 2023, 60(5): 749-765. DOI:10.1139/cgj-2022-0038.SHPB experiments and FDM-DEM coupled simulations on calcareous sand under uniaxial to triaxial deformation
[J]. International Journal of Impact Engineering, 2023, 181: 104751. DOI:10.1016/j.ijimpeng.2023.104751.Strength, deformation, and particle breakage behavior of calcareous sand: Role of anisotropic consolidation
[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2023, 149(3):The use of light weight deflectometer for in situ evaluation of sand degree of compaction
[J]. HBRC Journal, 2014, 10(3): 298-307. DOI:10.1016/j.hbrcj.2013.12.003.Responses of calcareous sand foundations to variations of groundwater table and applied loads
[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2022, 14(4): 1266-1279. DOI:10.1016/j.jrmge.2021.08.003.Study on the effect of particle morphology on single particle breakage using a combined finite-discrete element method
[J]. Computers and Geotechnics, 2020, 122: 103532. DOI: 10. 1016/j.compgeo.2020.103532.Modeling of rockfill behavior with crushable particles
[M]// Numerical Modeling in Micromechanics via Particle Methods. Routledge, 2017: 219-224. DOI: 10.1201/978020374533 5-29.A bonded-particle model for rock
[J]. International Journal of Rock Mechanics and Mining Sciences, 2004, 41(8): 1329-1364. DOI:10.1016/j.ijrmms.2004.09.011.Engineering characteristics of coral reef and site assessment of hydraulic reclamation in the South China Sea
[J]. Construction and Building Materials, 2021, 300: 124263. DOI:10.1016/j.conbuildmat.2021.124263.Study on horizontal bearing characteristics of pile foundations in coral sand
[J]. Canadian Geotechnical Journal, 2021, 58(12): 1928-1942. DOI:10.1139/cgj-2020-0623.Macro-microscopic mechanical behavior of geogrid reinforced calcareous sand subjected to triaxial loads: Effects of aperture size and tensile resistance
[J]. Geotextiles and Geomembranes, 2024, 52(4): 526-541. DOI:10.1016/j.geotexmem.2024.01.006.Black band disease as a possible factor of the coral decline at the northern reef-flat of Yongxing Island, South China Sea
[J]. Science China Earth Sciences, 2014, 57(4): 569-578. DOI:10.1007/s11430-013-4734-y.Influence of the particle morphology and internal porosity characteristics of coral sand in the South China Sea on its limit void ratio
[J]. Powder Technology, 2023, 428: 118771. DOI:10.1016/j.powtec.2023.118771.Strength and permeability of bentonite-assisted biocemented coarse sand
[J]. Canadian Geotechnical Journal, 2021, 58(7): 969-981. DOI:10.1139/cgj-2020-0045.Seismic architecture of Yongle isolated carbonate platform in Xisha Archipelago, South China Sea
[J]. Frontiers in Earth Science, 2023, 11: 1100675. DOI: 10.3389/feart.2023.1100675.Anisotropic behaviors of calcareous sand dependent on loading direction and initial shear stress
[J]. Applied Ocean Research, 2023, 141: 103775. DOI:10.1016/j.apor.2023.103775.Detailed amount of particle breakage in nonuniformly graded sands under one-dimensional compression
[J]. Canadian Geotechnical Journal, 2020, 57(8): 1239-1246. DOI:10.1139/cgj-2019-0283.Characteristics of particle breakage of sand in triaxial shear
[J]. Powder Technology, 2017, 320: 656-667. DOI:10.1016/j.powtec.2017.08.001.Stress-dilatancy behaviour of fouled ballast: Experiments and DEM modelling
[J]. Granular Matter, 2021, 23(4): 90. DOI:10.1007/s10035-021-01150-1.Physical and mechanical properties of coral aggregates in the South China Sea
[J]. Journal of Building Engineering, 2023, 63: 105478. DOI:10.1016/j.jobe.2022.105478.The detailed particle breakage around the pile in coral sand
