# Unloading Creep Characteristics of Frozen Clay Subjected to Long-Term High-PressureK0 Consolidation before Freezing

Authors: Jinbo Jia; Yansen Wang; Yangguang Leng
Journal: Advances in Civil Engineering
 (2019)

---

## Abstract

Artificial ground freezing has been widely applied in the construction of vertical shafts in deep and thick alluvia. As an important factor, the in situ creep behavior of deep, frozen soil affects the mechanical properties of frozen walls and the safety and stability of shaft linings. Acquiring creep characteristics and deep soil parameters by methods that ignore the engineering and geological situations is currently inadvisable. A series of triaxial unloading tests were conducted with frozen clay subjected to long-term high-pressureK0 consolidation before freezing to research the unloading creep characteristics, creep strength, and other parameters of the clay, and the results indicated the following: (1) The creep behaviors of frozen clay are affected by the consolidation time and consolidation stress. Long-term high-pressure K0 consolidation reduces the creep strain and creep rate of frozen clay. (2) The decrease in the ice and the unfrozen water contents of frozen clay caused by the prolongation of consolidation time result in an increase in the long-term strength and instantaneous strength. Consolidation time has an obvious effect on long-term strength and weakens the creep property of frozen clay. Consolidation stress significantly affects the instantaneous strength. (3) The deformation resistance capability of frozen clay is enhanced by compaction; thus, E1, η1, and η2 increase with prolonged consolidation, and the nonlinearity of the accelerated creep increases.


---

## Body

## 1. Introduction

Artificial ground freezing is frequently prescribed for constructing vertical shafts in deep and thick alluvia. Evidence suggests that interactions between the frozen soil and shaft lining, which are subjected to the effect of creep, are among the important factors controlling stability. Therefore, it is essential for the stability of shaft construction to evaluate the creep properties of frozen, deep clay. In an investigation into deep clay, Cui [1] found that the creep properties of frozen, deep clay cannot be obtained accurately by traditional soil mechanics tests because the high density, low ice content, and special microstructure exhibited under long-term high K0 stress. This work is especially complex because creep properties are affected by sedimentary conditions and consolidation-freeze modes [2]; the acquired creep characteristics and parameters would be inaccurate if these factors were ignored.To date, a considerable number of studies have been published on the creep behavior characteristics of frozen soils. Ladanyi [3] and Takegawa et al. [4] studied the creep characteristics of frozen clay, and the results indicated that nonattenuated and attenuated creep occurred in frozen soil subjected to different stresses due to the strengthening and weakening effects caused by the damage and healing of the microstructure. Zhu and Carbee [5] performed creep testing, the results of which showed that nonattenuated creep occurred due to the predominance of structural strengthening in frozen soil when the stresses were less than the long-term strength; attenuated creep occurred owing to the prominence of the weakening effect under stresses greater than the long-term strength. Therefore, it is necessary to study the long-term strength in more detail. Yang et al. [6] proposed that the long-term strength first decreased and then increased with increasing ice content based on the results of uniaxial tests of frozen soil with ice contents of 40%–120%. Fish [7] established an equation that described the decrease in the long-term strength of frozen soil with creep time. Nadezhdin and Sorokin [8] investigated the strength characteristics of deep, frozen clay by the method of freezing before K0 consolidation, and the results revealed that preloading had different effects on the ultimate long-term strength and instantaneous strength: the ultimate long-term strength of soil increased but the instantaneous strength decreased. Roman and Krivov [9] conducted uniaxial compression and spherical plate indentation tests to determine the long-term strength of frozen soil, and a reasonable prediction equation was selected to describe the variation in the long-term strength. The initial moisture content, freezing temperature, and creep stress were regarded as influence factors in a number of investigations about the creep and strength properties of deep, frozen clay. Reconstituted frozen soils that underwent ephemeral consolidation under high pressure before freezing were mostly used in these tests. However, the initial consolidation state, engineering stress path, and test mode should be considered comprehensively in the study of deep, frozen clay. Otherwise, the applicability of test results will be limited. Hence, the influence of high-pressure K0 consolidation age should not be neglected.To define the creep mechanism of frozen soils, many scholars have made important contributions to the creep constitutive model of frozen soils. Component combination theory was frequently applied to studies on creep models of frozen soils, e.g., the Kelvin model, the Burgers model, and the Nishihara model [10]. Li et al. [11] proposed that the parabolic yield criterion was suitable for artificially frozen soil under high and complex stress and established a creep model based on viscoelastic-plastic damage theory [12]. Subsequently, numerical simulations and laboratory tests were conducted, and the results illustrated the applicability of the strength criterion and the rationality of this creep model [13, 14]. Li et al. [15] proposed an improved Nishihara model that considered the effects of hardening and weakening caused by temperature and external stress during creep, which could produce a reasonable prediction of three creep stages of frozen soil. Nevertheless, the effects of consolidation stress and consolidation age on creep modes and parameters have not been thoroughly considered.When studying the creep properties of deep artificially frozen clay, it is crucial to consider the characteristics of long-term high-pressure consolidation and then freezing. Thus, in this paper, the variation rules of the unloading creep characteristics and the long-term strength of deep, frozen clay are analyzed with consideration of the consolidation time and stress by the experimental mode of “long-termK0 consolidated-freezing-constant axial pressure and unloading confining pressure.” In addition, the improved Nishihara model is applied to reasonably describe the creep behavior, and the influences of the consolidation time on the creep parameters are analyzed. This study provides a basis for further revealing the creep mechanism of deep, artificially frozen clay.


