### Appearance of samples

The calcareous sand was obviously different after the high-temperature treatment (Fig. 2), and its particles changed from translucent gray white crystals to pure white opaque crystals, indicating that the calcareous sand was completely converted from calcium carbonate to calcium oxide. The content of the remaining components was negligible.

### Effect of shear velocity on the shear strength, residual shear stress, and apparent viscosity

Under the same conditions, the mechanical behavior of the calcareous sand samples sheared at different shear velocities was different. Figure 3 shows the relationship between time and the shear stress for different shear velocities. In Fig. 3, the shear strength and the residual shear stress can be clearly observed. The average, maximum, and minimum residual shear stresses were obtained separately, as plotted in Fig. 4. With shear velocities of 3°/min, 36°/min, and 180°/min, the shear strengths of the calcareous sand samples were 108.3 kPa, 110.4 kPa, and 108.9 kPa, respectively; the average residual shear stresses were 101.8 kPa, 103.1 kPa, and 102.8 kPa, respectively; the maximum residual shear stresses were 108.8 kPa, 111.8 kPa, and 114.2 kPa, respectively; and the minimum residual shear stresses were 97.5 kPa, 93.5 kPa, and 92.6 kPa, respectively.

At lower shear velocity (3°/min), the initial peak shear strength of the sample appeared later compared with those of samples with higher shear velocities. The fluctuation amplitude of the residual shear stress was small and gentle. At higher shear velocities (36°/min and 180°/min), the initial peak shear strength of the samples appeared faster and the residual shear stress fluctuated significantly. In this unsteady state, the residual shear stress was greater than the shear strength. As the shear velocity increased, the residual shear stress fluctuation of the samples with a large displacement shear became more intense and even exceeded the shear strength. This is related to the shear breakage and rearrangement of the soil particles in the shear box. Therefore, the residual shear stress of calcareous sand may exceed the shear strength and increase with the shear velocity when the other experimental conditions remain the same. Moreover, the residual shear stress of the sample with a shear velocity of 180°/min kept increasing, which indicates that the residual shear stress of the sample increased with the particle breakage. To quantify the shear stress fluctuation, the standard deviation of the shear stress was used to measure the fluctuation amplitude of the shear stress, as shown in Fig. 5. The results indicate that a higher shear velocity led to an increase in the sample’s shear fluctuation amplitude. The shear behavior of the calcareous sand exhibited the phenomenon of shear stress fluctuation, which is related to the continuous formation and reconstruction of the force chain structure (Sun and Wang 2008). Existing studies on dense granular flow consider the shear stress to be independent of the shear rate; however, this conclusion was reached considering simple particles and clay particles with large moisture contents (Forterre 2008). The results obtained via the ring-shear test in this study differ from the theoretical results. Even though the shear flow in the ring-shear test belongs to the quasi-static flow regime, the shear stress and shear rate are not completely independent; this is strongly related to the unsteady state of the soil under large-displacement shear.

The shear rate can be calculated as follows:

$${\dot{\gamma }} = \frac{{vD_{m} }}{2h},$$

where *v* is the shear velocity [°/s]; \(D_{m}\) is the average diameter of the ring-shear sample [mm]; *h* is the thickness of the ring-shear sample [mm].

The apparent viscosity \({\upeta }\) can be expressed by the relationship between the shear stress and the shear rate:

$$\uptau = {\upeta \dot{\gamma }}.$$

Accordingly, the specific value of the apparent viscosity can be calculated.

Because the residual shear stress fluctuated continuously as the shearing progressed, the average, maximum, and minimum residual shear stresses were calculated as shown in Fig. 6. The approximate shear flow characteristics of the calcareous sand samples were obtained under a normal stress of 200 kPa. Here, the rheological curve does not pass through the origin point and is concave to the shear rate axis. The sample has both yield characteristics and pseudoplastic fluid characteristics and can therefore be thought of as a yield pseudoplastic fluid. In Fig. 7, the curve of the average value of the apparent viscosity is slightly different from the curve drawn according to the maximum and minimum values; however, the overall trends of the two are essentially identical. The apparent viscosity decreased as the shear rate increased; therefore, the viscosity of the calcareous sand decreased as the shear rate increased and the relationship between the shear stress and the shear rate is nonlinear, with a certain degree of shear dilution.

