Analysis of Shear Crushing Behavior of Graded Calcareous Sand in Building Applications

Abstract

Calcareous sand, a critical construction material in reef engineering and building foundations, possesses unique internal microstructures and inherent mechanical properties. Given these characteristics, it is essential to thoroughly evaluate its strength under various loading conditions to ensure its reliability in building applications. This study examines the strength, deformation, and failure characteristics of calcareous sand through consolidated drained shear failure tests using a GDS stress path triaxial apparatus. The effects of shear rate, particle gradation, and compactness are systematically investigated to assess their impact on structural stability in building foundations and load-bearing applications. The results indicate that at low confining pressures, calcareous sand exhibits strain softening, whereas at higher confining pressures, strain hardening is observed. For samples with the same gradation, both peak deviatoric stress and failure strain increase linearly with confining pressure. The volume strain evolution during shear follows three stages: shear shrinkage, shear dilatancy, and stabilization. At low confining pressures, dilatancy is favored, while high confining pressures promote shrinkage. Additionally, under constant confining pressure, peak strength increases and failure strain decreases linearly with compactness. Increasing the loading rate from 0.01 to 0.1 mm/min results in a slight increase in the friction angle, with minimal impact on cohesion. Particle gradation plays a significant role in determining the shear strength of calcareous sand, as its effects vary depending on the combination of compactness and gradation. These findings provide valuable insights for the design and construction of stable building foundations, roadbeds, and other load-bearing structures in reef engineering and coastal developments, where calcareous sand is widely used.

1. Introduction

Calcareous sand is widely distributed in offshore environments, making it a crucial material for island reclamation and coastal infrastructure projects [1,2]. Due to its unique physical properties—such as high porosity, irregular particle shapes, and intra-particle voids—calcareous sand exhibits distinct mechanical behavior compared to conventional silica sand [3,4]. One of the primary engineering challenges associated with calcareous sand is its susceptibility to particle fragmentation under shear stress, which can significantly affect its load-bearing capacity and long-term stability in building foundations and roadbeds. This fragmentation often leads to excessive settlement, reduced strength, and potential structural failure in geotechnical applications [5,6]. Therefore, a thorough understanding of the shear-induced breakage characteristics of calcareous sand is essential for optimizing its use in building and infrastructure applications while ensuring long-term reliability.

Recent studies have extensively explored the crushing behavior of calcareous sand particles. Terzariol et al. [7] conducted a particle-scale investigation of liquefaction on Mayotte’s slopes and found that, even in deposits with high fines content, biological grains can undergo pulverization under both cyclic and static loading. Giang et al. [8] examined the effects of particle shape on the small-strain shear modulus (G₀) of silica and calcareous sands, finding that uniformity coefficient, shape, and stiffness significantly influence G₀. Yaru Lv et al. [9] conducted conventional triaxial creep tests on calcareous sand and found that its volume creep strain decreases while axial strain increases under deviatoric stress. Microscopic observations revealed that honeycomb-like voids within the sand contribute to breakage and deformation [10]. Similarly, Xiao [11] studied stress wave attenuation in calcareous sand using an improved Split Hopkinson Pressure Bar (SHPB) system, concluding that attenuation is influenced by particle size, wavelength, and relative density rather than amplitude.

Other investigations have focused on the shear response of calcareous sand under different loading conditions. Ji and Cai [12,13] found that particle breakage is not proportionally related to sand size, showing a complex distribution pattern. Lv et al. [14,15] analyzed the effects of impact energy, density, moisture content, and gradation on breakage rates, revealing a linear relationship between strain rate and particle fragmentation. Jin et al. [16] demonstrated that calcareous sand exhibits superior peak strength, stability, and liquefaction resistance compared to siliceous sand. Moreover, the peak strength derived from monotonic shear tests serves as a critical indicator for assessing sand liquefaction resistance. Qian and Wang [17,18] applied the Mohr–Coulomb strength criterion to evaluate the shear strength of calcareous sand at varying densities and confining pressures, finding that internal friction angle and cohesion increase with relative density.

