Study on the Strength and Deformation Characteristics of Coarse-Grained Soil under End-Restraint and End-Free (Microfriction) Conditions

Featured Application

The study of the end constraint effect is very useful for improving the precision of triaxial tests.

Abstract

In this study, for triaxial compression testing in geotechnical engineering, large-scale triaxial shear tests of coarse-grained soil were performed under end-restraint and end-free (microfriction) conditions utilizing a large-scale triaxial shear apparatus and a self-developed microfriction load-transfer plate. Under end-restraint and end-free (microfriction) circumstances, the strength and deformation characteristics of the coarse-grained soil were investigated. Further, the effect of the end restraint on the stress–strain characteristics of the coarse-grained soil was analyzed. The findings showed that the coarse-grained soil’s stress–strain curves under the end-restraint and end-free (microfriction) conditions displayed both softening under low confining pressures and hardening under high confining pressures. However, the stress–strain curves’ tendency to soften under low confining pressures was more pronounced under the end-free (microfriction) condition. Due to the influence of the end constraint, the peak strength of the coarse-grained soil increased under the same confining pressure, although the increase was less than 10% when the specimen had the typical height-to-diameter ratio of 2 in the drained triaxial test. Meanwhile, the coarse-grained soil first displayed volumetric contraction under the low confining pressures, followed by volumetric dilation, and it displayed volumetric dilation under the high confining pressures. The volumetric contraction tendency of the coarse-grained soil was more pronounced in the first stages of shearing when the low confining pressures were present. As the shear increased, it became more obvious that the coarse-grained soil had a tendency to dilate under the end-free (microfriction) conditions. Throughout the shearing operation, the coarse-grained soil exhibited a high propensity toward shear contraction. The coarse-grained soil’s strength values were not greatly impacted by the end limitation, but the deformation parameters were. Under the end-restraint conditions, the deformation parameter increased significantly, while the strength parameter only changed slightly.

1. Introduction

As coarse-grained soil is the main filling material in earth–rockfill dams, the accuracy of its strength and deformation characteristics is important for the safety stability analysis of dams. At present, laboratory triaxial tests are often used to study the strength and deformation characteristics of coarse-grained soil due to their simple operation, and even they have realized relatively complex stress paths [1,2] (Omar et al., 2015; Wei et al., 2009). However, the end of a triaxial sample is restrained by a rigid sample cap (base) during stress-induced deformation. The frictional shear stress between the cap (base) and the sample limits the radial deformation at the end of a specimen. When the specimen is close to failure, it is either pressed into a “drum shape” or squeezed into a “neck shape”. This phenomenon is called the end-restraint problem in triaxial testing [3] (Li, 2007). The end restraint causes strain and stress inhomogeneity within a triaxial sample, which affects the stress–strain characteristics, pore water pressure or volume change, shear band distribution, and strength characteristics of the specimen [4] (Duncan et al., 1968). The end-restraint effect prevents the triaxial test results from reflecting the true mechanical properties of coarse-grained soil.

Therefore, reasonably analyzing the mechanical properties of soil under the influence of end restraints has become a popular research topic. Since the beginning of the 20th century, scholars around the world have conducted thorough and systematic studies on the effect of the end restraints of soils, obtaining abundant research results in laboratory tests and numerical simulations. Numerous experimental studies have investigated the effect of end restraints on stress–strain behavior during the triaxial testing of soils. Timoshenko (1983) [5] reported that as early as 1900, Foppal coated a solid sample end with paraffin in a compression test to reduce the influence of the end effect. The failure mode and stress distribution pattern were obtained for specimens with different height-to-diameter ratios. Taylor (1941) [6] used specimens with a larger height-to-diameter ratio to study the effect of end restraints. Results have shown that when the height-to-diameter ratio is greater than or equal to 2, the effect of end restraints on the strength can be ignored. In 1964, Rowe et al. [7] used an unrestrained sample cap (base) in triaxial tests for the first time along with a pressure plate, lubricant, and rubber film, which was called a lubricated sample cap. Blight (1965) [8] used a soil block as a transitional pad. The pad surface was soaked in a layer of latex rubber to eliminate the influence of the volume change or pore water pressure of the pad. Subsequently, Bishop and Green (1965) [9] performed a series of triaxial tests on cohesionless soil to examine the influence of the boundary restraint on the observed strength and on the relationships among the stress, strain, and volume change. The results indicated that for the material tested, the effect of the end restraint increased the apparent strength of a specimen, but this decreased with an increase in the height-to-diameter ratio and became of little significance when the usual ratio was approximately 2.

