In the cold regions of China, coarse-grained materials are frequently encountered or used as backfilling materials in infrastructure construction, such as dams, highways, railways, and mineral engineering structures. Effects of confining pressure (0.2, 0.5, and 1 MPa) and frozen temperature (−2, −5, −10, and −15°C) on the stress-strain response and elastic modulus were investigated using triaxial compression tests. Moreover, the microscale structures of a coarse-grained material were obtained by X-ray computed tomography. The coarse-grained material specimens exhibited strain-softening and significant dilatancy behaviors during shearing. A modified model considering microstructures of the material was proposed to describe these phenomena. The predicted values coincided well with the experimental results obtained in this study and other literatures. The sensitivity analysis of parameters indicated that the model can simulate the initial hardening and post-peak strain-softening behavior of soils. And the transition of volume strain from contraction to dilatancy can also be described using this model. The results obtained in this study can provide a helpful reference for the analysis of frozen coarse-grained materials in geotechnical engineering.
Civil infrastructures in cold regions, such as dams, highways, railways [
Frozen soil is a special kind of geotechnical material, which is composed of ice inclusions, mineral particles, gaseous inclusions, and liquid water [
Many constitutive models (e.g., hyperelastic model, nonlinear elastic model, and viscoelastic-plastic model) have been established to describe the mechanical features of frozen soils [
The purpose of this paper is to propose a model that can describe the mechanical behavior of frozen coarse-grained material. The effects of confining pressure and temperature on the frozen coarse-grained materials were studied with triaxial tests and X-ray computed tomography (CT). Then, an empirical formula that reflects the relationship between microstructural change and residual strength is proposed. Furthermore, the stress-strain response of frozen coarse-grained material considering microstructures was predicted. At last, the parameter sensitivity of the statistical damage model was discussed.
The typical grain size distribution of the tested coarse-grained material is shown in Figure
Grain size distribution of the coarse-grained material.
Basic physical characteristics of the frozen coarse-grained material.
Parameters | Values |
---|---|
Maximum diameter, | 10 |
Diameter at 10% finer, | 0.508 |
Diameter at 30% finer, | 4.8 |
Diameter at 60% finer, | 7 |
Uniformity coefficient, | 13.78 |
Curvature coefficient, | 6.48 |
Maximum dry density, | 2.02 |
Optimum moisture content, | 4.5 |
An appropriate amount of distilled water was mixed fully with the dried coarse-grained material to obtain the optimum moisture content (Table
The picture of the specimen machine.
The cryogenic triaxial compression tests were performed on a material test system (MTS-810) exhibited in Figure
Triaxial equipment and tested samples: (a) the triaxial test device; (b) the CT scanner; (c) the specimen before and after testing.
Experimental schemes of the triaxial tests.
Samples | CT scanning | ||||
---|---|---|---|---|---|
S1 | 4.5 | 2.02 | −2 | 0.2 | — |
S2 | 0.5 | Sections I–V | |||
S3 | 1 | — | |||
S4 | −5 | 0.2 | Sections I–V | ||
S5 | 0.5 | Sections I–V | |||
S6 | 1 | Sections I–V | |||
S7 | −10 | 0.2 | — | ||
S8 | 0.5 | Sections I–V | |||
S9 | 1 | — | |||
S10 | −15 | 0.2 | — | ||
S11 | 0.5 | Sections I–V | |||
S12 | 1 | — |
The undrained static triaxial test was conducted according to the following procedures: (1) the target temperature was kept for 10 h to ensure the uniform temperature distribution in the pressure chamber; (2) the frozen specimen was transferred from the refrigerator to the triaxial pressure chamber; (3) the confining pressure (
In the past few years, CT has been widely applied in geotechnical studies as a tool of describing the microstructure due to the advantage of being nondestructive [
The typical relationships under different confining pressures and temperatures between deviator stress (
Stress-strain behaviors under different testing temperatures and confining pressures: (a)
It can be seen from Figure
The key to determine the volumetric strain of the specimen is to determine its volume change, which is difficult to measure because there is no seepage for the frozen coarse-grained material. In this study, the volume changes of specimens were measured by the volume change caused by the leakage of hydraulic oil in the pressure chamber. The minus sign indicates an increase in volume. With the increase of the axial strain, the volumes of specimens reduce from a starting state to a phase transition state and then expand gradually into a residual state. As observed in Figure
The characteristics of the soil could be reflected by two important parameters: elastic modulus and strength properties. The stress-strain curve slope in the elastic deformation stage can be defined as the elastic modulus, according to a previous report [
Variation in elastic modulus versus frozen temperature and confining pressure.