Additional studies have examined the effects of particle morphology and gradation on the compressibility of calcareous sand [19]. Researchers have noted that, compared to silica sand, calcareous sand exhibits higher angularity and larger pores, leading to greater compressibility. Zhou et al. [20] investigated anisotropic consolidation behavior under cyclic loading, concluding that pore water pressure fluctuations play a significant role in failure mechanisms. Liang et al. [21]. investigated the influence of particle sphericity on sand shear strength and found that lower sphericity corresponds to higher shear resistance, as reflected by increases in both the peak and critical-state friction angles. Meanwhile, Luzzani and Coop [22,23] conducted large-strain ring shear tests, observing that particle breakage persists even after reaching a critical state, balancing volume compression and expansion. Zhu et al. [24] utilized 3D scanning to quantify alterations in particle size and morphology of calcareous sand following MICP treatment and coating. Fractal analysis indicated that the thickness of the coating plays a pivotal role in governing the particles’ local crushing behavior.

Based on these findings, graded calcareous sand has shown strong potential as a roadbed and foundation material in building applications. Additionally, its load-bearing capacity can be significantly improved through various compaction techniques. However, particle breakage remains a critical challenge: it predominantly occurs within specific size fractions and is highly sensitive to loading protocol, relative density, and environmental conditions. Despite extensive investigation, the micromechanical mechanisms driving calcareous sand fragmentation under shear remain incompletely understood. Accordingly, this study systematically investigates the effects of relative density, shear rate, and particle gradation on the shear behavior of calcareous sand through triaxial testing, with the objective of providing practical insights for its optimized application in construction and geotechnical engineering.

2. Laboratory Test

2.1. Test Materials

The calcareous sand sample used in this study was collected from the waters near a reef in the Nansha Islands. This sand primarily consists of coral and biological skeletal remains, often referred to as coral sand, and is predominantly composed of calcium carbonate. Due to significant regional variations in the mineral composition of calcareous sand, X-ray diffraction (XRD) analysis and X-ray fluorescence spectroscopy (XRF) were employed to characterize the composition of the cleaned calcareous sand samples. Figure 1 presents the XRD spectrum, which indicates that the cleaned calcareous sand is relatively pure. The sample is primarily composed of aragonite and magnesium-bearing calcite, with mass fractions of 65.1% and 34.9%, respectively. The XRF results show that calcium (Ca) constitutes 93.53% of the calcareous sand, while other inorganic elements such as aluminum (Al), phosphorus (P), sulfur (S), chlorine (Cl), and strontium (Sr) are also present [25].

In this test, two gradations were selected and labeled as Gradation 1 and Gradation 2. Gradation 1 represents the initial gradation of the sample, which is commonly used in engineering, where particles larger than 10 cm have been removed. It is characterized by poor gradation, a coefficient of uniformity of 4.0, a coefficient of curvature of 1.2, and a maximum dry density of 1.57 g/cm³ [26,27]. Gradation 2, on the other hand, was developed through multiple gradation optimizations to avoid the particle breakage sensitivity caused by load. The uniformity coefficient of Gradation 2 is 20.5, and its curvature coefficient is 2.3. The maximum dry density of Gradation is 1.67 g/cm³ [28]. The gradation curves for both samples are shown in Figure 2. The shape factors for Gradation 1 and 2 are 0.644 and 0.528, respectively. The shape factor is defined as the ratio of sphericity to roundness, with a value approaching 1 indicating that the particle shape is closer to that of a sphere [29,30].

2.2. Instrument and Specimen Preparation

Prior to testing, pretreatments for the calcareous sand, including gradation screening, flushing, drying, and re-screening, were conducted to ensure both purity and proper gradation. The consolidation drainage shear test was performed using a GDS stress path triaxial apparatus (model: STDTTS), as shown in Figure 3. The sand was added to the test mold in three stages. Due to the fragility of calcareous sand, compaction was achieved by gently tapping around the mold, rather than using the traditional heavy-weight compaction method. Before conducting the consolidation drainage shear test, it was necessary to saturate the specimen. Saturation was achieved through a series of processes: carbon dioxide saturation, water saturation, and graded backpressure saturation. The specimen was considered fully saturated when the B-value exceeded 0.9, at which point the consolidation drainage shear test was conducted on the saturated specimen.