## 2. Experimental Program

### 2.1. Materials and Experimental Apparatus

The clay investigated in the present study was derived from a mine shaft at a depth of approximately 520–550 m, and the physical parameters are listed in Table1. The reconstituted specimens were prepared as cylinders with diameters of 61.8 mm and heights of 125 mm. The initial water content and the dry density of the specimens tested were 27.8% and 1.49 g/cm3, respectively. These specimens were saturated with air-free water under vacuum for 24 hours to achieve a saturation of 0.98.Table 1
The basic physical properties of the clay specimens.
G
s
ρ
d (g·cm−3)
Composition of grains (%)
w
L (%)
w
p (%)
>0.25 mm
0.25∼0.1 mm
0∼0.075 mm
0∼0.045 mm
<0.045 mm
2.71
1.49
3
6.32
2.71
6.11
81.86
58.83
28.93Consolidation tests of reconstituted clay specimens were conducted on an SKA-1K0 consolidation instrument and a custom high-pressure lever-type loading system (0.05–60 kN), and the K0 values were monitored; a DL-4050 cryogenic cooling circulating pump (−40–0°C) was applied to freeze the specimens under constant axial load; in addition, constant axial pressure and unloading confining pressure creep tests of frozen clay specimens were conducted with the TATW-500 subzero dynamic and static high-pressure triaxial test system, whose confining and axial pressure can be controlled simultaneously to a maximum axial pressure and confining pressure of 500 kN and 20 MPa, respectively. The schematic diagrams of the test apparatus are shown in Figures 1 and 2.Figure 1
High-pressure consolidation and loading-freezing equipment. (a) SKA-1K0 consolidation instrument. (1) Axial loading bar; (2) pressure cell; (3) oil inlet; (4) oil outlet; (5) drainage channel; (6) specimen; (7) hydraulic sensor. (b) Loading-freezing system. (1) Consolidation load; (2) steel consolidometer; (3) cryogenic coolant; (4) thermostatic bath; (5) specimen; (6) thermocouple.
(a)
(b)Figure 2
Triaxial creep test system for frozen soil. (1) Axial loading cell; (2) antiforce frame; (3) pressure cell; (4) cryogenic coolant; (5) specimen; (6) thermocouple; (7) thermostatic bath; (8) confining pressure controller; (9) axial loading controller; (10) computer.


### 2.2. Experimental Procedure and Conditions

(1)
The unfrozen specimens underwentK0 consolidation tests to simulate the formation of deep clay in alluvia. Meanwhile, the K0 value and water content were measured. The consolidation time (tc) and pressure (σ1) were 3–28 days and 8–10 MPa, respectively.
(2)
After the specimens had been consolidated for the predetermined time, loading-freezing tests were conducted at −15°C. In these tests, the temperature of the internal central position and the axial frost heaving deformation of the specimens were monitored. After the temperature and the axial deformation stabilized, freezing lasted for almost 24 hours to ensure uniformity. The frozen specimens removed from the mold were preserved in a thermostat box. The rebound deformations were very small before and after stripping in these tests.
(3)
The frozen specimen was placed into the pressure cell of the TATW-500 high-pressure triaxial test system, and silicone oil was used as a filler. Then, the test temperature was recovered by the circulating cryogenic liquids and kept for 12 hours. Furthermore, during the creep tests, a constant temperature was maintained. Thereafter, a triaxial pressure state was applied to the frozen specimen to recover theK0 stress state.
(4)
According to the test requirements, the confining pressure was unloaded in three steps. The load values were determined based onkiσs, where σs represents the difference between the instantaneous shear strength and the initial deviator stress of a frozen specimen under the same condition, which were obtained from the shear strength test under the triaxial unloading stress path and the K0 consolidation test, respectively, and ki is the stress coefficients (i.e., ki = 0.2, 0.4 and 0.6 or ki = 0.3, 0.5, and 0.7). After maintaining the target deviator stress for 10 hours, the next stage of unloading was performed. The test ended when the specimen had been destroyed or a test time of 30 hours had been reached.
(5)
The confining and axial pressures were gradually released, the samples were removed, and the steps above were repeated to continue the tests.The detailed unloading creep test arrangements are listed in Table2.Table 2
Arrangements of triaxial unloading creep test on frozen clay.
Number
σ
1 (MPa)
T (°C)
t
c (d)
σ
1 − σ3 (MPa)
1
8
−15
3
3.5/4.0/4.5
2
8
−15
7
3.5/4.0/5.0
3
8
−15
14
4.0/4.5/5.0
4
10
−15
3
3.5/4.0/4.5
5
10
−15
7
4.3/4.7/5.1
6
10
−15
14
4.5/5.0/5.5
7
10
−15
28
4.2/4.7/5.2


