Stress relaxation of warm frozen soil under drained or undrained conditions

SongHe Wang, JiLin Qi

State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China

Stress relaxation of warm frozen soil under drained or undrained conditions

SongHe Wang, JiLin Qi*

State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China

To investigate the influence of drainage conditions on stress relaxation characteristics of warm frozen soil, a series of laboratory tests were carried out under drained and undrained conditions. The results indicate that confining pressure obviously influences the relaxation process of warm frozen soil. Under undrained condition, with increase in confining pressure, the critical relaxation duration tends to grow as well as instantaneous relaxation. But the relaxation rate is sensitive to confining pressure in the initial stage,and with further development, the effect tends to diminish. Under drained condition, the relaxation rate is greater than that under undrained condition in the initial stage but with the development of relaxation, the difference decreases. The volumetric deformation of warm frozen clay under drained condition is much larger than that under undrained condition.

warm frozen soil; stress relaxation; confining pressure; drained and undrained conditions; volumetric change

1. Introduction

Stress relaxation demonstrates the internal stress reduction under constant deformation. As a frequently encountered mechanical process,e.g., instability of sliding zones,unloading process of surrounding rock in excavation of underground caverns, it is of great significance for the long-term stability of geotechnical engineering (Liu, 1994).

To grasp the specific effect of stress relaxation on engineering practices, a series of uniaxial and triaxial relaxation tests in the laboratory and in situ borehole relaxation were carried out to analyze the relaxation properties of geomaterials (Ladanyi and Johnston, 1978; Ladanyi, 1979). The development of stress relaxation consists of two aspects: stage characteristics and stress variation. The first aspect is the preliminary cognition of stress relaxation and is empirically divided into certain stages,e.g., decelerated relaxation and slow relaxation for sliding soils (Wanget al., 2008), intense relaxation and slow relaxation for frozen Lanzhou loess (Wu and Ma, 1994). Moreover, the deviatoric stress is generally considered to change linearly with logarithm of time and the slope and intercept depend on the initial test conditions;meanwhile, the pore pressure shows little variation during relaxation process (Lacerda and Houston, 1973). Afterwards,the relevance between the aforementioned characteristic parameters and initial test conditions were further discussed(Akaiet al., 1975; Arai, 1985; Oda and Mitachi, 1988). The confining pressure exhibits little influence on the stress relaxation of clay (Murayama and Shibata, 1956) and frozen Ottawa sand (Ladanyi and Benyamina, 1995). Goldstein(1959) discussed the difference in stress relaxation between stiff and soft clay. Liuet al. (2007) found that the dynamic relaxation of compacted loess is related to moisture content,vibration frequency, initial strain and test duration. Wu and Ma (1994) observed obvious deceleration in the relaxation process with decrease in soil temperature (from -2 °C to-10 °C).

The aforementioned test results provide a basis for estimation of intrinsic relationship between stress-strain and time. Adachi and Okano (1974) proposed a general model for the description of creep and stress relaxation. Akaiet al.(1975) deduced the equivalence of mechanical behaviors,i.e., constant strain rate loading, stress relaxation and creep,and emphasized the uniqueness of stress-strain-time relationship. However, Christensen (1982) analyzed the specific mathematical relationship between relaxation modulus and creep compliance (Jα=Gα-1), and found an incompatibility while extending the theory into viscoelasticity mechanics.Besides, the creep models primarily place an emphasis on the incremental loading conditions, which may not reasonably describe the stress-strain-time relationship under unloading stress path. The empirical relationship is the primary theoretical support for previous rheological research, which well reflect the rheological process and the parameters can be simply obtained from in situ and laboratory tests (Wu and Ma, 1994).

However, previous studies have primary focused on the relaxation of conventional and frozen soils under low temperature. For warm frozen soil, it is rarely seen in the literature so far. Considering the actual state in situ, the relaxation of warm frozen soil under drained and undrained conditions needs to be studied.

In this paper, the frequently encountered silty clay is taken as the research object and the effect of confining pressure on the relaxation of warm frozen soil samples under drained and undrained conditions is discussed in the following sections.

2. Testing program

Silty clay for the relaxation tests is frequently encountered along the Qinghai-Tibet Highway. Soil samples were reconstituted in a steel tube, with dry unit density of 17.0 kN/m3. The samples, with a diameter of 61.8 mm and height of 125.0 mm, were fixed into the copper mold and saturated in a vacuum and then frozen unidirectional for 48 hrs. Physical properties of the soil samples are listed in Table 1.

The relaxation tests were carried out in the TAW-100 multifunctional environmental tester (Figure 1). It consists of an axial and lateral loading system, air-conditioning and main control systems. Controlled temperatures range from-40 °C to 30 °C, with accuracy of ±0.1 °C.

Table 1 Physical properties of soil samples

Figure 1 Multifunctional environmental tester

The threshold for warm frozen soil was suggested to be-1.0 °C according to characteristic mechanical properties(Qi and Zhang, 2008). Thus, during the relaxation tests, ambient temperature was controlled at -1.0 °C. After the confining pressure was maintained to be stable, the pre-strain process was initiated with a strain rate of 0.01%. Stress relaxation occurred simultaneously until the target magnitude of pre-strain was reached.

To analyze the effect of confining pressure and drainage condition on the relaxation characteristics of warm frozen soil, the specific test arrangements were listed in Tables 2 and 3.