The variations of peak strength (
Variation in (a) peak strength and (b) residual strength versus frozen temperature and confining pressure.
The strength of the frozen coarse-grained material enhances as the confining pressure increases, which can be interpreted as the following two aspects. Firstly, the rising confining pressure makes the ice particles and soil particles closer, forming a stronger interlocking friction between these particles. Secondly, the rising confining pressure increases the normal pressure on the shear plane, increasing the resistance of sliding friction.
The angle of the internal friction (
Variation of (a) cohesion and (b) internal friction angle versus frozen temperature.
The variations of internal friction angle with different frozen temperatures are presented in Figure
In order to describe the microstructure changes of a specimen before and after the triaxial test, the typical CT images of the specimen under 0.5 MPa and −2°C are presented in Figure
Typical CT images of the frozen coarse-grained specimen of case S2 before and after testing.
Apart from soil particles, the unfrozen water and internal ice are related to the fabric of frozen soil. The distribution of unfrozen water, internal ice, and soil particles on the cross section of the specimen can be characterized by the average density, which is defined by the CT value (AV) [
The relationships between CT values and section positions are shown in Figure
Relationship between CT value and normalized height
CT value under (a) different frozen temperatures and (b) confining pressures.
As reported in a previous study, the gradual failure of cemented structure and interlocking structure gradually reduces the mechanical resistance, resulting in post-peak softening response. The residual strength is closely related to the structure of the shear specimen [
Figure
Relationship between residual strength and the average change ratio of CT value.
Based on the above analysis, it is speculated that the residual strength of frozen coarse-grained material is linear with
The relationship between parameter
Relationship between parameter
Thereafter, a simple empirical formula is proposed by substituting equation (
It is assumed that the frozen coarse-grained material consists of microunits. And the material strength of microunits differs. By incorporating the statistical strength theory and the continuous damage theory, the damage variable is described as follows:
When the Weibull distribution is assumed to be the density function of microdamage, the probability density distribution function
The strength criterion [
The damage variable based on the Weibull distribution is obtained by substituting equation (
Then, the stress-strain relationship is described as follows:
As shown in equation (
The prediction model of the stress-strain behavior of the frozen coarse-grained material is obtained by combining equation (
All of the parameters are related to the mechanical properties of frozen coarse-grained material. The residual strength
As observed in Figure
Relationship between
After combining equations (
In the binary-medium constitutive model [
After substituting equations (
Figure
Predicted and experimental deviatoric stress-strain results of frozen coarse-grained materials: (a)
Model parameters of the frozen coarse-grained material in this study.