Lee (1978) [10] performed triaxial tests using specimens with regular and frictionless ends. The results showed that for medium-density sand, there was a significant (up to 20%) increase in the static undrained strength of the specimens with frictionless ends compared to that of the specimens with regular ends. The effect was significantly greater than that observed in drained tests on sand and undrained tests on clay. Ueng et al. (1988) [11] studied the distribution of the internal volume change and particle failure of uniform sand in drained triaxial tests with and without end lubrication. Zhang et al. (2002) [12] found that radial strain with end lubrication was more than twice as large as that without end lubrication, but it was still much smaller than radial strain without boundary constraints due to the end-restraint effect test of the sand. Lu et al. (2010) [13] carried out end-friction-reduced triaxial tests by using the lubricated sample cap method and studied the influence of the end restraint on the deformation and strength characteristics of coarse-grained soil. At present, in triaxial tests, the method of lubricating the sample cap is mainly used to reduce the effect of the end restraint. Although a lubricated sample cap can effectively reduce the end effect, it also has some negative effects, such as sample side slip and large pore ratio errors (Garga et al., 1997) [14].

In recent years, with the development of computer applications, digital image measurement technology has become an effective method to study the nonuniform deformation of specimens [15,16,17] (Rechenmacher, 2006; Han et al., 2006; Jacquot et al., 1999). Shao et al. (1999; 2006) [18,19], Wang et al. (2003) [20], and Dong et al. (2010) [21] used digital image measurement technology to directly test the axial and radial deformation of soil samples in triaxial tests and to quantitatively analyze the end-restraint effect. The digital image measurement method avoids the influence of the end effect by measuring the middle one-third of the specimen, but it cannot effectively eliminate the effect of the end restraint.

Several numerical studies have been carried out to study the effect of the end restraint on soil behavior in triaxial tests. Airey (1991) [22] studied the effects of different end and drainage conditions in triaxial tests by finite element simulations using the Modified Cam Clay model and concluded that significant inhomogeneities may have occurred during isotropic consolidation, but that the effect on the undrained stress–strain response was small. Schanz and Gussman (1994) [23] indicated that the shear strength of an idealized linearly elastic–perfectly plastic triaxial specimen increased as the end restraint increased and was not significantly influenced by the specimen geometry. Sheng et al. (1997) [24] carried out numerical analyses of nonuniformities in a triaxial specimen caused by the end restraint and insufficient drainage. The results showed that the end restraint in both drained and undrained tests and the insufficient drainage in the drained tests may have caused the nonuniform barrel-shaped deformation of the specimen at large strains. Jeremic et al. (2004) [25] used numerical methods to simulate and calculate the constitutive behavior of specimens under different end conditions and compared the differences in detail to obtain the true elastoplastic constitutive relationship of the specimens. Liyanapathirana et al. (2005) [26] studied the effect of the end restraint on the nonhomogeneous behavior of structured soils in triaxial tests using a finite element model based on the Structured Cam Clay model with Biot consolidation. The destruction phase of the structured soil was not significantly influenced by the end restraint, but after destruction, during hardening, the stress–strain behavior of the soil was significantly influenced by the end restraint. Hashish et al. (2009) [27] proposed a self-learning simulation analysis framework to discuss sand drainage behavior in a triaxial compression test under a fully frictional platen, and it was found that the entire specimen exhibited rotation of the principal stress, variation in the intermediate principal stress, and uneven volume changes.