2.3. Test Program

Four groups of consolidation drainage shear tests, as outlined in

Table 1. Triaxial shear test scheme of calcareous sand.

Group	Particle Size Distribution	Shear Rate (mm/min)	Compactness (%)	Confining Pressure (kPa)
Group 1	Particle ratio 1	0.01	90	50, 100, 200, 300, 400, 600
Group 2	Particle ratio 1	0.1	90	50, 100, 200, 300, 400
Group 3	Particle ratio 2	0.1	90	50, 100, 200, 400
Group 4	Particle ratio 1	0.01	90, 92, 95	200

, were conducted based on varying particle gradations, shear rates, compactness, and confining pressures. To investigate the influence of key factors on the shear behavior of calcareous sand under realistic engineering conditions, all tests were conducted on specimens prepared with Particle Ratio 1 at a relative density of 90%. To assess the effect of shear rate on the shear failure characteristics of calcareous sand, two shear rates—0.1 mm/min and 0.01 mm/min—were selected. According to the actual situation of the project, six confining pressures, ranging from 50 kPa to 600 kPa, were applied to analyze the stress–strain and strain–volume strain characteristics of the specimens under both low and high confining pressures [31,32]. In order to assess the effect of densification on stress–strain and strain–volume strain behavior, three densification classes (90%, 92%, and 95%) were tested at a confining pressure of 200 kPa, and the densification equations are shown in Formula (1). Additionally, two gradations, Gradation 1 and Gradation 2, were used to assess the influence of particle gradation on mechanical properties. A total of 16 samples were tested in the study. Sample preparation and loading followed the guidelines specified in the Standard for Soil Test Methods.

$$\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}={\displaystyle \frac{{\rho }_{\mathrm{d}}}{{\rho }_{\mathrm{m}\mathrm{a}\mathrm{x}}}}\times 100\%$$

(1)

where ${\rho }_{\mathrm{d}}$ is the actual dry density of the specimen and ${\rho }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum dry density.

3. Results and Analysis

3.1. Deviatoric Stress–Strain Characteristics

Figure 4 illustrates the deviatoric stress–strain curves of calcareous sand specimens under varying confining pressures and loading conditions. Figure 4a–c demonstrate the relationship between deviatoric stress and axial strain for Gradation 1 samples tested at loading rates of 0.01 mm/min and 0.1 mm/min, and Gradation 2 samples tested at 0.1 mm/min under varying confining pressures. From Figure 4, it can be observed that sand specimens with different gradations exhibit strain-softening behavior at lower confining pressures. Initially, the deviatoric stress increases with axial strain, reaches a peak, and subsequently decreases before stabilizing. Conversely, under higher confining pressures, the specimens demonstrate strain-hardening characteristics. This trend is identical to the findings of Lyu et al. [33]. In this case, the deviatoric stress continuously increases with axial strain, but the rate of increase gradually diminishes, approaching an asymptotic limit. This trend reflects the rise in internal friction as confining pressure increases, resulting in pronounced plastic hardening in the stress–strain response. Consequently, the deviatoric stress–strain curves display significant plastic hardening behavior with increasing confining pressure. Taking Figure 4a as an example, at confining pressures of 300 kPa and 600 kPa, distinct behaviors emerge. At 300 kPa, the specimen exhibits strain-softening, reaching a peak deviatoric stress of 1340.3 kPa at a failure strain of 9.4%. Subsequently, the deviatoric stress rapidly decreases with increased axial strain, eventually stabilizing at a residual strength of approximately 962.5 kPa, which is about 72% of the peak value. At a confining pressure of 600 kPa, however, the specimen shows strain-hardening behavior, with deviatoric stress reaching 2359.0 kPa at 15% axial strain. Additionally, Figure 4 presents fitted curves for deviatoric stress at each confining pressure, demonstrating a linear relationship between deviatoric stress amplitude and corresponding strain (thick solid line in Figure 4). The correlation coefficients for these linear fits exceed 0.95, indicating a strong relationship between peak deviatoric strength and internal friction. Comparing Figure 4b,c, it is notable that at the same loading rate, the deviatoric stress and volumetric strain rates for Gradation 2 specimens become relatively stable post-peak, unlike the rapid decrease observed in Gradation 1 specimens.