### Variation of the shear strength, residual shear stress, and friction coefficient caused by high temperature

The ring-shear tests on the calcareous sand samples before and after heat treatment were performed under the same normal stress and shear velocity conditions. The shear characteristics of the samples were obtained before and after the heat treatment, and the shear stress curves are shown in Fig. 8. The shear strengths of the samples before and after heat treatment were 110.4 kPa and 104.1 kPa, respectively. This indicates that the shear strength of the calcareous sand decreased after the calcareous sand was subjected to high temperature and that the calcareous sand became more prone to shear failure. The average residual shear stresses were 103.1 kPa and 110.2 kPa before and after heating, respectively. Hence, the residual shear strength of the sample increased after the high-temperature treatment. A comparison of the friction coefficient of the sample before and after heat treatment (Fig. 9) indicated that the average friction coefficient increased from 0.51 to 0.55. After the heat treatment at 800 °C, the friction coefficient of the sample was obviously higher compared with that prior to the heat treatment. Figure 10 shows the state of the calcareous sand sample particles after heat treatment at different temperatures. Considering Fig. 10 in conjunction with the sample images captured after the ring-shear tests (Fig. 9), it was determined that the variation behavior of the shear flow was primarily influenced by the change in the sand particles subjected to high temperature, after which the calcareous sand particles were smaller and more brittle and capable of being crushed with greater ease. After the heat treatment, the sand particles could more easily be destroyed and the sample became denser. This eventually led to an increase in the friction coefficient and the residual shear strength. The calcareous sand subjected to heat treatment had smaller particles, and its residual shear stress fluctuation amplitude was relatively reduced, which affects the stability of the soil to large-displacement flows. From the above discussion, it is understood that the amplitude of the shear stress fluctuation in the calcareous sand shear flow behavior is related to the particle size and the particle hardness. Hence, the increase in the residual shear stress and the decrease in the friction coefficient and residual shear stress fluctuation amplitude following the high-temperature treatment were caused by the decrease in the particle size.

### Effect of normal stress on the shear stress and friction coefficient of calcareous sand

The variation in the shear characteristics of the calcareous sand subjected to different normal stresses is similar to that obtained in other studies. The shear stresses of the calcareous sand samples under different normal stresses are shown in Fig. 11. The shear strengths of the calcareous sand samples under normal stresses of 200 kPa, 400 kPa, and 600 kPa were 110.4 kPa, 221.8 kPa, and 323.7 kPa, respectively, and the average residual shear stresses were 199.8 kPa, 215.2 kPa, and 334.4 kPa, respectively. The shear strength and residual shear stress increased with the normal stress. The fluctuation amplitude of the residual shear stress increased, particularly when the normal stress reached 600 kPa, and the fluctuation amplitude of the residual shear stress of the calcareous sand obviously increased. The average residual shear stress exceeded the shear strength and was similar to that of the calcareous sand sample at high shear velocity.

Figure 12 shows the variation in the friction coefficient of the calcareous sand samples under different normal stresses. The average friction coefficients of the samples under normal stresses of 200 kPa, 400 kPa, and 600 kPa were 0.51, 0.53, and 0.55, respectively. Therefore, the friction coefficient of the samples increased as the normal stress increased. This indicates that, as the normal stress increased, the friction coefficient increased and the fluctuation amplitude of the friction coefficient obviously decreased. The shear characteristics of the calcareous sand samples under different normal stresses are essentially the same as those of other sand types, such as quartz sand. Therefore, as the normal stress increased, the particle breakage and the residual shear stress increased.