## 2.1. Materials and Experimental Apparatus

The clay investigated in the present study was derived from a mine shaft at a depth of approximately 520–550 m, and the physical parameters are listed in Table1. The reconstituted specimens were prepared as cylinders with diameters of 61.8 mm and heights of 125 mm. The initial water content and the dry density of the specimens tested were 27.8% and 1.49 g/cm3, respectively. These specimens were saturated with air-free water under vacuum for 24 hours to achieve a saturation of 0.98.Table 1
The basic physical properties of the clay specimens.
G
s
ρ
d (g·cm−3)
Composition of grains (%)
w
L (%)
w
p (%)
>0.25 mm
0.25∼0.1 mm
0∼0.075 mm
0∼0.045 mm
<0.045 mm
2.71
1.49
3
6.32
2.71
6.11
81.86
58.83
28.93Consolidation tests of reconstituted clay specimens were conducted on an SKA-1K0 consolidation instrument and a custom high-pressure lever-type loading system (0.05–60 kN), and the K0 values were monitored; a DL-4050 cryogenic cooling circulating pump (−40–0°C) was applied to freeze the specimens under constant axial load; in addition, constant axial pressure and unloading confining pressure creep tests of frozen clay specimens were conducted with the TATW-500 subzero dynamic and static high-pressure triaxial test system, whose confining and axial pressure can be controlled simultaneously to a maximum axial pressure and confining pressure of 500 kN and 20 MPa, respectively. The schematic diagrams of the test apparatus are shown in Figures 1 and 2.Figure 1
High-pressure consolidation and loading-freezing equipment. (a) SKA-1K0 consolidation instrument. (1) Axial loading bar; (2) pressure cell; (3) oil inlet; (4) oil outlet; (5) drainage channel; (6) specimen; (7) hydraulic sensor. (b) Loading-freezing system. (1) Consolidation load; (2) steel consolidometer; (3) cryogenic coolant; (4) thermostatic bath; (5) specimen; (6) thermocouple.
(a)
(b)Figure 2
Triaxial creep test system for frozen soil. (1) Axial loading cell; (2) antiforce frame; (3) pressure cell; (4) cryogenic coolant; (5) specimen; (6) thermocouple; (7) thermostatic bath; (8) confining pressure controller; (9) axial loading controller; (10) computer.


## 2.2. Experimental Procedure and Conditions

(1)
The unfrozen specimens underwentK0 consolidation tests to simulate the formation of deep clay in alluvia. Meanwhile, the K0 value and water content were measured. The consolidation time (tc) and pressure (σ1) were 3–28 days and 8–10 MPa, respectively.
(2)
After the specimens had been consolidated for the predetermined time, loading-freezing tests were conducted at −15°C. In these tests, the temperature of the internal central position and the axial frost heaving deformation of the specimens were monitored. After the temperature and the axial deformation stabilized, freezing lasted for almost 24 hours to ensure uniformity. The frozen specimens removed from the mold were preserved in a thermostat box. The rebound deformations were very small before and after stripping in these tests.
(3)
The frozen specimen was placed into the pressure cell of the TATW-500 high-pressure triaxial test system, and silicone oil was used as a filler. Then, the test temperature was recovered by the circulating cryogenic liquids and kept for 12 hours. Furthermore, during the creep tests, a constant temperature was maintained. Thereafter, a triaxial pressure state was applied to the frozen specimen to recover theK0 stress state.
(4)
According to the test requirements, the confining pressure was unloaded in three steps. The load values were determined based onkiσs, where σs represents the difference between the instantaneous shear strength and the initial deviator stress of a frozen specimen under the same condition, which were obtained from the shear strength test under the triaxial unloading stress path and the K0 consolidation test, respectively, and ki is the stress coefficients (i.e., ki = 0.2, 0.4 and 0.6 or ki = 0.3, 0.5, and 0.7). After maintaining the target deviator stress for 10 hours, the next stage of unloading was performed. The test ended when the specimen had been destroyed or a test time of 30 hours had been reached.
(5)
The confining and axial pressures were gradually released, the samples were removed, and the steps above were repeated to continue the tests.The detailed unloading creep test arrangements are listed in Table2.Table 2
Arrangements of triaxial unloading creep test on frozen clay.
Number
σ
1 (MPa)
T (°C)
t
c (d)
σ
1 − σ3 (MPa)
1
8
−15
3
3.5/4.0/4.5
2
8
−15
7
3.5/4.0/5.0
3
8
−15
14
4.0/4.5/5.0
4
10
−15
3
3.5/4.0/4.5
5
10
−15
7
4.3/4.7/5.1
6
10
−15
14
4.5/5.0/5.5
7
10
−15
28
4.2/4.7/5.2


## 3. Experimental Results and Analysis

### 3.1. Axial Creep Strain Characteristics

Figures3(a)–3(c) and 4(a)–4(d) demonstrate variations in axial creep strain and axial creep rate with time for specimens that were frozen at −15°C and subjected to various consolidation conditions. From these figures, the following conclusions can be reached.Figure 3
Variations in axial creep strain and axial creep rate with time (σ1 = 8 MPa): (a) tc = 3 d, (b) tc = 7 d, and (c) tc = 14 d.
(a)
(b)
(c)Figure 4
Variations in the axial creep strain and axial creep rate with time (σ1 = 10 MPa): (a) tc = 3 d, (b) tc = 7 d, (c) tc = 14 d, and (d) tc = 28 d.
(a)
(b)
(c)
(d)(1)
The specimens subjected to various consolidation conditions show both attenuation creep and nonattenuation creep as the deviator stress varies. When the deviator stress is low, the creep strain presents obvious attenuation characteristics. The nonattenuation creep occurs with high deviator stress. The creep strain and creep rate increase with the deviator stress, at the same creep time
(2)
Long-term high-pressureK0 consolidation reduces the creep strain and creep rate of the specimens under the same deviator stress at the same creep time.The average creep rate based on the steady creep stage in the creep rate curve is taken as the steady creep rateε˙s. The steady creep rates of each specimen under various deviator stresses are listed in Table 3.Table 3
The steady creep rate of the frozen clay specimens (−15°C).
Specimen
Primary deviator stress
Secondary deviator stress
Tertiary deviator stress
σ
1 − σ3 (MPa)
ε
˙
s (%·h−1)
σ
1 − σ3 (MPa)
ε
˙
s (%·h−1)
σ
1 − σ3 (MPa)
ε
˙
s (%·h−1)
8 MPa-3 d
3.5
0.159
4.0
0.313
4.5
0.681
8 MPa-7 d
3.5
0.111
4.0
0.184
5.0
0.718
8 MPa-14 d
4.0
0.181
4.5
0.325
5.0
0.582
10 MPa-3 d
3.5
0.143
4.0
0.266
4.5
0.591
10 MPa-7 d
4.3
0.215
4.7
0.364
5.1
0.618
10 MPa-14 d
4.5
0.221
5.0
0.401
5.5
0.729
10 MPa-28 d
4.2
0.120
4.7
0.207
5.2
0.355The relationship between the creep rate and the deviator stress of frozen clay can be described with the exponential equation (1) [16, 17]. According to the data on the steady creep rate of the specimens with various consolidation conditions, the regression curves of ε˙s−(σ1 − σ3) were determined, as shown in Figure 5, and the regression parameters are listed in Table 4.(1)ε˙s=aebσ1−σ3,where ε˙s represents the steady creep rate, σ1 − σ3 is the creep deviator stress, and a and b are the material constants related to the consolidation time and consolidation stress.Figure 5
The regression curves ofε˙s−(σ1 − σ3): (a) σ1 = 8 MPa and (b) σ1 = 10 MPa.
(a)
(b)Table 4
The regression parameters ofε˙s–(σ1 − σ3).
Parameters
8 MPa
10 MPa
3 d
7 d
14 d
3 d
7 d
14 d
28 d
a
0.000839
0.001031
0.001714
0.000674
0.000736
0.001033
0.001257
b
1.488
1.309
1.165
1.506
1.320
1.192
1.086For frozen specimens subjected to long-term high-pressureK0 consolidation before freezing, the steady creep rate increases with creep deviator stress; under the same deviator stress, the steady creep rate decreases with the extension of the consolidation time. The regression parameter a increases with the extension of the consolidation time, while b decreases; on the contrary, a decreases with the increase in the consolidation stress, whereas b increases.