Many experimental and numerical studies on the end-restraint effect in triaxial tests have been performed in the literature. Neither the lubricated sample cap method nor the digital image measurement method can effectively eliminate the end-restraint effect. Previous investigations of the end-restraint effect in triaxial tests have mainly focused on small-scale triaxial tests of sand and clay, but few have focused on large-scale triaxial tests of coarse-grained soil. In this study, large-scale triaxial shear tests of coarse-grained soil with end-restraint and end-free (microfriction) conditions were carried out using a large-scale high-pressure triaxial shear apparatus and a self-developed microfriction load-transfer plate for large triaxial tests (Cheng et al., 2014) [28].

In conclusion, using data from traditional triaxial tests to estimate the stress and deformation of high earth–rockfill dams may cause significant mistakes. In order to successfully address the end restraint problem of triaxial tests and precisely determine soil mechanical characteristics, geotechnical microfriction triaxial test technology must be adopted. In this study, the strength and deformation characteristics of coarse-grained soil under normal end-restraint and end-free (microfriction) conditions were studied. The influence of the end restraint on the stress–strain characteristics of the coarse-grained soil was analyzed. The results provide a theoretical foundation and scientific basis for the safety and stability analysis of high earth–rockfill dams.

2. Large-Scale Triaxial Test with Different End Restraint Conditions

2.1. Test Equipment

The test equipment was the YLSZ30-3 high-pressure large-scale triaxial shear apparatus and a microfriction load-transfer plate developed by the Yangtze River Scientific Research Institute for triaxial tests. Figure 1 shows the YLSZ30-3 high-pressure triaxial shear apparatus. It is a stress and strain control triaxial apparatus composed of a vertical pressure loading and control system, a confining pressure loading and control system, a triaxial pressure chamber, a loading frame, a high-voltage accumulator, a displacement and volume change measurement system, load sensors, and a data acquisition system. Its maximum confining pressure is 6 MPa. Its maximum vertical load is 2500 kN. Its maximum vertical stroke is 300 mm. Its shear speed can be adjusted in the range of 0.2–2 mm/min, and its vertical load voltage stabilization error is not more than 1%.

To solve the end-restraint problem in triaxial tests of coarse-grained soil, a load-transfer plate with a microfriction load for triaxial compression testing in geotechnical engineering was developed by the Yangtze River Scientific Research Institute. Using this, the contact between the soil and loading plate is varied from the whole contact to the distributed contact and from the sliding friction to the rolling friction.

A schematic of the plate structure is shown in Figure 2a, and a photograph of the physical product is shown in Figure 2b. The load-transfer plate is a 300-mm-diameter, 60-mm-thick disc that consists of a circular load-bearing plate, a sliding block stop bar, guide rails, steel balls, and sliding blocks. The sliding block stop bar is placed in the middle of the circular load-bearing plate. The plate has 24 rectangular grooves that are radially and evenly distributed in the circumferential direction. A guide rail with an arc-shaped groove is embedded in each rectangular groove. Steel balls are arranged in arc-shaped grooves, and multiple turns of sliding blocks are arranged on the guide rail in the radial direction of the circular load-bearing plate. The sliding blocks can slide freely on the guide rail in the radial direction through contact between the steel balls and the guide rail. In this mechanical structure, multiple turns of automatic sliding blocks are used to apply an axial load to a specimen. The steel balls that connect the sliding block and the circular load-bearing plate convert the sliding friction to rolling friction. As a result, there is no or minimal friction (microfriction) in the tangential direction of the contact interface between the specimen and the load-transfer plates. Thus, the specimen can freely deform in the tangential direction of the contact surface, effectively solving the end-restraint problem. Therefore, triaxial shear tests of coarse-grained soil with end-restraint and end-free (microfriction) conditions can be carried out with this device and the YLSZ30-3 high-pressure triaxial shear apparatus.

