# Experimental Study on Viscoplastic Property of Unsaturated Reticulate Red Clay Used as an Engineered Barrier

Authors: Chuang Zhang; Jian-Zhong Li; Yong He
Journal: Geofluids
 (2020)

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## Abstract

In this study, to explore the feasibility of a compacted red clay as an engineered barrier in landfills, the viscoplastic property of remodeled unsaturated reticulate red clay was studied through a series of triaxial tests. According to the deviatoric stress–axial strain curves obtained through loading tests with varying strain rates and under different conditions, the viscoplastic parameterβ of remodeled reticulate red clay was obtained. The effects of different matric suctions and net confining pressures on the viscoplasticity of unsaturated reticulate clay were analyzed. The test results showed that remodeled reticulate red clays with different degrees of saturation have similar viscoplastic properties, and their stress–strain curves are all isotach. The stiffness of unsaturated reticulate red clay increased with increasing confining pressure and matric suction. The relationship between β and the net confining pressure can be described using a linear equation. The β value of the specimens increased with increasing matric suction under a constant net confining pressure. A similar linear relationship was observed between β and the matric suction. These relationships are explained considering the loading rate effect mechanism.


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## Body

## 1. Introduction

Landfills can potentially cause severe environmental pollution [1]. Engineering practice has shown that the key to ensuring the environmental safety of a landfill is to control the diffusion of contaminants in the underlying soil. Installation of an engineered barrier (or liner system) is the key measure to prevent or mitigate such diffusion [2]. However, vertical engineered barriers and horizontal liners are affected by different geo-stresses in different locations in the landfill and are dependent on landfill depth. In addition, time effects can arise when the barrier or liner is subjected to geo-stress for a prolonged period of time. With the continuous addition of municipal solid waste, the vertical load on a horizontal liner system increases gradually. As a result, engineered barriers and liners can undergo creep deformation. Furthermore, during long-term operation of a landfill, the consolidation, seepage, biological and chemical processes, gas migration, and their coupling effects in the landfill produce different stress histories in the vertical engineered barrier and the horizontal liner system.Engineered barriers in landfills are often placed in an unsaturated condition to avoid direct contact with the atmosphere and changes in the groundwater level [3, 4]. Because of their low permeability, self-healing through swelling, low cost, and high adsorption capacity, clays such as red clays (or laterite) and bentonite are widely used in seepage control systems in contaminated sites [5–7]. The viscoplastic property of compacted clay is a relevant factor that must be considered in the design and operation of engineered barriers and liner systems.The viscoplasticity of soil is a significant issue in soil mechanics and geotechnical engineering. With the development of research on the viscoplasticity of soil, several theories have been proposed related to creep deformation [8], loading rate effects [9–11], and constitutive modeling [12, 13] that have greatly promoted the development of soil mechanics. Some researchers have proposed parameters for describing clay viscoplasticity [14, 15]. Some viscoplastic parameters focus on the creep properties of clay [16]; others focus on the loading rate effects of clay [17, 18]. A number of researchers [19–25] have reported the considerable effects of loading rate on soils, through stress–strain experiments conducted in a laboratory. The effects of a variable strain rate on the stress–strain relation, creep deformation, and stress relaxation were significant. Alonso et al. [26] presented the first comprehensive elastoplastic model to describe the load collapse characteristics of unsaturated soils. The model is known as the “Barcelona basic model” (BBM). In the BBM, it is assumed that the slope of the normal consolidation line (NCL) is a suction function, and the yield surface appears in the space of net stress and suction. Wheeler et al. [27] further detailed the BBM model. Fredlund and Morgenstern [28] established models using independent stress state variables. These constitutive models used net stress and suction to simulate the behavior of unsaturated soils found to be the most satisfactory for engineering purposes [29–34]; however, these models have some disadvantages [35]. The Sekiguchi model [36, 37] is one of the earliest to model the viscoplastic behavior of soils. This model could demonstrate creep deformation and creep rupture under undrained conditions. However, it has a restriction in explaining the infinite deformation behaviors from inviscid to viscous. The majority of Perzyna’s overstress-based models [38, 39] assumed that the viscoplastic strain rate is only associated with the current stress state, rather than the stress history and