### 3.2. Long-Term Strength

During the exposure duration of the shaft excavation section, the long-term strength of the artificially frozen, deep clay has an important influence on the long-term mechanical stability of the frozen wall. However, human error makes it very difficult to determine the stress inflection point of frozen clay accurately with the conventional stress-strain isochronal curve method. More accurate long-term measurements of strength are obtained from the creep tests in this paper by applying the relationship between the experimental steady creep rate and creep deviator stress and the method of equal interval tangent to eliminate human error.The specific methods for this approach are as follows:(1)
According to the creep tests, the steady creep rate under different deviator stresses was obtained.(2)
The exponential equation shown as equation (1) was applied to fit the relationship between steady creep rate and deviator stress.(3)
Tangent lines were drawn every 5° in the range from 5 to 85° on the fitting curve. The intersection points of each tangent line with the deviator stress axis were marked as A, B, C, D, E, and so on. The upper and lower limits of the long-term strength correspond to the two creep deviator stresses of the intersection points with the smallest spacing.(4)
Tangent lines were drawn every 1° between the two intersection points with the smallest spacing on the fitting curve. Step (3) was repeated to obtain a more accurate range of the long-term strength, and then the average value was taken as the long-term strength of the frozen clay specimen.A schematic diagram of this method is shown in Figure6.Figure 6
The method used to obtain the long-term strength.K
0 values, moisture contents, instantaneous strengths, long-term strengths, and strength decay rates based on the high-pressure K0 consolidation tests, triaxial shear tests, and triaxial creep tests of frozen clay were determined, as listed in Table 5 σf represents the instantaneous strength, and σf∞ represents the long-term strength. The strength decay rate is expressed as σ, i.e., σ = (σf  −  σf∞)/σf.Table 5
Instantaneous and long-term strengths of the frozen clay.
Specimen
w (%)
K
0
σ
f (MPa)
σ
f∞ (MPa)
σ (%)
8 MPa-3 d
29.57
0.701
5.55
3.81
31.35
8 MPa-7 d
27.01
0.657
5.93
4.28
27.82
8 MPa-14 d
25.90
0.593
6.08
4.48
26.31
10 MPa-3 d
26.7
0.699
5.68
3.91
31.28
10 MPa-7 d
25.41
0.661
6.19
4.49
27.46
10 MPa-14 d
24.27
0.609
6.37
4.74
25.70
10 MPa-28 d
23.77
0.590
6.49
5.05
20.49To analyze the evolution and mechanisms of the instantaneous and long-term strengths, their variations and rates of increase are shown in Figures7 and 8, respectively. Figure 9 shows the variations in the strength decay rates.Figure 7
Variations in the long-term and instantaneous strengths of the frozen clay: (a)σf and σf∞ vs. tc, (b) σf and σf∞ vs. w, and (c) σf and σf∞ vs. K0.
(a)
(b)
(c)Figure 8
Variations in the rates of increase in the instantaneous and long-term strengths of the frozen clay: (a) dσf/dtc and σf∞/dtc vs. tc and (b) dσf/dtc and σf∞/dtc vs. tc.
(a)
(b)Figure 9
Variations in the strength decay rate of the frozen clay: (a) strength decay rate vs.tc, (b) strength decay rate vs. w, and (c) strength decay rate vs. K0.
(a)
(b)
(c)The following conclusions were reached:(1)
The instantaneous and long-term strengths of the specimens subjected to consolidation under 8 MPa increase by 0.53 MPa and 0.67 MPa, respectively, which are within consolidation times of 1 to 14 days, and those under 10 MPa increase by 0.81 MPa and 1.14 MPa with consolidation times of 1 to 28 days. The strengths increase rapidly for consolidation times of 3 to 7 days, and as the consolidation time increases, the rates of increase in the strengths tend to be stable.(2)
The long-term strengths and instantaneous strengths of specimens consolidated under 10 MPa are higher than those consolidated under 8 MPa.(3)
The water contents of saturated specimens subjected to long-term consolidation at 8 MPa and 10 MPa are 25.9%–29.57% and 23.77%–26.7%, respectively. The increase in dry density caused by the prolongation of consolidation time results in the decrease in the saturated ice content of the specimen. Meanwhile, the cohesion and friction between soil particles increase, as well as the cementation between the soil and ice. The contribution of compaction to the instantaneous and long-term strengths of the frozen specimens increases gradually, and the effect on the long-term strength is prominent.(4)
TheK0 values decrease with the consolidation time. Consequently, with the decrease in excess pore water pressure and the increase in effective stress between clay particles, the unfrozen water content in frozen specimens decreases. Meanwhile, the friction force of the soil particles increases, and the relative motion under the deviator stress decreases. As indicated by the test results, the instantaneous and long-term strengths decrease with the K0 value.(5)
The consolidation time-related increase rates in the instantaneous and long-term strengths gradually decrease with the extension of the consolidation time. In addition, the increase rates of the long-term strength are higher than those of the instantaneous strength, i.e., the long-term strength of frozen clay is more greatly affected. In contrast, the consolidation stress-related increase rates of the instantaneous and long-term strengths increase with the consolidation time. In addition, the instantaneous strength is affected more than the long-term strength.(6)
The long-term strengths of the specimens consolidated under 8 MPa and 10 MPa are 31.35%–26.31% and 31.28%–20.49% less than the instantaneous strengths, respectively. The decay rates of strength are reduced with the consolidation time, and the strengths of the specimens consolidated under 8 MPa decay more drastically. It can be inferred that the creep time effect on the strength of frozen clay is weakened by long-term high-pressure consolidation before freezing, i.e., the creep property weakens.