2.2. Test Materials

The coarse-grained soil used in the tests was collected from the main rockfill of a dam in Sichuan Province, China. The mother rock of the coarse-grained soil was black slate. The maximum particle size of the coarse-grained soil was 600 mm, which exceeded the maximum controlled particle size of the laboratory test. The combination method was adopted to reduce the particle scale following the Test Regulations for Coarse-Grained Soils of Hydropower Engineering (DL/T5356-2006) of China. First, a similar gradation method was used to reduce the scale, using the scale multiple of gradation 4, and then an equivalent replacement method was used to scale down the supersized particles (>60 mm) to 5–60 mm as required. The curves of the original gradation and test gradation are shown in Figure 3.

The maximum and minimum dry densities were measured by the surface vibration method and the fixed volume method, respectively, and the result was shown in

Table 1. Density test results.

Minimum Dry Density, ρdmin (g/cm3)	Maximum Dry Density, ρdmax (g/cm3)	Specific Gravity Gs	Test Dry Density, ρd (g/cm3)	Porosity N (%)	Relative Density Dr
1.629	2.178	2.72	2.11	22.4	0.90

. The measured maximum and minimum dry densities of the samples were 2.178 and 1.629 g/cm³, respectively. The specific gravity of the coarse-grained soil particles (G_S) was 2.72. The relative density of the coarse-grained soil in the test was controlled to 0.90, and the corresponding dry density was 2.10 g/cm³.

2.3. Triaxial Testing Procedure

Large-scale triaxial shear tests under both end-restraint and end-free (microfriction) conditions were performed on the coarse-grained soil. First, according to the determined relative density and test grading, remolded soil specimens were prepared by a multilayer wet stamping method involving dimensions of 300 mm (diameter) × 600 mm (height). For the end-restraint test, the test procedure was consistent with the conventional triaxial test. The remolded samples were composed of four layers; each layer had the same weight and was compacted to a thickness of 120 mm. In order to guarantee close contact between the layers, the interface was compressed. After the last layer of the specimen had been prepared, the surface was flattened, and the upper portion was covered with filter paper and a sample cap. After vacuuming the forming cylinder and tightening the rubber membrane up and down, a pressure chamber was added. After the preparation of the final layer of the specimen was finished, a cap-shaped rubber cap was initially placed on the top of the specimen and fastened with the rubber film in order to carry out the end-free (microfriction) test. The lateral top half of the test instrument had an exhaust hole that was connected to the drainage hole at the bottom to provide drainage. As shown in Figure 4, after vacuuming, the forming cylinder was removed, the specimen was lifted, the microfriction load-transmitting plate was positioned on the specimen’s bottom, the microfriction load-transmitting plate and loading plate were positioned on the specimen’s upper portion, and finally, the pressure chamber was installed.

3. Test Results and Discussion

3.1. Stress–Strain Relationship

Figure 5 shows the deviator stress–strain curves of the coarse-grained soil under the end-restraint (ER) and end-free (EF) conditions. These curves showed similar characteristics under both conditions. Under both conditions, the deviator stress increased as the axial strain increased. The larger the effective confining pressure was, the steeper the deviator stress–strain curve was; that is, the larger the tangential elastic modulus was, the more evident the curve hardening characteristics and the greater the peak strength were. The deviator stress–strain behavior in the triaxial tests was greatly affected by the end restraint during isotropic compression as well as during the drained shear process; this was mainly seen in the following two aspects: (1) For the dense coarse-grained soil, when the confining pressure was small (0.2 MPa), the deviator stress–strain curves of the specimen with the end restraint exhibited strain-softening behavior, while the deviator stress–strain curves of the specimen under the larger confining pressures (0.4, 0.6, or 0.8 MPa) exhibited strain-hardening behaviors. The deviator stress–strain curve of the end-free specimen under the low confining pressure had more evident softening tendencies. (2) The deviator stress of the specimen with the end restraint was greater than that of the end-free specimen under the same axial strain. The main reason for this was that in the conventional triaxial consolidation drained shear test, the end-restraint force at the end of the specimen performed in order to work on the specimen and improve its bearing capacity.