Figure 4d illustrates that, at a confining pressure of 200 kPa, the relationship between deviatoric stress and axial strain exhibits strain softening for samples of different densities. The peak deviatoric stress increases significantly as density increases. This is attributed to the closer particle contacts in denser samples, which result in higher friction and interlocking forces between the particles. As a result, greater stress is required to induce shear failure. Once the peak stress is reached, the deviatoric stress decreases with increasing axial strain and eventually stabilizes at a plateau. The residual strength at this point is primarily supported by the friction and interlocking forces between particles after shear band failure [34]. Since the frictional resistance within the shear band is primarily influenced by the confining pressure, the residual strength of all samples under the same confining pressure is similar.

3.2. Volume Strain–Axial Strain Characteristics

In this paper, the volume strain (ε_v) is defined as positive for volume shrinkage and negative for volume dilatancy [35]. Figure 5 presents the volumetric strain versus axial strain curves under varying confining pressures. The trends observed in Figure 5 align closely with the results reported by Zhang et al. [36]. The volume strain behavior can be divided into three distinct stages under different confining pressures. Initially, the volume strain increases with the increase in axial strain, indicating specimen volume shrinkage, which corresponds to the volume shrinkage stage. As the volume decreases to a certain extent, volume expansion begins to occur with further increase in axial strain. Finally, when the volume reaches a certain threshold, the volume strain no longer increases with increasing axial strain, signaling the transition to the volume stabilization stage.

To further investigate the failure process of calcareous sand, we consider the calcareous sand sample under a 300 kPa confining pressure, as shown in Figure 4a and Figure 5a. Initially, the volume strain exhibits volume shrinkage as the axial deviatoric stress increases. This behavior can be attributed to the fact that, at this stage, the particles have not yet broken under the confining pressure and relatively low deviatoric stress. The rearrangement of particles fills part of the voids, leading to a reduction in the specimen volume. As the axial strain reaches 5.5%, the volume strain reaches 2.2%, and the sand sample volume decreases to its minimum value. Subsequently, as the axial deviatoric stress continues to increase, volume dilatancy occurs. Due to the low strength of the calcareous sand particles, they begin to break under the increasing shear stress, resulting in the formation of larger pores and an increase in volume. This behavior corresponds to the volume dilatancy stage. After the axial deviatoric stress reaches the peak value of 1340.3 kPa, the rate of volume dilatancy gradually decreases. When the axial deviatoric strain approaches the residual stress value of 962.5 kPa, the volume stabilizes. At this point, the residual strength is primarily supported by the friction and interlocking forces between the fractured particles [37].

As shown in Figure 5c, under low confining pressure, the volumetric strain curves of both gradations remain nearly constant, and the abrupt post-peak decrease observed in Gradation 1 is absent in Gradation 2. This indicates that the Gradation 2 specimen exhibits superior strength and deformation stability compared to the Gradation 1 specimen. Figure 5d illustrates that, under a 200 kPa confining pressure, samples with three different levels of compactness predominantly experience continuous volume shrinkage during the initial stages of triaxial compression, with the volume shrinkage being smaller for specimens with higher compactness. Specifically, for compactness levels of 90%, 92%, and 95%, the volume shrinkage is 3.34%, 2.65%, and 0.83%, respectively. The tighter particle contacts and lower porosity in high-compactness specimens contribute to reduced volume shrinkage. During the volume dilatancy stage, specimens with higher compactness exhibit more significant volume expansion. The volume dilatancy increases by 1.27%, 1.58%, and 4.07% for the specimens with compactness values of 90%, 92%, and 95%, respectively. Ultimately, the volume changes of specimens stabilize as the compactness increases. For specimens with lower compactness, the particle rearrangement and particle breakage processes within the shear band fill the initial pores, making the volume dilatancy less pronounced. In contrast, for high-compactness specimens, due to the lower porosity, the particle rearrangement and breakage only partially fill the initial pores, resulting in a more significant volume dilatancy process.