### 3.3. Long-Term Mohr–Coulomb Strength Parameters

In previous studies, the strength criterion of frozen soil under triaxial stress paths followed the Mohr–Coulomb strength criterion [18]. Based on triaxial shear tests and triaxial creep tests of frozen clay, strength envelopes following the Mohr–Coulomb strength criterion are shown in Figure 10, and the Mohr–Coulomb strength parameters are listed in Table 6.Figure 10
Strength envelopes of frozen clay: (a) instantaneous strength and (b) long-term strength.
(a)
(b)Table 6
Instantaneous and long-term Mohr–Coulomb strength parameters.
t
c (d)
c (MPa)
φ (°)
c
∞ (MPa)
φ
∞ (°)
c−c∞/c (%)
φ−φ∞/φ (%)
3 d
2.586
2.079
1.740
1.546
32.70
25.59
7 d
2.623
3.986
1.817
3.207
29.91
24.84
14 d
2.652
4.586
1.908
3.497
28.05
23.75From the analysis, the following results were found:(1)
As shown in Figure11, the instantaneous and long-term Mohr–Coulomb strength parameters increased with the consolidation time, and the instantaneous internal friction angles and cohesions are greater than the long-term internal friction angles and cohesions.(2)
The decay rates of the long-term internal friction angles and cohesions, compared to those of the instantaneous internal friction angles and cohesions, are reduced by long-term consolidation before freezing. It is illustrated that the creep property of frozen clay is weakened under these conditions.Figure 11
Variations in instantaneous and long-term Mohr–Coulomb strength parameters vs.tc: (a) friction angle and (b) cohesion.
(a)
(b)


## 3.1. Axial Creep Strain Characteristics

Figures3(a)–3(c) and 4(a)–4(d) demonstrate variations in axial creep strain and axial creep rate with time for specimens that were frozen at −15°C and subjected to various consolidation conditions. From these figures, the following conclusions can be reached.Figure 3
Variations in axial creep strain and axial creep rate with time (σ1 = 8 MPa): (a) tc = 3 d, (b) tc = 7 d, and (c) tc = 14 d.
(a)
(b)
(c)Figure 4
Variations in the axial creep strain and axial creep rate with time (σ1 = 10 MPa): (a) tc = 3 d, (b) tc = 7 d, (c) tc = 14 d, and (d) tc = 28 d.
(a)
(b)
(c)
(d)(1)
The specimens subjected to various consolidation conditions show both attenuation creep and nonattenuation creep as the deviator stress varies. When the deviator stress is low, the creep strain presents obvious attenuation characteristics. The nonattenuation creep occurs with high deviator stress. The creep strain and creep rate increase with the deviator stress, at the same creep time
(2)
Long-term high-pressureK0 consolidation reduces the creep strain and creep rate of the specimens under the same deviator stress at the same creep time.The average creep rate based on the steady creep stage in the creep rate curve is taken as the steady creep rateε˙s. The steady creep rates of each specimen under various deviator stresses are listed in Table 3.Table 3
The steady creep rate of the frozen clay specimens (−15°C).
Specimen
Primary deviator stress
Secondary deviator stress
Tertiary deviator stress
σ
1 − σ3 (MPa)
ε
˙
s (%·h−1)
σ
1 − σ3 (MPa)
ε
˙
s (%·h−1)
σ
1 − σ3 (MPa)
ε
˙
s (%·h−1)
8 MPa-3 d
3.5
0.159
4.0
0.313
4.5
0.681
8 MPa-7 d
3.5
0.111
4.0
0.184
5.0
0.718
8 MPa-14 d
4.0
0.181
4.5
0.325
5.0
0.582
10 MPa-3 d
3.5
0.143
4.0
0.266
4.5
0.591
10 MPa-7 d
4.3
0.215
4.7
0.364
5.1
0.618
10 MPa-14 d
4.5
0.221
5.0
0.401
5.5
0.729
10 MPa-28 d
4.2
0.120
4.7
0.207
5.2
0.355The relationship between the creep rate and the deviator stress of frozen clay can be described with the exponential equation (1) [16, 17]. According to the data on the steady creep rate of the specimens with various consolidation conditions, the regression curves of ε˙s−(σ1 − σ3) were determined, as shown in Figure 5, and the regression parameters are listed in Table 4.(1)ε˙s=aebσ1−σ3,where ε˙s represents the steady creep rate, σ1 − σ3 is the creep deviator stress, and a and b are the material constants related to the consolidation time and consolidation stress.Figure 5
The regression curves ofε˙s−(σ1 − σ3): (a) σ1 = 8 MPa and (b) σ1 = 10 MPa.
(a)
(b)Table 4
The regression parameters ofε˙s–(σ1 − σ3).
Parameters
8 MPa
10 MPa
3 d
7 d
14 d
3 d
7 d
14 d
28 d
a
0.000839
0.001031
0.001714
0.000674
0.000736
0.001033
0.001257
b
1.488
1.309
1.165
1.506
1.320
1.192
1.086For frozen specimens subjected to long-term high-pressureK0 consolidation before freezing, the steady creep rate increases with creep deviator stress; under the same deviator stress, the steady creep rate decreases with the extension of the consolidation time. The regression parameter a increases with the extension of the consolidation time, while b decreases; on the contrary, a decreases with the increase in the consolidation stress, whereas b increases.