[J]. Acta Geotechnica, 2021, 16(6): 1971-1981. DOI:10.1007/s11440-020-01089-2.Three-dimensional numerical modelling of progressive failure of caisson foundation in sand using a coupled FDM–DEM method
[J]. Ocean Engineering, 2022, 253: 111332. DOI:10.1016/j.oceaneng.2022.111332.An improved VOF-DEM model for soil-water interaction with particle size scaling
[J]. Computers and Geotechnics, 2020, 128: 103818. DOI:10.1016/j.compgeo.2020.103818.Performance of screw–shaft pile in sand: Model test and DEM simulation
[J]. Computers and Geotechnics, 2018, 104: 118-130. DOI:10.1016/j.compgeo.2018.08.013.Calibration of parallel bond parameters in bonded particle models via physics-informed adaptive moment optimisation
[J]. Powder Technology, 2020, 366: 527-536. DOI:10.1016/j.powtec.2020.02.077.DEM analysis of angular ballast breakage under cyclic loading
[J]. Geomechanics and Geoengineering, 2007, 2(3): 175-181. DOI:10.1080/17486020701474962.Micromechanical analysis of the particle corner breakage effect on pile load performance in coral sand
[J]. Acta Geotechnica, 2023, 18(12): 6353-6370. DOI:10.1007/s11440-023-01975-5.Review of particle breakage simulation based on DEM
[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(5): 880-889. DOI:10.11779/CJGE201805013.Micromechanical analysis of the particle corner breakage effect on pile penetration resistance and formation of breakage zones in coral sand
[J]. Ocean Engineering, 2022, 259: 111859. DOI:10.1016/j.oceaneng.2022.111859.Discrete element modelling of ballast abrasion
[J]. Géotechnique, 2006, 56(9): 651-655. DOI:10.1680/geot.2006.56.9.651.Scale effects in rockfill behaviour
[J]. Géotechnique Letters, 2012, 2(3): 155-160. DOI:10.1680/geolett.12.00025.Macro–micro responses of crushable granular materials in simulated true triaxial tests
[J]. Granular Matter, 2015, 17(4): 497-509. DOI:10.1007/s10035-015-0571-3.Bearing capacity of square footings on geosynthetic reinforced sand
[J]. Geotextiles and Geomembranes, 2009, 27(4): 281-294. DOI:10.1016/j.geotexmem.2009.02.001.Estimation of the installation torque–capacity correlation of helical pile considering spatially variable clays
[J]. Canadian Geotechnical Journal, 2024, 61(10): 2064-2074. DOI:10.1139/cgj-2023-0331.Discrete element modeling of cone penetration tests incorporating particle shape and crushing
[J]. International Journal of Geomechanics, 2019, 15:Discrete element simulations of shallow plate-load tests
[J]. International Journal of Geomechanics, 2016, 16(3):DEM modelling of screw pile penetration in loose granular assemblies considering the effect of drilling velocity ratio
[J]. Granular Matter, 2019, 21(3): 74. DOI:10.1007/s10035-019-0933-3.Effect of loading rate on sand pile failure: 2D DEM simulation
[J]. Geotechnical and Geological Engineering, 2017, 35(2): 889-896. DOI:10.1007/s10706-016-0142-3.Calibration of granular material parameters for DEM modelling and numerical verification by blade–granular material interaction
[J]. Journal of Terramechanics, 2009, 46(1): 15-26. DOI:10.1016/j.jterra.2008.12.004.Downwards force–displacement response of buried pipelines during dip–slip faulting in sandy soil
[J]. Canadian Geotechnical Journal, 2021, 58(3): 377-397. DOI:10.1139/cgj-2019-0446.Discrete element simulation of crushing behavior of calcareous sands during pile jacking
[J]. Rock and Soil Mechanics, 2015, 36(1): 272-278. DOI:10.16285/j.rsm.2015.01.037.Applicability of discrete element method with spherical and clumped particles for constitutive study of granular materials
