# The Undrained Characteristics of Tengger Desert Sand from True Triaxial Testing

Authors: Xuefeng Li; Weinan Lu; Zhigang Ma; Ni Tuo
Journal: Advances in Civil Engineering
 (2021)

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## Abstract

Aimed at the characteristics of aeolian sand under rapid construction conditions in desert geotechnical engineering, a series of the true triaxial undrained test were carried out on the GDS apparatus. The 3D deformation, failure, and other characteristics of the dense sand are obtained. Under the condition of samepc, the state transition point where the void water pressure changes from increasing to decreasing appears earlier and leads to enhanced dilatancy with the increase of b, which means the enhanced dilatancy of dense sand caused the increase in strength. The results of the same b shows that the void water pressure generally indicates a decrease at low confining pressure and an increase at high confining pressure, indicating that the aeolian sand shows dilatancy at low confining pressure and contraction at high confining pressure. The state transition point increases with the increase of pc, but all points tend to the same critical state line and state transition line. When b = 0, the critical state line is q = 1.57 p′, and the state transition line is q = 1.23 p′. When b = 1, the critical state line is q = 1.24 p′, and the state transition line is q = 1.04 p′. The results at same b obtained the unified critical state line and the state transition line. Therefore, the true triaxial test can obtain the unified relationship of void ratio, pc and b, which overcomes the fact that the existing test cannot consider the influence of b. The test results provide a basis data for the design, construction, and maintenance of geotechnical engineering in Tengger Desert.


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## Body

## 1. Introduction

The policy of Western development in China has greatly promoted the infrastructure construction in desert areas, and a large number of desert geotechnical engineering will be built [1]; however, the experimental research on aeolian sand is lagging behind. Tengger Desert is the fourth largest desert in China, covering an area of 42,700 square kilometers. Due to its arid nature environment and aeolian characteristics, aeolian sand is characterized by fine particles, irregular morphology, poor surface activity, low water content, and high permeability. Restricted by arid natural environment and underdeveloped social conditions in the west of China, the test results of aeolian sand are scarce, and only a few test results serve the engineering construction, such as the construction of roads [2], railways [3, 4], and power transmission lines [5, 6] crossing the desert, and its eco-environmental construction. A targeted research has been done on accidents such as quicksand, collapse, and excessive settlement of the superstructure during construction [7]. The research on the compaction characteristics of subgrade [8–10] shows that the aeolian sand has a high degree of compaction under dry conditions and saturated conditions, so it has the unique characteristics of compaction “bimodal,” which provides a dry compaction technology of subgrade construction in the desert area. Aeolian sand is also collapsible, which is attributed to the high content of fine sand and low dry density [11, 12]. Wang et al. [13] found that the sand collapsibility is indirectly verified by the additional settlement of the sand after wetting. The bimodal characteristics and the collapsibility are two unique properties of aeolian sand obtained from the tests at present. However, many other properties of aeolian sand in 3D space, such as the strength, the stress-strain relationship, the dilatancy, and the critical state, have rarely been studied.In practical engineering, the characteristics of sand are meaningful in 3D stress state [14, 15]. However, there are relatively few results from triaxial tests of aeolian sand in China. For the true triaxial test of aeolian sand, only Li et al. [16] carried out the drainage test of Tengger Desert sand. For the conventional triaxial test, Deng [17] and Song [18] had carried out static-dynamic tests. Zhang et al. [19], Zhang et al. [20], and Li et al. [21] studied on the freeze-thaw cycle properties. Li and Zhang [22] carried out undrained tests for the Mu Us Desert sand with different confining pressure. Hao et al. [23] studied the structural strength index of unsaturated sand. The study of Badanagki’s [24] undrained test for the Sahara sand states that the shear strength decreases with the increase of relative compaction.At present, only the true triaxial tests of other types of sand are studied, but the results are relatively few. Choi et al. [25] carried out true triaxial tests for drained and undrained with different stress path. Suits et al. [26] studied the influence of intermediate principal stress on the stress-strain relationships and found that the obvious anisotropy was shown in the sand. Lade and Wang [27] studied the deformation and failure characteristics of sand with the different densities and found that the peak failure of sand was mainly caused by shear bands. For Toyoura sand, Yamada and Ishihara [28] and Yoshimine et al. [29] found that the larger b is, the greater the void water pressure is, which has a greater impact on the deformation. Pan et al. [30] found that triaxial compression and triaxial extension tests show significantly different characteristics and triaxial compression is characterized by shear dilatation but the extension test is dominated by strain softening. For the Fujian standard sand, Xu et al. [31] found that the b-value has little effect on stress ratio, and Li and Yang [32] found that the confining pressure has little effect on the strength of the specimen. For the Ottawa sand, Murthy et al. [33] found that the critical state of the drainage test is the same as the undrained test, and the undrained shear strength increases with the increase of specimen density. For Shanghai sily sand, Hu et al. [34] found that the peak stress is raised with the increase of the confining pressure at failure, but the relationships between shear stress and the b-value are complicated. Liang and Ping [35] found that the peak shear stress increases with the increase of b and the void water pressure first increases and then decreases. Therefore, in geotechnical engineering [36] the sand foundation will lose its bearing capacity due to the increase of void water pressure under the condition of instantaneous strong load or cyclic load. So it is necessary to carry out the undrained test.The research on the strength of subgrade has accumulated some experience, which mainly focuses on highway design, construction technology, and meteorological and hydrological detection in the Tengger Desert area. However, the results of triaxial tests on aeolian sand are seriously lacking, which affect the understanding of its engineering characteristics. Especially because the critical state line of sand is not unique, it is mainly affected by the stress path and anisotropy [37, 39]. The true triaxial test can be used to study various complex stress paths and the critical state of soil in true 3D space. In this paper, the true triaxial undrained test of aeolian sand in Tengger Desert is carried out by the British GDS true triaxial apparatus. The deformation, failure, dilatancy, and critical state characteristics of sand are studied with different b-values and pc. Through the analysis of void water pressure, generalized shear stress, stress ratio, and other mechanical characteristics, the undrained strength of Tengger Desert sand will be explored.