stress rate, indicating that the consistency rule is ineffective. These models cannot indicate tertiary creep and creep failure. Gennaro and Pereira [40] presented a viscoplastic constitutive model for unsaturated geomaterials. The model indicated double effects of strain rate and suction on the viscoplastic behavior of geomaterials. Several researchers [41–45] investigated the effect of strain on the mechanical behavior of soil. However, the research was restricted to few soil types (sandy soils, low plasticity soils, stiff soils) and a small range of strain rates. Zhu et al. [46] conducted undrained creep tests to illustrate the stress–strain behavior of stiff soils at different strain rates. Tatsuoka et al. [47] and Yamamuro et al. [48] studied the stress–strain behavior of sands by conducting triaxial compression tests on loose and medium dense sand at high strain rates. The results showed that the strain rate has an important effect on the shear band orientation and the relevant destruction mechanism of sand. The shear strength and deformation features of clayey soil under monotonic and cyclic loading conditions have been studied by several researchers [49–53]. Whitman and Healy [54] conducted triaxial tests on Ottawa sand, Fort Peck sand, and Camp Cooke sand; the test results indicate that there is a critical loading rate for the three types of sand. When the loading rate is less than the critical rate, the compressive strength decreases with an increase in the loading rate; beyond the critical rate, the compressive strength increases as the loading rate increases. The plane strain compression and triaxial compression tests were conducted under a certain confining pressure by Peng et al. [55]. The test results showed that the stress–strain relationship of the sand was almost unaffected when the loading rate was constant. However, when the strain loading rate changed abruptly during loading, the corresponding stress–strain curve increased or decreased suddenly. Li et al. [56] used computer-controlled strain triaxial apparatus and precise LDT strain measurement methods to perform different constant strain rate loading tests on Japanese Kitan clay, Ohi-machi clay, and Fujinomori clay at different loading stages. The tests showed that the viscoplastic properties of the three clays exhibited isochronic properties.Saturated and unsaturated soils should be evaluated during the analysis and design of geotechnical engineering projects, because most parts of the world are covered by unsaturated soil, which could be converted to saturated soil by climate and groundwater changes [57–59]. In the early study of unsaturated soil mechanics, researchers affirmed that the loading rate had a significant effect on the stress–strain behavior of unsaturated soils. Veyera [60] used three types of clays and three types of sands to study the loading rate effect of unsaturated soils under high loading rates. The results of the study showed that under high-speed loading conditions, the loading rate effects of unsaturated soils were obvious. Martin et al. [61] conducted similar tests with sand. The test results showed that the loading rate effect existed in unsaturated sand. Rojas and Mancuso [62] conducted a triaxial test on the suction control of pyroclastic silt, demonstrating that when the suction was small, the loading rate effect was not evident, and when the suction was large, the loading rate effect was very prominent. David and Fredlund [63] studied the stress–strain features of unsaturated soils under different loading rates and established a theoretical model for forecasting the shear deformation of unsaturated soils. Huat et al. [64] used three different loading rates to study the effect of the loading rate on unsaturated soils. The experimental results showed that under the constant suction condition, the unsaturated soil showed an obvious loading rate effect. Based on the Barcelona model, Gennaro and Pereira [65] proposed a viscoplastic theory model that could consider the loading rate effect. Li et al. [66] studied the creep and loading rate effects of unsaturated soils with different water contents and proposed a three-element model that can be used to simulate the loading rate effect of unsaturated soils.This study attempts to illustrate the loading rate effect of unsaturated reticulate red clay through triaxial tests. Loading rate effect tests with constant net confining pressure and variable matric suction and with constant matric suction and variable net confining pressure were conducted by the unsaturated triaxial instrument. The viscoplastic parameterβ of remolded reticulate red clay was calculated according to the stress–axial strain curves under different test conditions. The effects of different matric suction and net confining pressure on the viscoplasticity of unsaturated reticulate red clay were analyzed. The innovation of this study is the viscoplastic parameter β to describe the viscoplasticity of reticulate red clay. The value of β is obtained via variable strain rate loading tests. The loading rate effect of soil is a manifestation of soil rheology. Therefore, the viscoplastic parameter β provides an important theoretical basis for analyzing the effect of loading rate on the viscoplasticity of the unsaturated reticulate red clay.


