To distinguish the stress and strain obtained from the triaxial shear test and triaxial creep test, the stress (strain) obtained from the triaxial shear test and triaxial creep test is called the instantaneous stress (instantaneous strain) and time-dependent stress (time-dependent strain), respectively, in this paper. Therefore, this paper analyzes the instantaneous and time-dependent mechanical properties of undisturbed loess under different moisture contents according to the test results.
3.1 Instantaneous stress-strain relationship of loess
To investigate the effect of moisture content on the instantaneous deformation characteristics of loess, the results of the consolidated undrained triaxial shear tests under a confining pressure of 200 kPa are considered. The instantaneous stress and strain curves of undisturbed loess under moisture contents of 5%, 10%, 17%, and 22% are shown in Fig. 2.
As shown in Fig. 2, the instantaneous deformation characteristics of undisturbed loess with different moisture contents are different during the shear process. Under a low moisture content, the instantaneous stress increases rapidly to the peak point at a relatively small strain (approximately 2%) and thereafter gradually decreases, i.e., showing strain softening behavior. With increasing moisture content (from 5–10%, 17% and 22%), the instantaneous stress increases rapidly with strain, and then the instantaneous stress remains stable or slowly increases with instantaneous strain. Thus, the stress-strain curve properties change from strain softening to strain hardening. Additionally, the higher the moisture content is, the later the inflection point on the stress and strain curve and the lower the degree of strain hardening. Although the instantaneous shear deformation characteristics of loess specimens with different moisture contents are different, the instantaneous stress-strain curves can be divided into two stages: (1) when the instantaneous strain is small, the instantaneous stress of loess specimens has a linear relationship with the instantaneous strain (corresponding to the elastic deformation stage); (2) when the peak point/inflection point of instantaneous stress is reached, the range of increase in the instantaneous stress decreases considerably with increasing strain (at this point, the loess specimens enter the stage of elastoplastic deformation).
The failure modes of undisturbed loess with different moisture contents are different. Under a low moisture content (hard plastic soils with a strong structure), although the specimen does not bulge significantly in the radial direction, a continuous shear band that is clearly visible on the side of the specimen forms, and its direction is oblique to the direction of major principal stress, i.e., shear failure (Fig. 2a and b). With increasing moisture content, the soil structure decreases, and the failure mode of the specimens changes from shear failure to homogeneous failure, which is characterized by uniform compaction of the whole specimen without obvious bulging deformation or shear fracturing (Fig. 2c and d).
3.2 Time-dependent strain characteristics of loess
Based on the triaxial creep test, when the confining pressure is 200 kPa, the correlations between the total time-dependent strain and time of undisturbed loess with different moisture contents at long-term static load are shown in Fig. 3. To more accurately study the time-dependent strain characteristics of loess, the Chen method (Tan and Kang, 1991) is adopted to obtain the time-dependent strain and time curves of loess specimens under different moisture contents and different static load levels, as shown in Fig. 4.
The total strain of loess specimen mainly includes the instantaneous strain during the static loading stage and the time-dependent strain during the static load stabilizing stage (Вялов 1987). As shown in the Fig. 3, with increasing static load, both the instantaneous deformation and the creep deformation of the loess specimens increase. Under certain conditions, the deformation generated by large loads is far greater than that generated by the accumulation of multiple small loads. Test results under a moisture content of 5% and different static loads are selected as examples. The total deformation under the action of the first five levels of load is 5.67 mm, and the deformation under the action of the sixth level of load is 12.8 mm, which indicates the destruction of the soil specimen.
Figure 4 shows that the time-dependent strain of the undisturbed loess has nonlinear characteristics. The curve of the change in time-dependent strain with time under long-term static loading can be divided into three typical deformation stages, namely, the decelerated deformation stage, the steady-state deformation stage and the accelerated deformation stage (Вялов 1987). According to Fig. 4, under the first five levels of static loading, the specimens experience the decelerated deformation stage only. As the static load continues to increase to level six, a specimen might continue to experience the deceleration stage (e.g., the moisture contents of the specimens in Fig. 4b and Fig. 4d are 10% and 22%, respectively), the acceleration stage and be destroyed immediately (e.g., the moisture content of the specimen in Fig. 4a is 5%), or the acceleration stage and finally break down after a short period of viscous flow (e.g., the moisture content of the specimen in Fig. 4c is 17%). Therefore, whether a specimen will undergo all three stages is related to the selection of the long-term static load.
Figure 5 shows the different loading stages strain curves in the three-dimensional space of moisture (ω) – long-term static load (σL) – strain(εt). The deformation characteristics of soil are different with increasing moisture content, which is mainly reflected in the following aspects: (1) The critical load value of specimens decreases with the increase of moisture content. (2)The instantaneous deformation and time-dependent deformation increases with moisture content. (3) With the increase of long-term static load, the instantaneous deformation and time-dependent deformation increase, and the lower the moisture content, the greater the degree of their change. In addition, with moisture content increase, it takes longer for specimens to undergo the stable stage under long-term static loading (Fig. 4), and the failure mode of undisturbed loess changes from shear failure (Fig. 3a) to homogeneous failure (Fig. 3b and c and d)
3.3 Time-dependent strain rate characteristics of loess
The strain rate can clearly and accurately reflect the variation in soil deformation per unit time. To better examine the effect of various factors (the moisture content, time and long-term static load) on loess deformation, based on the data shown in Fig. 4, the relationship between the time-dependent strain rate of the undisturbed loess with different moisture contents and time is shown in Fig. 6.