3.3. Effects of Shear Rate on Strength and Deformation

To evaluate the effects of shear rate on the strength of calcareous sand, further analyses were conducted on specimens with 90% compactness under confining pressures of 50 kPa, 100 kPa, 200 kPa, 300 kPa, 400 kPa, and 600 kPa, and shear rates of 0.01 mm/min and 0.1 mm/min. In this study, for strain-softening behavior, the failure strength and failure strain correspond to the peak strength of the deviatoric stress and the strain at peak strength. For strain-hardening behavior, the failure strain is defined as 15%, and the failure strength corresponds to the strength value at this failure strain.

Figure 6 presents the relationship between confining pressure and the failure strength of deviatoric stress at different shear rates. It can be observed that the fitted linear equation at a shear rate of 0.01 mm/min is y = 4.63x + 149.47, with a correlation coefficient of 0.99. The fitted equation at a shear rate of 0.1 mm/min is y = 4.85x + 86.01, with a correlation coefficient of 0.99. The failure strengths calculated from the fitted linear equations for both shear rates at a confining pressure of 0 kPa are 149.47 kPa and 148.85 kPa, respectively, indicating that the strengths are nearly identical. However, as the confining pressure increases, the failure strength at a shear rate of 0.1 mm/min increases significantly compared to that at 0.01 mm/min. This phenomenon can be attributed to the superficial effects at higher shear rates. At higher loading rates, the moisture in the sand sample cannot be efficiently expelled, making it more difficult to compress. Consequently, the strength increase is more pronounced at faster loading rates. In this study, compared to the shear rate of 0.01 mm/min, the failure strengths at 50 kPa, 100 kPa, 200 kPa, 300 kPa, and 400 kPa confining pressures at a shear rate of 0.1 mm/min increased by 13.56%, 5.93%, 1.00%, 21.0%, and 10.85%, respectively. It is evident that a tenfold increase in shear rate leads to an increase in failure strength of less than 20%. Additionally, minor scattering in the data reflects inevitable variations in specimen preparation and loading.

As shown in Figure 7, the fitted linear equation at a shear rate of 0.1 mm/min is y = 4.85x + 86.01, with a correlation coefficient of 0.99. The fitted linear equation at a shear rate of 0.01 mm/min is y = 0.015x + 4.33, with a correlation coefficient of 0.95. As the confining pressure increases, the specimen at a shear rate of 0.1 mm/min exhibits a slightly faster increase in failure strain; however, the failure strain remains consistently smaller than that of the specimen tested at 0.01 mm/min. This behavior can be attributed to a relative delay in strain development due to the difficulty in expelling moisture from the sand sample during the rapid loading process.

In the traditional method, the Mohr–Coulomb theory is commonly used to determine the cohesive force and internal friction angle. However, artificial drawing of the common tangent has a certain subjectivity, so when dealing with the triaxial consolidation shear drainage test data in this paper, the p-q method proposed by Chen [38] was adopted. That is, we drew the test results on the p-q axis, where p = (σ1 + σ3)/2, q = (σ1 − σ3)/2; then, the test data were fitted in a straight line and a p-q relation curve was obtained, as shown in Figure 8. The intercept and slope of the line are, respectively, k and b; then, cohesive force c and internal friction angle φ can be solved by Formulas (2) and (3):

$$\varnothing ={\mathrm{S}\mathrm{i}\mathrm{n}}^{-1}\left(k\right)$$

(2)

$$c=b/\mathrm{C}\mathrm{o}\mathrm{s}\varnothing$$

(3)

For sand, from the M-C theory, the angle θ between the direction of the shear belt and the direction of the minor principal stress is shown in Formula (4):

$$\theta =\pi /4+\varnothing /2$$

(4)