## 2. Materials and Methodology

### 2.1. Materials

Reticulate red clay specimens used for the experiments were sampled from the Yuelu Mountain of Changsha City in China. This red clay can be used as a horizontal (liner) or vertical engineered barrier in landfills, suffering upper load of municipal solid waste or surrounding soil pressure. The physical properties of reticulate red clay are summarized in Table1.Table 1
Physical properties of reticulate red clay.
PropertiesValueWater content (%)24.3Density (g/cm3)1.9Specific gravity2.71Liquid limit (%)40.8Plastic limit (%)22Cohesion (kPa)59Friction angle (°)20.3Effective size (mm)0.047Control size (mm)0.694Optimum moisture content (%)20±1Maximum dry density (g/cm3)1.75±0.05


### 2.2. Test Apparatus

The standard GDS unsaturated triaxial apparatus was adopted in the experiment. The experimental setup is shown in Figure1. The main apparatus consisted of a pressure chamber, a pressure system, and a measurement and collection system. The peripheral pressure, axial pressure, pore air pressure, and pore water pressure could be controlled independently and arbitrarily. The air pressure and water pressure of the specimens were controlled using the perforated plate in the specimen cap and the ceramic plate in the specimen bottom, respectively [67, 68]. The test range and accuracy of GDS unsaturated triaxial apparatus are 1.0 MPa and 0.1 kPa, respectively.Figure 1
The GDS unsaturated triaxial test system.


### 2.3. Test Procedures

#### 2.3.1. Specimen Preparation

To avoid the unevenness of undisturbed specimens, remolded specimens were used in this investigation. The specimen was pretreated through air-drying and grinding using a mortar, and the powder was passed through a 2-mm sieve. Subsequently, an amount of soil was sprayed with distilled water and placed in a plastic bag for 24 h for homogenization of the specimen. Subsequently, the soil powder was put into the cylindrical mold (Figure2(a)), applied pressure to the soil through a round pestle rod (Figure 2(a)) by a universal testing machine (Figure 2(b)). The pressure rate was controlled at 0.2 mm/min. After the specimen was compacted to the design height, the compaction is stopped, and the universal testing machine stopped at this position for 1 h to make the deformation of the specimen stable, and then take out the specimen (Figure 2(c)). The diameter and height of the remolded soil specimens were 61.8 mm and 125 mm, respectively. The remolded specimens used for experiments had a dry density of 1.6 g/cm3 and a moisture content of 24%. The formed specimens were saturated using the vacuum saturation method for at least 24 h. The saturation was completed when the degree of saturation reached approximately 95%. The specimens were removed from the container and placed in the triaxial apparatus for the tests.Figure 2
The compaction process (a) Mold. (b) Universal testing machine. (c) Remolded specimen.
(a)(b)(c)


#### 2.3.2. Loading Rate Effect Tests

The loading rate effect experimental scheme is shown in Table2. σn is the net confining pressure (σn=σ3−ua), s is the matric suction (s=ua−uw), σ3 is the confining pressure, ua is the pore air pressure, and uw is the pore water pressure. All experiments were conducted at a constant temperature of approximately 22°C. The experiments were performed through the following steps.(1)
Installation of specimen: first, the ceramic plate on the base of the pressure chamber was saturated, and the air in the water pressure pipeline was exhausted. The saturated specimen was sheathed with a rubber membrane and fixed on the ceramic plate. A permeable stone and a specimen cap were placed on top of the saturated specimen, connected by a rubber membrane. The instrument was installed and checked for leaks, and the instrument reading was cleared.(2)
Isotropic consolidation: consolidation was performed by applying a confining pressure to the target value instantaneously. The water in the specimen was discharged from the ceramic plate. The balance standard of consolidation is that the volume change of the back pressure within 24 h is less than 0.05% of the specimen volume [69].(3)
Matric suction equilibration: the matric suction was applied and controlled through the axis-translation technique. The pore water pressure applied for the unsaturated specimen was 0 kPa; the matric suction was equal to the pore air pressureua. The net confining pressure σn was maintained at a constant value, and the pore air pressure ua was increased, until the target values were reached. When the volume of water drained within 24 h was less than 0.05% of the specimen volume, the matric suction equilibration was reached [67].(4)
Loading: the net confining pressureσn and matric suction s were maintained at constant values. The specimen was loaded at a variable strain rate. The sequence of variable strain rate was: 0.1ε̇⟶10ε̇⟶0.1ε̇⟶10ε̇⟶ε̇⟶0.1ε̇⟶ε̇⟶10ε̇⟶0.1ε̇⟶ε̇⟶10ε̇ (ε̇=0.005%/min).Table 2
Specifications of the viscoplastic tests.
Specimenσn (kPa)s (kPa)R1-11000R1-22000R1-33000R1-44000R2-14000R2-240050R2-3400100R2-4400200R3-11000R3-210050R3-3100100