3.2. Strength Characteristics

To analyze the effect of the end restraint on the strength of the coarse-grained soil, the peak strength values of the coarse-grained soil in the triaxial tests with end-restraint and end-free (microfriction) conditions under different confining pressures were obtained, as shown in

Table 2. Peak strength values of coarse-grained soil under different confining pressures.

Confining Pressure (MPa)	Peak Strength (MPa)			Error
	End Restraint	End Free (Microfriction)	Peak Strength Increasing Ratio (%)
0.2	0.981	0.907	7.5	-
0.4	1.789	1.703	4.8	-
0.6	2.447	2.382	2.7	-
0.8	3.045	2.910	4.4	-

. The end restraint slightly increased the peak strength under the same confining pressure, but when the specimen had the usual height-to-diameter ratio of 2 and was under the drained conditions, the influence of the end restraint on the peak strength of the coarse-grained soil was smaller, not exceeding 10%, a finding which is the same as the conclusion reached by Lee et al. (1978) [10].

Soil strength is divided into the categories of linear strength and nonlinear strength. There is a linear relationship between the shear strength and normal stress in the linear strength region of soil. The shear strength can be calculated using the strength index cohesion c and internal friction angle $\phi$. There is a nonlinear relationship between the shear strength and the normal stress in the nonlinear strength region of soil. For noncohesive soil, there is no cohesion. The internal friction angle is related to the normal stress. It is expressed by the following equation (Duncan and Chang, 1970) [29]:

$$\phi ={\phi }_0-\Delta \phi \lg \left({\sigma }_3/p_a\right)$$

(1)

where ${\sigma }_3$ is the small principal stresses, $p_a$ is the atmospheric pressure, ${\phi }_0$ is the value of $\phi$ when ${\sigma }_3/p_a$ equals 1 (°), and $\Delta \phi$ is the reduction value of $\phi$ when ${\sigma }_3$ is increased 10 times (°).

Figure 6 shows the Mohr stress circles and linear strength envelopes of the coarse-grained soil. Figure 7 shows the Mohr stress circles and nonlinear strength envelopes of the coarse-grained soil. The results were sorted according to the linear and nonlinear strength values. It can be seen that the end restraint slightly increased the linear strength index cohesion $c$, internal friction angle $\phi$, nonlinear strength index ${\phi }_0$, and $\Delta \phi$ of the coarse-grained soil.

3.3. Volumetric Strain Characteristics

To investigate the influence of the end restraint on the volumetric strain behavior of the specimens during the drained shear tests, the volumetric strain (${\epsilon }_v$) versus axial strain (${\epsilon }_a$) curves obtained from the specimens under the end-restraint and end-free (microfriction) conditions were compared, as shown in Figure 8. Under different end-restraint conditions, the coarse-grained soil exhibited volumetric dilation at low confining pressures and volumetric contraction at high confining pressures. The end restraint had a significant influence on the volumetric strain characteristics of the coarse-grained soil. At a low confining pressure (0.2 MPa), the end deformation of the end-restraint specimen was smaller, and the swelling in the middle of the end-restraint sample was not significant compared with that of the end-free (microfriction) specimen. The overall volume of the specimen was reduced, and the tendency for the volumetric contraction of the end-restraint sample was more evident in the initial stage of shearing. With shearing, the bulging in the middle of the specimen further intensified, and the specimen as a whole showed volumetric dilation. At this time, the dilatation tendency of the end-free specimen (microfriction) was more evident. At high confining pressures (0.4, 0.6, and 0.8 MPa), the volumetric strain of the specimen with the end restraint was always greater than that of the end-free specimen, which showed a strong volumetric contraction tendency during the whole shearing process.