The shear strength indexes of the specimen at different shear rates can be calculated by Formulas (2) and (3). When the shear rate is 0.1 mm/min, the friction angle in the specimen is 1.59° larger than that at a shear rate of 0.01 mm/min, while when the shear rate is 0.1 mm/min, the cohesive force of the specimen is 9.24 kPa, which is smaller than that at a shear rate of 0.01 mm/min. It can be seen that the loading rate has a small effect on the internal friction angle. The larger the loading rate is, the smaller the cohesion is. This effect is attributed to the fact that, under fully saturated, consolidated, and drained conditions, rapid shearing generates transient positive pore pressure Δu^m within the micro-pores; the local capillary network and micro-voids cannot dissipate this excess water quickly enough, thereby causing a temporary reduction in contact effective stress. The extended Mohr–Coulomb model accounts for this pore pressure generation rate, as expressed in Equation (5) [39].

$$c={\mathrm{c}}^{\prime }-∆u_{m}tan\varnothing$$

(5)

where c is the true cohesion. Koji et al. [40] reported a similar rate-dependent softening phenomenon in fully saturated siliceous sand.

The material strength and failure parameters such as cohesive force c, internal friction angle φ and the intersection angle θ between shear belt direction and minor principal stress direction are shown in

Table 2. Failure parameters such as cohesive force c, internal friction angle φ and intersection angle θ between shear belt direction and minor principal stress direction.

Failure Parameters	Group 1	Group 2	Group 3
θ/(°)	66.42	67.21	64.54
ϕ (°)	42.84	44.43	39.07
c (kPa)	92.57	83.33	83.67
Measured shear angle (θ) of shear failure (°)

.

3.4. Effects of Compactness

In this test, a confining pressure of 200 kPa, compactness levels of 90%, 92%, and 95%, and a loading rate of 0.01 mm/min were adopted for the triaxial saturation consolidation drainage test to analyze the strength characteristics of coral sand at different densities. From Figure 9 and Figure 10, it is evident that both peak strength and volume strain increase linearly with increasing compactness, while failure strain decreases linearly as compactness increases. This can be attributed to the stronger interlocking forces between sand particles in denser sand. The interlocking and frictional forces must be overcome first when relative shear sliding occurs [41]. As axial displacement increases, some particles experience shear failure due to the low strength of the calcareous sand particles. At this stage, the specimen exhibits shear dilatancy and enters the strain-softening phase after the deviatoric stress–strain curve reaches its peak stress. With further increases in stress and strain, the number of particles breaking and sliding within the shear band gradually increases. Consequently, it can be concluded that, after reaching the limit strength, the residual strength is primarily provided by the interlocking and frictional forces between particles in the shear band as it forms and develops. When particles within the shear band can no longer be broken, the strength of the specimen is supported by the friction between the broken particles and the internal friction within the material. Under different confining pressure conditions, the residual strength increases with confining pressure, and thus, the residual stress shows a linear dependence on confining pressure.

3.5. Effects of Particle Gradation

Figure 11 illustrates the relationship between confining pressure and the deviatoric stress failure strength for sand samples of different gradations. As shown in the figure, for Sand Sample 1, the fitted linear equation is y = 4.63x + 149.47, with a correlation coefficient of 0.99, while for Sand Sample 2, the fitted linear equation is y = 3.44x + 294.21, with a correlation coefficient of 0.98. It is evident that the strength of Gradation 1 is lower than that of Gradation 2 at confining pressures of 50 kPa and 100 kPa. However, when the confining pressure exceeds 100 kPa, the strength of Gradation 1 surpasses that of Gradation 2. Figure 12 shows that the failure strains of both specimens increase with the increasing confining pressure, and the volume strain of the Gradation 1 specimen is lower than that of the Gradation 2 specimen. It is also observed that, for specimens with the same gradation, strength increases and deformation decreases as compactness increases. These observations are consistent with the results reported by Wang et al. [41]. However, for specimens with different particle gradations, the material strength does not necessarily follow this trend. The effect of gradation on material strength will be further investigated in subsequent research.