## 3.2. Long-Term Strength

During the exposure duration of the shaft excavation section, the long-term strength of the artificially frozen, deep clay has an important influence on the long-term mechanical stability of the frozen wall. However, human error makes it very difficult to determine the stress inflection point of frozen clay accurately with the conventional stress-strain isochronal curve method. More accurate long-term measurements of strength are obtained from the creep tests in this paper by applying the relationship between the experimental steady creep rate and creep deviator stress and the method of equal interval tangent to eliminate human error.The specific methods for this approach are as follows:(1)
According to the creep tests, the steady creep rate under different deviator stresses was obtained.(2)
The exponential equation shown as equation (1) was applied to fit the relationship between steady creep rate and deviator stress.(3)
Tangent lines were drawn every 5° in the range from 5 to 85° on the fitting curve. The intersection points of each tangent line with the deviator stress axis were marked as A, B, C, D, E, and so on. The upper and lower limits of the long-term strength correspond to the two creep deviator stresses of the intersection points with the smallest spacing.(4)
Tangent lines were drawn every 1° between the two intersection points with the smallest spacing on the fitting curve. Step (3) was repeated to obtain a more accurate range of the long-term strength, and then the average value was taken as the long-term strength of the frozen clay specimen.A schematic diagram of this method is shown in Figure6.Figure 6
The method used to obtain the long-term strength.K
0 values, moisture contents, instantaneous strengths, long-term strengths, and strength decay rates based on the high-pressure K0 consolidation tests, triaxial shear tests, and triaxial creep tests of frozen clay were determined, as listed in Table 5 σf represents the instantaneous strength, and σf∞ represents the long-term strength. The strength decay rate is expressed as σ, i.e., σ = (σf  −  σf∞)/σf.Table 5
Instantaneous and long-term strengths of the frozen clay.
Specimen
w (%)
K
0
σ
f (MPa)
σ
f∞ (MPa)
σ (%)
8 MPa-3 d
29.57
0.701
5.55
3.81
31.35
8 MPa-7 d
27.01
0.657
5.93
4.28
27.82
8 MPa-14 d
25.90
0.593
6.08
4.48
26.31
10 MPa-3 d
26.7
0.699
5.68
3.91
31.28
10 MPa-7 d
25.41
0.661
6.19
4.49
27.46
10 MPa-14 d
24.27
0.609
6.37
4.74
25.70
10 MPa-28 d
23.77
0.590
6.49
5.05
20.49To analyze the evolution and mechanisms of the instantaneous and long-term strengths, their variations and rates of increase are shown in Figures7 and 8, respectively. Figure 9 shows the variations in the strength decay rates.Figure 7
Variations in the long-term and instantaneous strengths of the frozen clay: (a)σf and σf∞ vs. tc, (b) σf and σf∞ vs. w, and (c) σf and σf∞ vs. K0.
(a)
(b)
(c)Figure 8
Variations in the rates of increase in the instantaneous and long-term strengths of the frozen clay: (a) dσf/dtc and σf∞/dtc vs. tc and (b) dσf/dtc and σf∞/dtc vs. tc.
(a)
(b)Figure 9
Variations in the strength decay rate of the frozen clay: (a) strength decay rate vs.tc, (b) strength decay rate vs. w, and (c) strength decay rate vs. K0.
(a)
(b)
(c)The following conclusions were reached:(1)
The instantaneous and long-term strengths of the specimens subjected to consolidation under 8 MPa increase by 0.53 MPa and 0.67 MPa, respectively, which are within consolidation times of 1 to 14 days, and those under 10 MPa increase by 0.81 MPa and 1.14 MPa with consolidation times of 1 to 28 days. The strengths increase rapidly for consolidation times of 3 to 7 days, and as the consolidation time increases, the rates of increase in the strengths tend to be stable.(2)
The long-term strengths and instantaneous strengths of specimens consolidated under 10 MPa are higher than those consolidated under 8 MPa.(3)
The water contents of saturated specimens subjected to long-term consolidation at 8 MPa and 10 MPa are 25.9%–29.57% and 23.77%–26.7%, respectively. The increase in dry density caused by the prolongation of consolidation time results in the decrease in the saturated ice content of the specimen. Meanwhile, the cohesion and friction between soil particles increase, as well as the cementation between the soil and ice. The contribution of compaction to the instantaneous and long-term strengths of the frozen specimens increases gradually, and the effect on the long-term strength is prominent.(4)
TheK0 values decrease with the consolidation time. Consequently, with the decrease in excess pore water pressure and the increase in effective stress between clay particles, the unfrozen water content in frozen specimens decreases. Meanwhile, the friction force of the soil particles increases, and the relative motion under the deviator stress decreases. As indicated by the test results, the instantaneous and long-term strengths decrease with the K0 value.(5)
The consolidation time-related increase rates in the instantaneous and long-term strengths gradually decrease with the extension of the consolidation time. In addition, the increase rates of the long-term strength are higher than those of the instantaneous strength, i.e., the long-term strength of frozen clay is more greatly affected. In contrast, the consolidation stress-related increase rates of the instantaneous and long-term strengths increase with the consolidation time. In addition, the instantaneous strength is affected more than the long-term strength.(6)
The long-term strengths of the specimens consolidated under 8 MPa and 10 MPa are 31.35%–26.31% and 31.28%–20.49% less than the instantaneous strengths, respectively. The decay rates of strength are reduced with the consolidation time, and the strengths of the specimens consolidated under 8 MPa decay more drastically. It can be inferred that the creep time effect on the strength of frozen clay is weakened by long-term high-pressure consolidation before freezing, i.e., the creep property weakens.