Table 2 Test conditions under different confining pressure

Table 3 Test conditions under different pre-strain

3. Testing results and discussions

Figure 2 presents the typical relaxation process of warm frozen soil under certain temperatures and confining pressure (ε=12.0%). An obvious instantaneous relaxation stage can be observed during the test, which manifests the transient release of strain energy. With increase in time, relaxation rate tends to decrease and a critical point (0.01 MPa/h) defines the threshold from intense relaxation to slow relaxation while the relaxation duration can be considered to be the critical relaxation duration.

Previous test results proved that mechanical properties of soil under high and low confining pressure show great differences (Fish, 1991; Wu and Ma, 1994), manifested in nonlinearity of strength envelope, volumetric changes and the disappearance of softening tendency. However, for frozen soil, pressure melting of pore ice can also be observed under high confining pressure (Jones and Parameswaran, 1983;Maet al., 1999).

The relaxation curves of warm frozen soil under drained and undrained conditions can be seen in Figure 3. With increase in confining pressure, the critical relaxation duration(tstab) tends to prolong, which demonstrates that under high confining pressure, clay particle breakage and weakening effect between particles and pore ice may intensify the instability of frozen soil structure. The redistribution of internal stress in a frozen soil sample could compensate for the structural damage while pressure melting disturbs the ice-water balance and postpones the internal stress transition, ultimately leading to longer critical relaxation duration. Moreover, the instantaneous relaxed stress (σins) tends to increase with confining pressure. This reveals that with higher confinement,more strain energy stored during pre-strain process results in bigger instantaneous relaxation. However, a slight decrease in instantaneous relaxed stress and critical relaxation duration can be observed under drained condition.

Figure 2 Typical relaxation process (Wang and Qi, 2011)

Figure 3 Influence of confining pressure on the instantaneous relaxed stress σins and critical relaxation duration tstab

Figure 4 shows the isochronous curves of relaxation rate versus confining pressure. Within certain relaxation duration,the relaxation rate tends to increase; with further development, the effect of confining pressure on relaxation rate gradually declines. It proves that confining pressure significantly affects the early relaxation process while little influence after critical relaxation duration, which is inconsistent with the behavior for frozen sand under lower confinement(Ladanyi and Benyamina, 1995). Relaxation rate reflects the activity of internal stress reduction and transition, and higher confining pressure obviously constrains micro movement of soil particles and ice-water bonding. The mechanism above dominates the early period of stress relaxation. However,after critical relaxation duration, structural adjustment and stress transition tend to be stable.

Figure 4 Isochronous curves of relaxation rate and confining pressure

The relaxation rate versus time relationship for frozen soil under drained and undrained conditions is presented in Figure 5. The general characteristics of relaxation process for warm frozen soil under different initial conditions have similar tendencies. Under undrained condition, the relaxation rate in initial period is slightly bigger than that under drained condition. This is closely related to drainage of pore water due to pressure melting under confining pressure. In the initial stage, micro structural adjustment may be more active and pressure melting promotes the drainage of pore water, which plays a significant role in stress transition and accelerates relaxation development. Thus, it can be reasonably deduced that for ice-rich frozen soil, the relaxation rate may be more sensitive to the drainage condition.

The volumetric changes of warm frozen soil under drained and undrained conditions are shown in Figure 6.Under undrained condition, the soil sample exhibits a slight initial contraction, followed by obvious expansion while under drained condition, the contraction dominates the process and tends to be stable with further relaxation process.Besides, the volumetric deformation under drained condition is greater than that under undrained condition, especially under higher confining pressure. This is primarily related to the drainage of pore water in a soil sample due to pressure melting. This is consistent with the variation of liquid level in a drain-pipe during relaxation process.

Figure 5 Relaxation rate versus time relationship under drained and undrained conditions

Figure 6 Volumetric changes during relaxation under drained and undrained conditions

4. Conclusions

A series of stress relaxation tests under drained and undrained conditions were carried out on the silty clay obtained along the Qinghai-Tibet Highway. The relaxation behaviors of warm frozen soil were analyzed. The following conclusions can be drawn:

(1) Confining pressure obviously affect the relaxation process of warm frozen soil. Under undrained condition, the critical relaxation duration prolongs with confining pressure and the instantaneously relaxed stress increases while a slight decrease can be observed under drained condition.

(2) Within a certain relaxation duration, the relaxation rate tends to increase; with further development, the effect of confining pressure on relaxation rate gradually declines under undrained condition. However, the relaxation rate in the initial stage is greater than that under undrained condition.

(3) With an increase in the magnitude of pre-strain, the soil sample exhibits a slight initial contraction, followed by obvious expansion while under drained condition; the con-traction dominates the process and tends to be stable with further relaxation process. The volumetric deformation under drained condition is greater than that under undrained condition, especially under higher confining pressure.

This work was supported in part by the National Natural Science Foundation of China (No. 40871039) and the 100 Young Talents Project granted to Dr. JiLin Qi.

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10.3724/SP.J.1226.2011.00468

*Correspondence to: Dr. JiLin Qi, Professor of Cold and Arid Regions Environmental and Engineering Research Institute,Chinese Academy of Sciences. No. 320, West Donggang Road, Lanzhou, Gansu 730000, China. Tel: +86-931-4967261;Email: qijilin@lzb.ac.cn

19 June 2011 Accepted: 5 September 2011