Samples | Stress-axial strain parameters | Volumetric strain-axial strain parameters | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
T (°C) | ||||||||||||
S1 | −2 | 0.2 | 1.193 | 76.164 | 0.019 | 0.981 | 0.991 | 76.667 | −0.263 | 0.693 | 0.013 | 0.999 |
S2 | −2 | 0.5 | 2.130 | 96.130 | 0.025 | 1.089 | 0.989 | 95.833 | −0.281 | 1.059 | 0.006 | 0.998 |
S3 | −2 | 1 | 3.428 | 138.049 | 0.018 | 1.114 | 0.988 | 136.625 | −0.408 | 1.888 | 0.004 | 0.943 |
S4 | −5 | 0.2 | 1.346 | 165.000 | 0.022 | 0.991 | 0.944 | 161.650 | −0.518 | 0.861 | 0.017 | 0.999 |
S5 | −5 | 0.5 | 2.889 | 179.791 | 0.021 | 0.945 | 0.994 | 184.967 | −0.419 | 1.060 | 0.012 | 0.997 |
S6 | −5 | 1 | 3.969 | 200.780 | 0.020 | 1.126 | 0.956 | 209.275 | −0.426 | 1.582 | 0.009 | 0.987 |
S7 | −10 | 0.2 | 1.440 | 217.218 | 0.027 | 1.135 | 0.972 | 192.542 | −0.842 | 1.044 | 0.016 | 0.999 |
S8 | −10 | 0.5 | 3.219 | 227.500 | 0.024 | 0.981 | 0.997 | 226.225 | −0.744 | 1.300 | 0.013 | 0.997 |
S9 | −10 | 1 | 5.000 | 251.082 | 0.022 | 1.077 | 0.948 | 261.542 | −0.487 | 1.388 | 0.011 | 0.993 |
S10 | −15 | 0.2 | 1.866 | 255.460 | 0.031 | 1.221 | 0.899 | 256.208 | −0.931 | 1.055 | 0.020 | 0.999 |
S11 | −15 | 0.5 | 3.801 | 273.700 | 0.020 | 0.879 | 0.996 | 285.308 | −0.955 | 1.399 | 0.012 | 0.997 |
S12 | −15 | 1 | 5.313 | 279.103 | 0.022 | 0.996 | 0.983 | 309.358 | −0.858 | 1.656 | 0.010 | 0.991 |
Two kinds of frozen soils in previous studies [
Predicted and experimental results of frozen soils in previous studies: (a) frozen saline sandy soil [
Model parameters of frozen saline sandy soil and frozen standard sand.
Soil types | Stress-axial strain parameters | Volumetric strain-axial strain parameters | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
T (°C) | ||||||||||||
Frozen saline sandy soil [ | −6 | 2 | 10.92 | 274.1 | 0.056 | 1.09 | 0.984 | 370.839 | −1.017 | 2.05 | 0.013 | 0.982 |
Frozen standard sand [ | −15 | 1 | 4.304 | 352.3 | 0.019 | 0.895 | 0.987 | 489.167 | −0.914 | 1.193 | 0.012 | 0.985 |
The parametric investigation results of the prediction model are analyzed in this section. Figures
Deviatoric stress-strain curves for different values of parameters (a)
Volumetric strain curves for different values of parameters (a)
In terms of the stress-strain responses, the behavior of specimens transform from strain hardening to strain softening with the increase of
The effects of confining pressure and temperature on the mechanical property of frozen coarse-grained material were investigated using the triaxial compression test and X-ray CT analysis. Based on the statistical damage theory, a modified model considering the microscale structure was developed. This model is able to describe the strain-softening and dilatancy behaviors of frozen coarse-grained materials. The following conclusions can be drawn: Temperature and confining pressure have significant influence on the mechanical properties of frozen coarse-grained materials. The specimens exhibit strain-softening and dilatancy behaviors during shearing. With the increase of the confining pressure and temperature, the stress-strain relationship transfers from strain softening to strain hardening. CT values of the tested material specimens decrease gradually with the decrease of the temperature. The increase of the confining pressure leads to the increase of CT values, which is consistent with the dilatancy phenomenon. Moreover, an empirical formula that reflects the relationship between microstructural and residual strength is proposed. A model based on statistical damage theory was proposed to predict the stress-strain response and volume change of frozen coarse-grained material. It was verified with the experimental results obtained by this study and other previous studies. The sensitivity analysis of the model parameters indicated that the model can predict the transition from initial hardening to strain softening. Moreover, the dilation response of volume strain can also be described.
The data used to support the findings of this study are included within the article.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This study was supported by the National Key Research and Development Project of China (grant nos. 2018YFC1505305 and 2018YFE0207100), the National Major Scientific Instruments Development Project of China (grant no. 41627801), the State Key Program of National Natural Science Foundation of China (grant no. 41731288), and the Technology Research and Development Plan Program of Heilongjiang Province (grant no. GA19A501).