3.4. Modulus Characteristics

Duncan’s hyperbolic model [30] is a nonlinear elastic model based on the incremental generalized Hug’s law. It is well known in geotechnical engineering and is widely used in numerical calculations. Using the E-B model as an example, the tangent deformation modulus $E_{ti}$ under a certain stress and the tangent volume modulus $B_{ti}$ under a certain stress can be expressed by the following formulas:

$$E_{ti}=\frac{d({\sigma }_1-{\sigma }_3)}{d{\epsilon }_1},$$

(2)

$$B_{ti}=\frac{d({\sigma }_1-{\sigma }_3)}{3d{\epsilon }_{\mathrm{v}}},$$

(3)

where ${\sigma }_1$ is the large principal stresses, ${\epsilon }_1$ is the axial strain, and ${\epsilon }_v$ is the volume strain.

The tangent deformation modulus, tangent volume modulus, and axial strain curves for given confining pressures are shown in Figure 9 and Figure 10. With an increase in axial strain at the beginning of shear, the tangent deformation modulus and tangent volume modulus of the rockfill materials declined. The end constraint simultaneously reduced the tangent volume modulus and increased the tangent deformation modulus, while its impact waned as the strain and confining pressure increased.

3.5. Duncan–Chang Model Parameters

In 1970, Duncan and Chang proposed the E-μ model based on the assumption of the Konder stress–strain hyperbola, and then Duncan et al. (1980) proposed a modified Duncan–Chang E-B model. The two models better reflect the nonlinear behavior of soil with a clear concept. They are widely used in the deformation and stability analysis of earth–rockfill dams.

In the Duncan–Chang E-μ model, the tangential elastic modulus $E_t$ of soil and the tangent Poisson’s ratio ${\mu }_t$ can be calculated as follows:

$$E_t=K{p}_a{\left(\frac{{\sigma }_3}{p_a}\right)}^n{\left[1-\frac{R_f({\sigma }_1-{\sigma }_3)(1-\sin \phi )}{2c\cos \phi +2{\sigma }_3\sin \phi }\right]}^2,$$

(4)

$${\mu }_t=\frac{G-F\lg \left(\frac{{\sigma }_3}{p_a}\right)}{{\left(1-A\right)}^2},$$

(5)

$$A=\frac{D({\sigma }_1-{\sigma }_3)}{K{p}_a\left(\frac{{\sigma }_3}{p_a}\right)\left[1-\frac{R_f({\sigma }_1-{\sigma }_3)(1-\sin \phi )}{2c\cos \phi +2{\sigma }_3\sin \phi }\right]},$$

(6)

where $R_f$ is the failure ratio, $K$ and $n$ are the experimental constants of the tangential elastic modulus, and $G$, $F$, and $D$ are the experimental constants of the tangent Poisson’s ratio.

In the Duncan–Chang E-B model, the tangent elastic modulus $E_t$ is calculated in the same way as in the E-μ model. The tangent bulk modulus $B_t$ is calculated as follows:

$$B_t=K_b{p}_a\left(\frac{{\sigma }_3}{p_a}\right),$$

(7)

where $K_b$ and $m$ are the tangent bulk modulus test constants.

The 10 parameters of the Duncan–Chang E-B (E-μ) models are $c$, $\phi$ (${\phi }_0$, $\Delta \phi$), $R_f$, $K$, $n$, $K_b$, $m$, $G$, $F$, and $D$. The parameters of the E-B (E-μ) model and the shear strength index according to the test curve are shown in

Table 3. Duncan–Chang E~B(μ) model parameters of coarse-grained soil.