[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2022, 14(1): 240-251. DOI:10.1016/j.jrmge.2021.09.015.Challenges of DEM: II. Wide particle size distributions
[J]. Powder Technology, 2014, 264: 627-633. DOI:10.1016/j.powtec.2014.04.096.Hierarchical modeling method for DEM simulation and its application in soil–pile–cap interaction and impact case
[J]. International Journal of Geomechanics, 2019, 19(7):Impact of reinforcement granular soils on the behaviour of strip footing nearby an excavation
[J]. Geomechanics and Geoengineering, 2022, 17(3): 927-958. DOI:10.1080/17486025.2021.1903094.Evolution of particle morphology and mode of fracture during the oedometric compression of sand
[J]. Géotechnique, 2021, 71(10): 853-865. DOI:10.1680/jgeot.18.p.300.Packing, compressibility, and crushability of rockfill materials with polydisperse particle size distributions and implications for dam engineering
[J]. Water Science and Engineering, 2022, 15(4): 358-366. DOI:10.1016/j.wse.2022.07.003.A unified fractional breakage model for granular materials inspired by the crushing tests of dyed gypsum particles
[J]. Construction and Building Materials, 2021, 270: 121366. DOI:10.1016/j.conbuildmat.2020.121366.Stress distribution and settlement of shallow foundations
[M]//Foundation Engineering Handbook.Stress distribution beneath rigid circular foundations on sands
[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1992, 16(1): 65-72. DOI:10.1002/nag.1610160106.Wind-wave combined effect on dynamic response of soil-monopile-OWT system considering cyclic hydro-mechanical clay behavior
[J]. Computers and Geotechnics, 2023, 154: 105124. DOI:10.1016/j.compgeo.2022.105124.Three-dimensional discrete-element-method analysis of behavior of geogrid-reinforced sand foundations under strip footing
[J]. International Journal of Geomechanics, 2022, 22(9):Displacement-based design of soil-foundation-structure systems
[J]. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering, 2019, 172(1): 16-29. DOI:10. 1680/jgeen.17.00196.Slope stability analysis to correlate shear strength with slope angle and shear stress by considering saturated and unsaturated seismic conditions
[J]. Applied Sciences, 2021, 11(10): 4568. DOI:10.3390/app1110 4568.Unstable behaviour of sand and its implication for slope instability
[J]. Canadian Geotechnical Journal, 2003, 40(5): 873-885. DOI:10.1139/t03-039.Micromechanical investigation of particle-size effect of granular materials in biaxial test with the role of particle breakage
[J]. Journal of Engineering Mechanics, 2022, 148(1):Micro-structure developed in shear bands of dense granular soils and its computer simulation: Mechanism of dilatancy and failure
[M]// IUTAM Symposium on Mechanics of Granular and Porous Materials.DEM-aided study of shear band formation in dip-slip faulting through granular soils
[J]. Computers and Geotechnics, 2016, 71: 221-236. DOI:10.1016/j.compgeo.2015.10.002.Microstructure of shear bands and its relation to the mechanisms of dilatancy and failure of dense granular soils
[J]. Géotechnique, 1998, 48(4): 465-481. DOI:10.1680/geot.1998.48.4.465.PENG Yu, LUO Zhao-gang, HE Shao-heng, QU Li-ming, and DING Xuan-ming declare that they have no conflict of interest.
PENG Yu, LUO Zhao-gang, HE Shao-heng, QU Li-ming, DING Xuan-ming. Micromechanical analysis of particle corner effect on bearing and deformation behaviors of coral sand slope foundation under a strip footing [J]. Journal of Central South University, 2025, 32(2): 624-642. DOI: https://doi.org/10.1007/s11771-025-5871-0.
彭宇,骆赵刚,何绍衡等.基于颗粒棱角效应的条形基础下珊瑚砂斜坡地基承载与变形行为微观分析[J].中南大学学报（英文版）,2025,32(2):624-642.