The influence of time on the strain rate of loess can be explained by Fig. 6: the strain rate of loess specimens decreases with time under a low long-term static load. In the initial stage of load stabilization, the strain rate decreases rapidly with time; as time increases, it remains almost constant and then decreases to zero. However, when the long-term static load is high, the strain rate increases with time in the initial stage, and as the strain rate increases to the peak point, it enters the decay stage, which is roughly the same as the attenuation trend under the condition of a low long-term static load. The phenomenon of the increase in strain rate can be interpreted as the fact that the internal resistance of the loess specimens cannot resist the applied force in a short time under a high static load, so the strain rate increases, and then the internal structure of the soil is adjusted to a stable state to make it resistant to external forces, causing the strain rate of the soil to decrease.
Figure 6 also clearly shows that the moisture content has a significant effect on the strain rate and the degree of variation under long-term static loading. The higher the moisture content is, the slower the soil strain rate decay, the smaller the peak strain rate, and the longer the time to reach the stable stage. In addition, the higher the moisture content is, the earlier the increase in the strain rate, and the longer the time to reach the peak point of the strain rate.
The abovementioned findings suggest that the peak point of the strain rate is the critical point at which the soil has the ability to resist external forces. According to the data in Fig. 6, the correlation between the peak strain rate and long-term static load at different moisture contents is shown in Fig. 7.
Figure 7 shows that the peak strain rate does not always increase with the long-term static load. To more accurately study the variation in peak rate, different moisture contents are comprehensively analyzed. According to the comprehensive analysis, there may be three inflection points of the peak strain rate of loess specimens with different long-term static loads, which can be regarded as the critical points of the transformation of the soil deformation state ((Вялов 1987) distinguished three critical stress levels, namely, the elastic limit stress, flow limit stress and complete failure stress according to the deformation state characteristics of soil).
The quartic polynomial is used to fit the experimental data in Fig. 7, as shown in Fig. 7, and their relationships are shown in Eq. (1):
![](https://myfiles.space/user_files/83064_0857a92044b57365/83064_custom_files/img1631186884.png)
(1)
Clearly, the fitting data of the peak strain rate and long-term static load show good agreement with the experimental data. Therefore, we obtain the critical stress of undisturbed loess with different moisture contents from the data in Fig. 7, and the specific values are shown in Table 3.
Table 3
Long-term strength of undisturbed with different moisture content
Critical stress (kPa)
|
Moisture content (%)
|
5
|
10
|
17
|
22
|
Elastic limit stress
|
133.11
|
72.87
|
39.63
|
47.43
|
Flow limit stress
|
248.61
|
224.93
|
182.45
|
139.1
|
Complete failure stress
|
515.54
|
325.15
|
246.55
|
180.79
|
The state of stress, strain and energy have been considered to judge the failure and yielding of soil (Sun, 1999). In this paper, we study the variation in the strain rate of loess specimens with time, which is used as a parameter to judge the deformation state of loess. The critical point from the flow limit stress to the complete failure stress is defined as the long-term strength.
3.4 Time-dependent strength characteristics of loess
To explore the strength characteristics of loess under the time-dependent strain state, the correlation between stress and strain at different moisture contents and different times is shown in Fig. 7. Additionally, the time points of 0 h, 0.3 h, 0.6 h, 1 h, 2 h, 4 h, 8 h, 12 h, 18 h, and 24 h were chosen for analysis.
Figure 8 shows that the stress-strain curves at different times and different moisture contents have nonlinear characteristics. When the static load is small, the stress of the loess specimens is proportional to the strain. With increasing static load, the stress-strain curves gradually change from linear to nonlinear and then show distinct inflection points. The inflection point can be explained by the structural characteristics of the undisturbed loess. This finding is in agreement with a previous study conducted by (Yang 2011), who concluded that the structure of soil is the main cause of the inflection point and that the stress at the inflection point can be considered the structural yield strength of the soil. Moreover, the structure of the soil decreases with increasing moisture content, which explains why the inflection points of the curves of the loess specimens with high moisture contents remain almost unchanged.
The strain-stress curves of loess specimens at different times and different moisture contents have basically the same variation trend. The main phenomena are as follows: first, the strain of the loess specimens increases with stress, and then the stress-strain curves bend in the horizontal direction (strain axis). Furthermore, the stress-strain curves at different times exhibit obvious discrete phenomena, but their degrees of discreteness are different. This paper takes the stress-strain curves of loess specimens with a moisture content of 22% at different times as an example. There is an obvious discrete phenomenon between the curves from t = 0 h to at t = 4 h, but the degree of discreteness gradually decreases. This can be explained as the time-dependent strain of soil gradually transforming from the decelerated stage to the steady-state stage. Under a long-term static load, the curve differences from t = 4 h to t = 24 h were minor. This is interpreted to be due to the strain of soil entering the steady-state stage and the small influence of the time effect on soil deformation.
The moisture content has a significant effect on the degree of dispersion of the time-dependent stress-strain curves at different times. The higher the moisture content is, the greater the degree of curve bending to the transverse axis (strain axis), the smaller the discreteness in the decelerated stage, and the longer the time required to enter the steady-state stage. For example, for the loess specimens with a moisture content of 10%, the specimen deformation enters the steady-state stage when the long-term load is loaded for 8 h; however, the specimen with a moisture content of 22% does not enter the steady-state stage when the long-term static load is loaded for 12 h.