## 2. The True Triaxial Equipment

The British GDS true triaxial apparatus is used (Figure1) in this paper, which can carry out the static and dynamic quick loading test. As shown in Figures 1 and 2, the specimen is placed in the pressure chamber, and the pressure is applied by the rigid loading plates and flexible loading systems. Rigid loading is controlled by a servo motor and flexible loading is applied by water. The flexible load is controlled by the pneumatic controller. The air pressure controller is connected to the air collector and air pump, indicated by the green line in Figure 1. For more detailed introduction of the loading method, see reference [16].Figure 1
The true triaxial test system.Figure 2
Loading diagram.


## 3. Test Processes and Schemes

### 3.1. Introduction to the Test

The sand is collected from Tengger Desert in the Shapotou area, Zhongwei City, Ningxia Hui Autonomous Region, where is the distribution area of typical aeolian sand. The sand particle size of 0.075∼0.5 mm accounts for more than 90%. The size gradation and some physical properties of aeolian sand are shown in Table1. According to the Unified Soil Classification System, Tengger Desert sand is fine sand [40]. The size of the specimen is 75 × 75 × 150 mm. According to the method of layering compaction, the cuboid specimen is divided into 10 layers. The relative compaction of the specimen is controlled at 0.7. The weight of the specimen is 1291 g. A dry deposition method is used for the preparation specimen.Table 1
The main physical properties of aeolian sand.
Maximum dry densityMinimum dry densityMoisture content (%)Grain composition>0.75 mm (%)0.75∼0.5 mm (%)0.5∼0.25 mm (%)0.25∼0.1 mm (%)<0.1 mm1.62 g/cm31.36 g/cm30.140.073.8394.411.690The specimen is saturated by two steps: one is head saturation, and another is backpressure saturation. After the backpressure saturation, the void water pressure coefficient (B) is computed. If B reaches more than 95%, the specimen can be considered to be saturated fully. B represents the saturation degree of the specimen, when B = 0, the specimen is completely dried, and when B = 1, the specimen is saturated 100%. The consolidation adopts an isotropic method of rigid and flexible combination. The criterion for the end of consolidation is that the change of water volume in the backpressure controller does not exceed 1% of the total amount within a certain time (30 min).In the shearing process, the strain control loading can be adopted to ensure constantb-value, and the strain control can also better control the collision of rigid loading. According to the definition of b-value, the expression equation (1) of the intermediate principal strain coefficient bε is given. The strain control loading under the condition of constant b can be realized through equations (1) and (2):(1)bε=ε2−ε3ε1−ε30≤bε≤1,where ε1,ε2, and ε3 are the maximum principal strain, the intermediate principal strain, and the minimum principal strain, respectively.Under the undrained condition, the volume of the soil sample remains unchanged, and the strain satisfies(2)εv=ε1+ε2+ε3,where εv is the volume strain.According to equations (1) and (2), the incremental relation is(3)dε1=dε1,dε2=bεdε1,dε3=0,where dε1, dε2, and dε3 are the increment of maximum principal strain, intermediate principal strain, and minimum principal strain, respectively. From equation (3), the loading method of constant b-value is performed. The loading in the direction of ε1 and ε2 is rigid, and the loading in the direction of ε3 is flexible (Figure 2). The pressure on the flexible surface is a constant, and two rigid plates in equation (3) can be used to control the intermediate principal stress coefficient.