Test Program	Shear Strength Index				E~B(μ) Model Parameters
	$\mathit{c}$ (kPa)	$\mathit{\phi }$ (°)	${\mathit{\phi }}_0$ (°)	$\Delta \mathit{\phi }$ (°)	$\mathit{K}$	$\mathit{n}$	${\mathit{R}}_{\mathit{f}}$	${\mathit{K}}_{\mathit{b}}$	$\mathit{m}$	$\mathit{G}$	$\mathit{F}$	$\mathit{D}$
End restraint	82.5	39.2	47.6	7.1	614	0.23	0.83	279	0.12	0.379	0.337	5.50
End free (microfriction)	77.1	38.8	46.0	6.0	521	0.21	0.77	218	0.10	0.383	0.113	1.91

. According to Table 3, the strength index of the sample with the end restraint was slightly larger than that of the end-free sample, indicating that the end restraint had a limited effect on the strength of the coarse-grained soil. The $K$ and $K_b$ values of the sample with the end restraint were greater than those of the end-free sample, indicating that the end restraint had a significant influence on the deformation characteristics of the coarse-grained soil.

3.6. Sample Deformation

Figure 11 shows the deformation of the coarse-grained soil after the triaxial tests under different end-restraint conditions. The end restraint restricted the radial deformation of the ends of the specimens, and the radial deformation of the middle portion of the specimen with the end restraint was significantly larger than that of the end-free specimen (microfriction), showing bulging around mid-height. The end-free specimen (microfriction) was relatively uniformly deformed up and down.

4. Conclusions

In this study, using a large-scale high-pressure triaxial shear apparatus and a self-designed microfriction load-transfer plate for triaxial compression tests in geotechnical engineering, large-scale triaxial shear tests of coarse-grained soil samples with end-restraint and end-free (microfriction) characteristics were conducted. Under typical end-restraint and end-free (microfriction) conditions, the strength and deformation characteristics of the coarse-grained soil were investigated. The effect of the end restraint on the stress and strain properties of the coarse-grained soil was analyzed. The following conclusions can be drawn:

(1)

The stress–strain relationship curves of the coarse-grained soil had similar properties under the end-restraint and end-free (microfriction) conditions. With regards to the dense coarse-grained soil, the deviator stress–strain curve of the specimen with the end restraint showed strain-softening behavior under a smaller confining pressure but strain-hardening behavior under a larger confining pressure. When it was subjected to a modest confining pressure, the behavior of the end-free specimen showed a more pronounced propensity to soften than the specimen with the end restraint.

(2)

The volumetric strain behavior of the coarse-grained soil was consistent both under the end-restraint and end-free (microfriction) conditions. Under a low confining pressure, the coarse-grained soil first exhibited volumetric contraction, followed by volumetric dilation, and only exhibited volumetric contraction under a higher confining pressure. The tendency of the coarse-grained soil to show volumetric shrinkage under a low confining pressure was more pronounced in the initial stages of shearing. With the emergence of shearing, the volumetric dilation tendency of the coarse-grained soil under the end-free (microfriction) condition became more pronounced. When the confining pressure was higher, the volumetric strain of the specimen with the end restraint was consistently greater than the end-free specimen, which displayed a marked tendency for volumetric contraction throughout the whole shearing process.

(3)

The end restraint had little effect on the strength parameters of the coarse-grained soil, but it had a greater impact on its deformation parameters. When the Duncan–Chang E-B and E-μ models were used for fitting, compared with the end-free (microfriction) model, the linear strength indices $c$ and $\phi$ and the nonlinear strength indices ${\phi }_0$ and $\Delta \phi$ of the end-restraint model were slightly increased. Further, the deformation parameter indicators $K$ and $K_b$ increased significantly, indicating that the end restraint condition had a higher effect than the end-free condition on the deformation properties of the coarse-grained soil.

(4)

For the end-restraint specimen, it can be seen that the end-restraint restricted the radial deformation at the specimen’s end, but the radial deformation of the specimen’s middle portion was significantly larger than that of the end-free specimen, indicating bulging. The microfriction-affected specimens had a substantially more consistent deformation distribution.