## 2.1. Materials

Reticulate red clay specimens used for the experiments were sampled from the Yuelu Mountain of Changsha City in China. This red clay can be used as a horizontal (liner) or vertical engineered barrier in landfills, suffering upper load of municipal solid waste or surrounding soil pressure. The physical properties of reticulate red clay are summarized in Table1.Table 1
Physical properties of reticulate red clay.
PropertiesValueWater content (%)24.3Density (g/cm3)1.9Specific gravity2.71Liquid limit (%)40.8Plastic limit (%)22Cohesion (kPa)59Friction angle (°)20.3Effective size (mm)0.047Control size (mm)0.694Optimum moisture content (%)20±1Maximum dry density (g/cm3)1.75±0.05


## 2.2. Test Apparatus

The standard GDS unsaturated triaxial apparatus was adopted in the experiment. The experimental setup is shown in Figure1. The main apparatus consisted of a pressure chamber, a pressure system, and a measurement and collection system. The peripheral pressure, axial pressure, pore air pressure, and pore water pressure could be controlled independently and arbitrarily. The air pressure and water pressure of the specimens were controlled using the perforated plate in the specimen cap and the ceramic plate in the specimen bottom, respectively [67, 68]. The test range and accuracy of GDS unsaturated triaxial apparatus are 1.0 MPa and 0.1 kPa, respectively.Figure 1
The GDS unsaturated triaxial test system.


## 2.3. Test Procedures

### 2.3.1. Specimen Preparation

To avoid the unevenness of undisturbed specimens, remolded specimens were used in this investigation. The specimen was pretreated through air-drying and grinding using a mortar, and the powder was passed through a 2-mm sieve. Subsequently, an amount of soil was sprayed with distilled water and placed in a plastic bag for 24 h for homogenization of the specimen. Subsequently, the soil powder was put into the cylindrical mold (Figure2(a)), applied pressure to the soil through a round pestle rod (Figure 2(a)) by a universal testing machine (Figure 2(b)). The pressure rate was controlled at 0.2 mm/min. After the specimen was compacted to the design height, the compaction is stopped, and the universal testing machine stopped at this position for 1 h to make the deformation of the specimen stable, and then take out the specimen (Figure 2(c)). The diameter and height of the remolded soil specimens were 61.8 mm and 125 mm, respectively. The remolded specimens used for experiments had a dry density of 1.6 g/cm3 and a moisture content of 24%. The formed specimens were saturated using the vacuum saturation method for at least 24 h. The saturation was completed when the degree of saturation reached approximately 95%. The specimens were removed from the container and placed in the triaxial apparatus for the tests.Figure 2
The compaction process (a) Mold. (b) Universal testing machine. (c) Remolded specimen.
(a)(b)(c)