### 3.2. Test Schemes

Three group schemes are designed in this experiment. The first is to adopt theb-values of 0, 0.25, 0.5, and 1, respectively, under the condition of keeping pc equal to 100 kPa. In the shearing progress, b-value and pc are constant. The stress paths are shown in Figure 3(a).Figure 3
The designed stress path of the test. (a) The first group. (b) The second group. (c) The third group.
(a)(b)(c)The second is to adoptpc of 50 kPa, 100 kPa, 200 kPa, 400 kPa, and 800 kPa, respectively, with b = 0. The purpose is to obtain the critical state line, state transition line, and the stress-strain relationship of dense aeolian sand under the undrained condition with b = 0. The stress paths are shown in Figure 3(b).The third is to adoptpc of 50 kPa, 100 kPa, and 200 kPa, respectively, with b = 1. The purpose is to obtain the critical state line and state transition line of the aeolian sand under the undrained condition with b = 1. The stress path is shown in Figure 3(c).In the direction ofσ1, the speed of strain loading is 0.315 mm/min, 0.315 mm equivalent to 0.21% of the height of specimen. The maximum vertical displacement is 37.5 mm, 37.5 mm equivalent to a maximum ε1 of 25%. In Figure 3, the horizontal axis and vertical axis are the mean principal stress p and generalized shear stress q, which are p=σ1+σ2+σ3/3 and q=σ1−σ22+σ2−σ32+σ3−σ12/2.


## 3.1. Introduction to the Test

The sand is collected from Tengger Desert in the Shapotou area, Zhongwei City, Ningxia Hui Autonomous Region, where is the distribution area of typical aeolian sand. The sand particle size of 0.075∼0.5 mm accounts for more than 90%. The size gradation and some physical properties of aeolian sand are shown in Table1. According to the Unified Soil Classification System, Tengger Desert sand is fine sand [40]. The size of the specimen is 75 × 75 × 150 mm. According to the method of layering compaction, the cuboid specimen is divided into 10 layers. The relative compaction of the specimen is controlled at 0.7. The weight of the specimen is 1291 g. A dry deposition method is used for the preparation specimen.Table 1
The main physical properties of aeolian sand.
Maximum dry densityMinimum dry densityMoisture content (%)Grain composition>0.75 mm (%)0.75∼0.5 mm (%)0.5∼0.25 mm (%)0.25∼0.1 mm (%)<0.1 mm1.62 g/cm31.36 g/cm30.140.073.8394.411.690The specimen is saturated by two steps: one is head saturation, and another is backpressure saturation. After the backpressure saturation, the void water pressure coefficient (B) is computed. If B reaches more than 95%, the specimen can be considered to be saturated fully. B represents the saturation degree of the specimen, when B = 0, the specimen is completely dried, and when B = 1, the specimen is saturated 100%. The consolidation adopts an isotropic method of rigid and flexible combination. The criterion for the end of consolidation is that the change of water volume in the backpressure controller does not exceed 1% of the total amount within a certain time (30 min).In the shearing process, the strain control loading can be adopted to ensure constantb-value, and the strain control can also better control the collision of rigid loading. According to the definition of b-value, the expression equation (1) of the intermediate principal strain coefficient bε is given. The strain control loading under the condition of constant b can be realized through equations (1) and (2):(1)bε=ε2−ε3ε1−ε30≤bε≤1,where ε1,ε2, and ε3 are the maximum principal strain, the intermediate principal strain, and the minimum principal strain, respectively.Under the undrained condition, the volume of the soil sample remains unchanged, and the strain satisfies(2)εv=ε1+ε2+ε3,where εv is the volume strain.According to equations (1) and (2), the incremental relation is(3)dε1=dε1,dε2=bεdε1,dε3=0,where dε1, dε2, and dε3 are the increment of maximum principal strain, intermediate principal strain, and minimum principal strain, respectively. From equation (3), the loading method of constant b-value is performed. The loading in the direction of ε1 and ε2 is rigid, and the loading in the direction of ε3 is flexible (Figure 2). The pressure on the flexible surface is a constant, and two rigid plates in equation (3) can be used to control the intermediate principal stress coefficient.