To determine the p-q relationship, the p-q scatter data at different confining pressures were fitted using a straight line, as shown in Figure 13. The shear strength parameters for the specimens of the two gradations were calculated using Formulas (1) and (2). The results indicate that the internal friction angle of the Gradation 1 specimen is 5.3° larger than that of the Gradation 2 specimen, although both specimens have nearly identical cohesive forces of 83.0 kPa. The material strength and failure parameters, including cohesive force, internal friction angle, and the intersection angle of the shear band direction with the minor principal stress direction, are summarized in Table 2.

3.6. Failure Mode

Table 2, which details failure parameters such as cohesive force c, internal friction angle φ, and the intersection angle θ between shear belt direction and minor principal stress direction, shows the results of the consolidation drainage shear test on saturated calcareous sand. Post-failure photographs show that shear-band width depends on confining pressure: the band is relatively narrow at high confinement but becomes markedly wider under low confinement, indicating a larger zone of shearing. This broader shear band under low confining pressure promotes extensive particle rearrangement and is the primary cause of the pronounced volumetric expansion observed after failure.

When comparing the cohesive force, internal friction angle, and shear angle obtained from the three sets of consolidation drainage shear tests, it is observed that the loading rate has a more significant effect on the cohesive force and a smaller impact on the internal friction angle. The cohesive force in the first group is 92.57 kPa, which is notably higher than that of the second and third groups. The particle gradation within the specimens has a clear influence on the internal friction angle of calcareous sand. The internal friction angles in groups 1 and 2 are 42.84° and 44.43°, respectively, both of which are greater than the internal friction angle in group 3, which is 39.07°. As shown in the shear failure images, under varying confining pressures and loading rates, all triaxial compression test failures exhibit typical shear failure. The intersection angle between the minor principal stress direction of the failed specimen and the shear band lies between 65° and 69°, which is consistent with the intersection angle θ predicted by the M-C theory for the shear band direction and the minor principal stress direction.

4. Conclusions

In this paper, saturated triaxial consolidation drainage shear tests were conducted on calcareous sand under various operating conditions. A series of experiments were performed to investigate the strength characteristics, deformation behavior, and failure properties of calcareous sand, considering factors such as shear rate, particle gradation, and compactness. The following conclusions can be drawn:

(1)

Calcareous sand exhibits strain-softening behavior at low confining pressures and strain-hardening behavior at relatively high confining pressures. For specimens with the same particle gradation, the confining pressure is linearly correlated with both the peak deviatoric stress and the failure strain. During triaxial compression, the specimen’s volume strain undergoes three distinct stages: volume shrinkage, volume dilatancy, and volume stabilization. At high confining pressures, the shearing process primarily involves volume shrinkage, with very little volume dilatancy. Conversely, at low confining pressures, volume dilatancy is dominant, with small volume shrinkage occurring.

(2)

Under a constant confining pressure, the peak strength of the specimen increases linearly with compactness, while the failure strain decreases linearly as compactness increases. During the volume shrinkage stage, the specimen’s volume shrinkage decreases as compactness increases. In the volume dilatancy stage, however, volume dilatancy increases with compactness. After shear failure, the residual strength of the specimen is mainly provided by particle friction in the shear zone. This friction is primarily influenced by the confining pressure, which results in similar residual stress values for materials with different compactness under the same confining pressure.

(3)

The results of the triaxial shear tests conducted at various confining pressures were analyzed using the p-q method proposed by Chen [42]. The analysis revealed that as the loading rate increases from 0.01 mm/min to 0.1 mm/min, the friction angle increases slightly, while the cohesive force remains nearly constant. Additionally, the intersection angle of the minor principal stress, as measured from the failure specimen and the shear band, closely matched the calculated value.

(4)

Particle gradation significantly affects the shear strength of calcareous sand. For specimens with the same gradation, the shear strength increases with compactness. The effects of particle gradation on the shear strength of calcareous sand will be further investigated in future studies.

This study focuses on the individual influence of single variables on the shear behavior of calcareous sand; future research should explore the combined effects of multiple interacting factors. Moreover, no microscopic observations were conducted to correlate the macroscopic mechanical behavior with the underlying microstructural changes.