## 3.3. Long-Term Mohr–Coulomb Strength Parameters

In previous studies, the strength criterion of frozen soil under triaxial stress paths followed the Mohr–Coulomb strength criterion [18]. Based on triaxial shear tests and triaxial creep tests of frozen clay, strength envelopes following the Mohr–Coulomb strength criterion are shown in Figure 10, and the Mohr–Coulomb strength parameters are listed in Table 6.Figure 10
Strength envelopes of frozen clay: (a) instantaneous strength and (b) long-term strength.
(a)
(b)Table 6
Instantaneous and long-term Mohr–Coulomb strength parameters.
t
c (d)
c (MPa)
φ (°)
c
∞ (MPa)
φ
∞ (°)
c−c∞/c (%)
φ−φ∞/φ (%)
3 d
2.586
2.079
1.740
1.546
32.70
25.59
7 d
2.623
3.986
1.817
3.207
29.91
24.84
14 d
2.652
4.586
1.908
3.497
28.05
23.75From the analysis, the following results were found:(1)
As shown in Figure11, the instantaneous and long-term Mohr–Coulomb strength parameters increased with the consolidation time, and the instantaneous internal friction angles and cohesions are greater than the long-term internal friction angles and cohesions.(2)
The decay rates of the long-term internal friction angles and cohesions, compared to those of the instantaneous internal friction angles and cohesions, are reduced by long-term consolidation before freezing. It is illustrated that the creep property of frozen clay is weakened under these conditions.Figure 11
Variations in instantaneous and long-term Mohr–Coulomb strength parameters vs.tc: (a) friction angle and (b) cohesion.
(a)
(b)