## 3.2. Test Schemes

Three group schemes are designed in this experiment. The first is to adopt theb-values of 0, 0.25, 0.5, and 1, respectively, under the condition of keeping pc equal to 100 kPa. In the shearing progress, b-value and pc are constant. The stress paths are shown in Figure 3(a).Figure 3
The designed stress path of the test. (a) The first group. (b) The second group. (c) The third group.
(a)(b)(c)The second is to adoptpc of 50 kPa, 100 kPa, 200 kPa, 400 kPa, and 800 kPa, respectively, with b = 0. The purpose is to obtain the critical state line, state transition line, and the stress-strain relationship of dense aeolian sand under the undrained condition with b = 0. The stress paths are shown in Figure 3(b).The third is to adoptpc of 50 kPa, 100 kPa, and 200 kPa, respectively, with b = 1. The purpose is to obtain the critical state line and state transition line of the aeolian sand under the undrained condition with b = 1. The stress path is shown in Figure 3(c).In the direction ofσ1, the speed of strain loading is 0.315 mm/min, 0.315 mm equivalent to 0.21% of the height of specimen. The maximum vertical displacement is 37.5 mm, 37.5 mm equivalent to a maximum ε1 of 25%. In Figure 3, the horizontal axis and vertical axis are the mean principal stress p and generalized shear stress q, which are p=σ1+σ2+σ3/3 and q=σ1−σ22+σ2−σ32+σ3−σ12/2.


## 4. Test Results and Analysis

### 4.1. The Stress Path of the Test

The purpose of the tests is to study the strength and the stress-strain relationship of dense sand in the different stress paths space. As designed in the schemes, it is to study the deformation and strength of sand with the samepc and different b-values, as well as the stress-strain relationship under the same b and different pc conditions, especially to focus on the variety of u, p′, q, and η to obtain the 3D deformation strength relationship, critical state line, and phase transition line of aeolian sand in Tengger Desert.Figure4 shows that the evolutions of the b-value in real time during the shearing process for all schemes. The data show that strain control loading can realize that the value of b remains constant during the loading process.Figure 4
The measured value of stress path.


### 4.2. The Strength and Deformation of Differentb at the Same Confining Pressure

Figure5 shows that the u−ε1 curves of the four b-values can be divided into two stages: the increasing and decreasing stages of u. The increasing of u indicated that the specimen is compressed at the initial shearing stage and the void water volume inside the specimen is compressed. In the decreasing stages, the aeolian sand is excessively dilated from contraction to dilatation, and the void ratio of sand is increased, which lead to a drop in void water pressure. The transition point from contraction to dilatation is focused around ε1 = 2.5%. Except for b = 1, the degree of dilatation after the state transition point showed a decreasing trend with the increase of b-value. The possible reason is that when b = 1, the direction of σ1 is in the horizontal direction of the specimen, and the anisotropy of the sand in these direction affects its dilatancy.Figure 5
Change of void water pressure with differentb-values at pc = 100 kPa.Figure6(a) shows that all the stress-strain curves of different b-values show the shear hardening at pc = 100 kPa and q gradually increases with the increase of ε1. When ε1 < 10%, all curves have the similar trend. But when ε1 ≥ 10%, the curves affected by void water pressure and dilatancy are quite different. Figure 6(b) the relationships between p′ and q shows that the contraction decreases with the increase of b-value before the state transition point and then the curves tend to be straight after the point and the slope of the straight line increases. When b = 1, the difference of the curves is related to the direction change of σ1. Figure 6(c) shows the same pattern for the stress ratio. With the increase of ε1,η increased rapidly before reaching a critical state and then η reached stability. When ε1 < 5%, the b-value has a greater effect on curves and the slope increases with the b-value increases.Figure 6
Stress-strain relationships of differentb-values at pc = 100 kPa. (a) Relationships of q−ε1. (b) Relationships of p′−q. (c) Relationships of η−ε1.
(a)(b)(c)