## 4. Creep Equation of Deep, Frozen Clay

Consisting of a Hooke body, viscoelastic body, and viscoplastic body, the Nishihara model can describe the variation in different creep types, thus reflecting the internal characteristics and creep mechanism of frozen clay. The mechanical model is shown in Figure12, where E0 represents the elastic modulus of the Hooke body, E1 is the elastic modulus of the viscoelastic body, η1 and η2 are the viscosity coefficients of the viscoelastic and viscoplastic bodies, and σ∞ is the long-term strength of the frozen clay.Figure 12
The Nishihara model.The creep equations corresponding to the triaxial stress state are shown in the following equation:(2)
ε
=
σ
1
−
σ
3
3
E
0
+
σ
1
−
σ
3
3
E
1
1
−
exp
−
2
E
1
η
1
t
,
σ
1
−
σ
3
<
σ
f
∞
,
ε
=
σ
1
−
σ
3
3
E
0
+
σ
1
−
σ
3
3
E
1
1
−
exp
−
2
E
1
η
1
t
+
σ
1
−
σ
3
−
σ
f
∞
η
2
t
,
σ
1
−
σ
3
≥
σ
f
∞
.A power function that reflects the nonlinearity of the viscoplastic body is applied to improve the creep constitutive equations (see equation (3)), where e is the nonlinear accelerated creep index. In addition, the variation rules of the attenuation creep, stable creep, and acceleration creep stages are mainly analyzed in this paper. Instantaneous creep, the instantaneous deformation under triaxial deviator stress, is neglected in this study to facilitate analysis:(3)ε=σ1−σ33E11−exp−2E1η1t,σ1−σ3<σf∞,ε=σ1−σ33E11−exp−2E1η1t+σ1−σ3−σf∞η2te,σ1−σ3≥σf∞.The improved model is verified through the data of creep tests and shown as Figures13 and 14. The fitting parameters are listed in Table 7.Figure 13
Comparisons between the experimental and calculation results (σ1 = 8 MPa): (a) 3 d, (b) 7 d, and (c) 14 d.
(a)
(b)
(c)Figure 14
Comparisons between the experimental and calculation results (σ1 = 10 MPa): (a) 3 d, (b) 7 d, (c) 14 d, and (d) 28 d.
(a)
(b)
(c)
(d)Table 7
The improved creep model parameters.
σ
c (MPa)
t
c (d)
σ
1 − σ3 (MPa)
σ
1 − σ3 − σf∞ (MPa)
E
1 (GPa)
η
1 (GPa·h)
η
2 (GPa·h)
e
8
3
3.5
−0.31
0.239
1.784
—
—
4.0
0.19
0.269
1.952
2.267
1.358
4.5
0.69
0.221
1.568
2.040
1.135
7
3.5
−0.78
0.265
2.124
—
—
4.0
−0.28
0.273
2.160
—
—
5.0
0.72
0.256
1.772
3.322
1.324
14
4.0
−0.48
0.277
2.310
—
—
4.5
0.02
0.309
2.412
4.149
2.257
5.0
0.52
0.292
2.002
3.703
1.381
10
3
3.5
−0.41
0.266
1.988
—
—
4.0
0.09
0.289
2.076
2.474
1.601
4.5
0.59
0.247
1.728
1.984
1.089
7
4.3
−0.18
0.304
2.313
—
—
4.7
0.22
0.317
2.366
3.448
1.406
5.1
0.62
0.305
1.980
3.225
1.340
14
4.5
−0.24
0.310
2.458
—
—
5.0
0.26
0.339
2.473
3.841
1.410
5.5
0.76
0.326
2.083
3.547
1.378
28
4.2
−0.85
0.311
2.486
—
—
4.7
−0.35
0.342
2.544
—
—
5.2
0.15
0.374
2.606
4.545
2.163Variations in the creep regression parameters of the frozen clay with the deviator stress are shown in Figures15 and 16. Considering that the deviator stress of each group test is different, as is the long-term strength, the variations in creep parameters with σ1 − σ3 − σf∞ taken as abscissa are analyzed.Figure 15
The variation in creep parameters (σ1 = 8 MPa): (a) E1, (b) η1, (c) η2, and (d) e.
(a)
(b)
(c)
(d)Figure 16
The variation in creep parameters (σ1 = 10 MPa): (a) E1, (b) η1, (c) η2, and (d) e.
(a)
(b)
(c)
(d)Taking the case of the specimen consolidated for 7 days before freezing, viscoelastic deformation and viscoplastic deformation are analyzed under different deviator stresses according to the improved creep model. The results are shown in Figure17.Figure 17
Viscoelastic and viscoplastic deformation of the frozen, deep clay (10 MPa-7 d): (a) viscoelastic strain and (b) viscoplastic strain.
(a)
(b)The analysis results above suggest the following conclusions:(1)
On the basis of Figures15(a) and 16(a), E1 first increasing and then decreasing reflect that the creep deformation of frozen clay under a low deviator stress is composed of only viscoelastic deformation, and strengthening effects occur. Viscoelastic deformation and viscoplastic deformation coexist, and the ratio of deviator stress to viscoelastic strain (E1) increases when the deviator stress exceeds the long-term strength. With a continual increase in the deviator stress, the effect of strengthening is weakened; therefore, the viscoelastic deformation increases, and E1 decreases accordingly.(2)
On the basis of Figures15(b) and 16(b), η1 first increasing and then decreasing reflects that, compared with the stabilization time of viscoelastic deformation at a low deviator stress, the stabilization time increases when the deviator stress exceeds the long-term strength, i.e., η1 increases. With a continual increase in the deviator stress, viscoelastic deformation stabilizes more quickly, i.e., η1 decreases.(3)
When the deviator stress exceeds the long-term strength, viscoplastic deformation increases gradually with the deviator stress; thus, the deformation resistance and the nonlinearity of the viscoplastic body decrease gradually, which causes the decrease inη2 and e.(4)
The increase in contact between clay particles, the thinning of the pore ice and the decrease in the unfrozen water result in the enhancement of long-term deformation resistance with the extension of consolidation time, which causes the increases inE1, η1, and η2. In addition, the nonlinear accelerated creep index e increases with consolidation time.


## 5. Conclusions

To lay a foundation for research of creep behaviors and revealing creep mechanism of artificially frozen, deep clay under complex stress states, a series of studies on the evolution of creep properties, strength, and creep parameters based on the experimental mode of “long-termK0 consolidated-freezing-constant axial pressure and unloading confining pressure” have been carried out in this paper. The following conclusions can be drawn:(1)
Long-term high-pressureK0 consolidation reduces the creep strain and creep rate of specimens under the same deviator stress at the same creep time. Thus, consolidation time and consolidation stress both are important factors affecting the creep properties of frozen clay.(2)
The increase in dry density and the decrease in excess pore water pressure caused by the prolongation of consolidation time result in the decrease in the ice and the unfrozen water contents of the specimen. Meanwhile, the cohesion and friction between soil particles increase, in addition to the increased cementation between the soil and ice, thus decreasing their relative motion under the deviator stress. The instantaneous strengths and long-term strengths both increase rapidly with consolidation times from 3 to 7 days, and as the consolidation time increases, the variations in the strengths tend to be stable. With the extension of consolidation time, the decay rates of strength decrease from 31.35% to 26.31% (σ1 = 8 MPa) and from 31.28% to 20.49% (σ1 = 10 MPa), respectively, and the creep property weakens.(3)
According to the rates of increase in the instantaneous and long-term strengths of the frozen specimens, which are related to consolidation time and consolidation stress, the consolidation time has an obvious influence on the long-term strength of frozen clay, and the consolidation stress clearly affects the instantaneous strength.(4)
This study presents an improved Nishihara model that accounts for the nonlinearity in the accelerated creep stage and rationally reflects the creep behavior characteristics of the deep, frozen clay. With a low deviator stress, creep deformations are only elastic. When the deviator stress exceeds the long-term strength, the soil-ice cementation (i.e., the bonding element) is weakened, soil particles are crushed, unfrozen water content is increased, and friction becomes influential; thus, viscoelastic and viscoplastic deformation are both observed. Therefore, the viscoelastic modulusE1 and viscoelastic viscosity coefficient η1 increase in this stage. However, with a continued increase in the deviator stress, the bonding and friction elements are rapidly destroyed, and the viscoplastic deformation increases; thus, E1, η1, and η2 decrease in this deviator stress stage.(5)
The creep parametersE1, η1, η2, and e all increase with consolidation time, thus illustrating that compaction before freezing enhances the long-term deformation resistance of frozen clay and increases the nonlinearity of accelerated creep.



---

*Source: 7192845-2019-09-18.xml*