### 4.3. The Characteristics of the Critical State

#### 4.3.1. The Critical State Line and the State Transition Line ofb = 0

Figure7 shows the changes of void water pressure under the conditions of different pc at b = 0. On the whole, the trends of the void water pressure are increasing first and then decreasing; it means that the dense aeolian sand shows the pattern of first contraction and then dilatancy. Before the state transition point, the rate of void water pressure increases with the increase of pc, and the contraction become more obvious. After the state transition point, the void water pressure decreases with the increase of pc. When pc reaches 800 kPa, the decreasing trends of void water pressure are weakened. The positive value of void water pressure indicates that the dilatancy become more and more obvious.Figure 7
The variation of void water pressure atb = 0.Figure8(a) shows the stress-strain relationship of dense aeolian sand under the conditions of different pc at b = 0. The curves are all hardened, and q increased with the increase of pc. The results in Figure 8(b) show that the curves of all different pc and the same b tend to the same critical state, q = 1.57p′. The state transition line from shear contraction to dilatancy under the undrained can be obtained as q = 1.23p′. In Figure 8(c), the relationships of η−ε1 can obtain the same η of 1.57, which is the same as the critical state line.Figure 8
Stress-strain relationship and critical state line atb = 0. (a) The stress-strain relationships. (b) The critical state line and the state transition line in p′−q space. (c) The critical state line of stress ratio and strain space.
(a)(b)(c)


#### 4.3.2. The Critical State Line and the State Transition Line ofb = 1

Figure9 shows the changes of void water pressure of dense aeolian sand under conditions of different pc when b = 1. The void water pressure is shown a trend of increasing first and then decreasing. However, the increase is greater than that in Figure 7, which indicates that the contraction of b = 0 is stronger than that of b = 1 at the same pc. When pc reaches 200 kPa, void water pressure is a positive value. Dense aeolian sand shows a shear contraction characteristic.Figure 9
The variation of void water pressure atb = 1.Figure10(a) shows the stress-strain relationship of dense aeolian sand under the conditions of different pc at b = 1. The curves are still hardened, and the generalized shear stress increases with the increase of pc, but the hardened trend is weaker than that in Figure 8(a) at the same pc and b = 0. The results in Figure 10(b) show that all curves tend to the same critical state line and the same state transition line, and they are q = 1.24p′ and q = 1.04p′. Compared with Figure 8(b), the critical state line and the state transition line are significantly smaller than those at b = 1. In Figure 10(c), the curves between the stress ratio and the large principal strain can obtain the same stress ratio of 1.24, which is the same critical state line.Figure 10
The stress-strain relationships and the critical state line atb = 1. (a) The stress-strain relationships. (b) The critical state line and the state transition line in p′−q space. (c) The critical state line of stress ratio.
(a)(b)(c)


## 4.1. The Stress Path of the Test

The purpose of the tests is to study the strength and the stress-strain relationship of dense sand in the different stress paths space. As designed in the schemes, it is to study the deformation and strength of sand with the samepc and different b-values, as well as the stress-strain relationship under the same b and different pc conditions, especially to focus on the variety of u, p′, q, and η to obtain the 3D deformation strength relationship, critical state line, and phase transition line of aeolian sand in Tengger Desert.Figure4 shows that the evolutions of the b-value in real time during the shearing process for all schemes. The data show that strain control loading can realize that the value of b remains constant during the loading process.Figure 4
The measured value of stress path.


## 4.2. The Strength and Deformation of Differentb at the Same Confining Pressure

Figure5 shows that the u−ε1 curves of the four b-values can be divided into two stages: the increasing and decreasing stages of u. The increasing of u indicated that the specimen is compressed at the initial shearing stage and the void water volume inside the specimen is compressed. In the decreasing stages, the aeolian sand is excessively dilated from contraction to dilatation, and the void ratio of sand is increased, which lead to a drop in void water pressure. The transition point from contraction to dilatation is focused around ε1 = 2.5%. Except for b = 1, the degree of dilatation after the state transition point showed a decreasing trend with the increase of b-value. The possible reason is that when b = 1, the direction of σ1 is in the horizontal direction of the specimen, and the anisotropy of the sand in these direction affects its dilatancy.Figure 5
Change of void water pressure with differentb-values at pc = 100 kPa.Figure6(a) shows that all the stress-strain curves of different b-values show the shear hardening at pc = 100 kPa and q gradually increases with the increase of ε1. When ε1 < 10%, all curves have the similar trend. But when ε1 ≥ 10%, the curves affected by void water pressure and dilatancy are quite different. Figure 6(b) the relationships between p′ and q shows that the contraction decreases with the increase of b-value before the state transition point and then the curves tend to be straight after the point and the slope of the straight line increases. When b = 1, the difference of the curves is related to the direction change of σ1. Figure 6(c) shows the same pattern for the stress ratio. With the increase of ε1,η increased rapidly before reaching a critical state and then η reached stability. When ε1 < 5%, the b-value has a greater effect on curves and the slope increases with the b-value increases.Figure 6
Stress-strain relationships of differentb-values at pc = 100 kPa. (a) Relationships of q−ε1. (b) Relationships of p′−q. (c) Relationships of η−ε1.
(a)(b)(c)


## 4.3. The Characteristics of the Critical State

### 4.3.1. The Critical State Line and the State Transition Line ofb = 0

Figure7 shows the changes of void water pressure under the conditions of different pc at b = 0. On the whole, the trends of the void water pressure are increasing first and then decreasing; it means that the dense aeolian sand shows the pattern of first contraction and then dilatancy. Before the state transition point, the rate of void water pressure increases with the increase of pc, and the contraction become more obvious. After the state transition point, the void water pressure decreases with the increase of pc. When pc reaches 800 kPa, the decreasing trends of void water pressure are weakened. The positive value of void water pressure indicates that the dilatancy become more and more obvious.Figure 7
The variation of void water pressure atb = 0.Figure8(a) shows the stress-strain relationship of dense aeolian sand under the conditions of different pc at b = 0. The curves are all hardened, and q increased with the increase of pc. The results in Figure 8(b) show that the curves of all different pc and the same b tend to the same critical state, q = 1.57p′. The state transition line from shear contraction to dilatancy under the undrained can be obtained as q = 1.23p′. In Figure 8(c), the relationships of η−ε1 can obtain the same η of 1.57, which is the same as the critical state line.Figure 8
Stress-strain relationship and critical state line atb = 0. (a) The stress-strain relationships. (b) The critical state line and the state transition line in p′−q space. (c) The critical state line of stress ratio and strain space.
(a)(b)(c)


### 4.3.2. The Critical State Line and the State Transition Line ofb = 1

Figure9 shows the changes of void water pressure of dense aeolian sand under conditions of different pc when b = 1. The void water pressure is shown a trend of increasing first and then decreasing. However, the increase is greater than that in Figure 7, which indicates that the contraction of b = 0 is stronger than that of b = 1 at the same pc. When pc reaches 200 kPa, void water pressure is a positive value. Dense aeolian sand shows a shear contraction characteristic.Figure 9
The variation of void water pressure atb = 1.Figure10(a) shows the stress-strain relationship of dense aeolian sand under the conditions of different pc at b = 1. The curves are still hardened, and the generalized shear stress increases with the increase of pc, but the hardened trend is weaker than that in Figure 8(a) at the same pc and b = 0. The results in Figure 10(b) show that all curves tend to the same critical state line and the same state transition line, and they are q = 1.24p′ and q = 1.04p′. Compared with Figure 8(b), the critical state line and the state transition line are significantly smaller than those at b = 1. In Figure 10(c), the curves between the stress ratio and the large principal strain can obtain the same stress ratio of 1.24, which is the same critical state line.Figure 10
The stress-strain relationships and the critical state line atb = 1. (a) The stress-strain relationships. (b) The critical state line and the state transition line in p′−q space. (c) The critical state line of stress ratio.
(a)(b)(c)


## 4.3.1. The Critical State Line and the State Transition Line ofb = 0

Figure7 shows the changes of void water pressure under the conditions of different pc at b = 0. On the whole, the trends of the void water pressure are increasing first and then decreasing; it means that the dense aeolian sand shows the pattern of first contraction and then dilatancy. Before the state transition point, the rate of void water pressure increases with the increase of pc, and the contraction become more obvious. After the state transition point, the void water pressure decreases with the increase of pc. When pc reaches 800 kPa, the decreasing trends of void water pressure are weakened. The positive value of void water pressure indicates that the dilatancy become more and more obvious.Figure 7
The variation of void water pressure atb = 0.Figure8(a) shows the stress-strain relationship of dense aeolian sand under the conditions of different pc at b = 0. The curves are all hardened, and q increased with the increase of pc. The results in Figure 8(b) show that the curves of all different pc and the same b tend to the same critical state, q = 1.57p′. The state transition line from shear contraction to dilatancy under the undrained can be obtained as q = 1.23p′. In Figure 8(c), the relationships of η−ε1 can obtain the same η of 1.57, which is the same as the critical state line.Figure 8
Stress-strain relationship and critical state line atb = 0. (a) The stress-strain relationships. (b) The critical state line and the state transition line in p′−q space. (c) The critical state line of stress ratio and strain space.
(a)(b)(c)


## 4.3.2. The Critical State Line and the State Transition Line ofb = 1

Figure9 shows the changes of void water pressure of dense aeolian sand under conditions of different pc when b = 1. The void water pressure is shown a trend of increasing first and then decreasing. However, the increase is greater than that in Figure 7, which indicates that the contraction of b = 0 is stronger than that of b = 1 at the same pc. When pc reaches 200 kPa, void water pressure is a positive value. Dense aeolian sand shows a shear contraction characteristic.Figure 9
The variation of void water pressure atb = 1.Figure10(a) shows the stress-strain relationship of dense aeolian sand under the conditions of different pc at b = 1. The curves are still hardened, and the generalized shear stress increases with the increase of pc, but the hardened trend is weaker than that in Figure 8(a) at the same pc and b = 0. The results in Figure 10(b) show that all curves tend to the same critical state line and the same state transition line, and they are q = 1.24p′ and q = 1.04p′. Compared with Figure 8(b), the critical state line and the state transition line are significantly smaller than those at b = 1. In Figure 10(c), the curves between the stress ratio and the large principal strain can obtain the same stress ratio of 1.24, which is the same critical state line.Figure 10
The stress-strain relationships and the critical state line atb = 1. (a) The stress-strain relationships. (b) The critical state line and the state transition line in p′−q space. (c) The critical state line of stress ratio.
(a)(b)(c)


## 5. Conclusions

In order to make up the shortage of experimental data for aeolian sand in Tengger Desert, this paper obtains the critical state line and state transition line of aeolian sand under different 3D stress path conditions, as well as differentb-values at the same pc. To grasp the true 3D mechanical properties of dense aeolian sand, a series of undrained tests were carried out using the British GDS true triaxial test system. The main conclusions are as follows:(1)
The test adopts the strain control method, which realizes the constantb-value of proportional stress loading by controlling the middle principal strain coefficient and verifies the accuracy of the strain control by real-time monitoring of the b-value.(2)
The results of differentb-values at the same pc show that the dilatancy of dense aeolian sand increased with the b-value according to the change of void water pressure. In p′−q space and η−ε1 space, the strength of aeolian sand increases with the b-value, which is consistent with the test design. When b = 1, the direction of the maximum principal stress is changed to the horizontal direction, and the stress-strain relationships are consistent with the design, which indicates that it is greatly influenced by anisotropy.(3)
Two commonly used limit state lines in geotechnical engineering are obtained from the test. The critical state line and phase transition line are obtained with the sameb-value and different pc. When b = 0, the critical state line and phase transition line are greater than b = 1, and the rules of dilatancy are relatively stable. The results fully confirm the purpose of the test design and provide the data for geotechnical engineering design, construction, and maintenance in the Tengger Desert area.



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*Source: 6320397-2021-07-07.xml*