### 2.3.2. Loading Rate Effect Tests

The loading rate effect experimental scheme is shown in Table2. σn is the net confining pressure (σn=σ3−ua), s is the matric suction (s=ua−uw), σ3 is the confining pressure, ua is the pore air pressure, and uw is the pore water pressure. All experiments were conducted at a constant temperature of approximately 22°C. The experiments were performed through the following steps.(1)
Installation of specimen: first, the ceramic plate on the base of the pressure chamber was saturated, and the air in the water pressure pipeline was exhausted. The saturated specimen was sheathed with a rubber membrane and fixed on the ceramic plate. A permeable stone and a specimen cap were placed on top of the saturated specimen, connected by a rubber membrane. The instrument was installed and checked for leaks, and the instrument reading was cleared.(2)
Isotropic consolidation: consolidation was performed by applying a confining pressure to the target value instantaneously. The water in the specimen was discharged from the ceramic plate. The balance standard of consolidation is that the volume change of the back pressure within 24 h is less than 0.05% of the specimen volume [69].(3)
Matric suction equilibration: the matric suction was applied and controlled through the axis-translation technique. The pore water pressure applied for the unsaturated specimen was 0 kPa; the matric suction was equal to the pore air pressureua. The net confining pressure σn was maintained at a constant value, and the pore air pressure ua was increased, until the target values were reached. When the volume of water drained within 24 h was less than 0.05% of the specimen volume, the matric suction equilibration was reached [67].(4)
Loading: the net confining pressureσn and matric suction s were maintained at constant values. The specimen was loaded at a variable strain rate. The sequence of variable strain rate was: 0.1ε̇⟶10ε̇⟶0.1ε̇⟶10ε̇⟶ε̇⟶0.1ε̇⟶ε̇⟶10ε̇⟶0.1ε̇⟶ε̇⟶10ε̇ (ε̇=0.005%/min).Table 2
Specifications of the viscoplastic tests.
Specimenσn (kPa)s (kPa)R1-11000R1-22000R1-33000R1-44000R2-14000R2-240050R2-3400100R2-4400200R3-11000R3-210050R3-3100100


## 2.3.1. Specimen Preparation

To avoid the unevenness of undisturbed specimens, remolded specimens were used in this investigation. The specimen was pretreated through air-drying and grinding using a mortar, and the powder was passed through a 2-mm sieve. Subsequently, an amount of soil was sprayed with distilled water and placed in a plastic bag for 24 h for homogenization of the specimen. Subsequently, the soil powder was put into the cylindrical mold (Figure2(a)), applied pressure to the soil through a round pestle rod (Figure 2(a)) by a universal testing machine (Figure 2(b)). The pressure rate was controlled at 0.2 mm/min. After the specimen was compacted to the design height, the compaction is stopped, and the universal testing machine stopped at this position for 1 h to make the deformation of the specimen stable, and then take out the specimen (Figure 2(c)). The diameter and height of the remolded soil specimens were 61.8 mm and 125 mm, respectively. The remolded specimens used for experiments had a dry density of 1.6 g/cm3 and a moisture content of 24%. The formed specimens were saturated using the vacuum saturation method for at least 24 h. The saturation was completed when the degree of saturation reached approximately 95%. The specimens were removed from the container and placed in the triaxial apparatus for the tests.Figure 2
The compaction process (a) Mold. (b) Universal testing machine. (c) Remolded specimen.
(a)(b)(c)


## 2.3.2. Loading Rate Effect Tests

The loading rate effect experimental scheme is shown in Table2. σn is the net confining pressure (σn=σ3−ua), s is the matric suction (s=ua−uw), σ3 is the confining pressure, ua is the pore air pressure, and uw is the pore water pressure. All experiments were conducted at a constant temperature of approximately 22°C. The experiments were performed through the following steps.(1)
Installation of specimen: first, the ceramic plate on the base of the pressure chamber was saturated, and the air in the water pressure pipeline was exhausted. The saturated specimen was sheathed with a rubber membrane and fixed on the ceramic plate. A permeable stone and a specimen cap were placed on top of the saturated specimen, connected by a rubber membrane. The instrument was installed and checked for leaks, and the instrument reading was cleared.(2)
Isotropic consolidation: consolidation was performed by applying a confining pressure to the target value instantaneously. The water in the specimen was discharged from the ceramic plate. The balance standard of consolidation is that the volume change of the back pressure within 24 h is less than 0.05% of the specimen volume [69].(3)
Matric suction equilibration: the matric suction was applied and controlled through the axis-translation technique. The pore water pressure applied for the unsaturated specimen was 0 kPa; the matric suction was equal to the pore air pressureua. The net confining pressure σn was maintained at a constant value, and the pore air pressure ua was increased, until the target values were reached. When the volume of water drained within 24 h was less than 0.05% of the specimen volume, the matric suction equilibration was reached [67].(4)
Loading: the net confining pressureσn and matric suction s were maintained at constant values. The specimen was loaded at a variable strain rate. The sequence of variable strain rate was: 0.1ε̇⟶10ε̇⟶0.1ε̇⟶10ε̇⟶ε̇⟶0.1ε̇⟶ε̇⟶10ε̇⟶0.1ε̇⟶ε̇⟶10ε̇ (ε̇=0.005%/min).Table 2
Specifications of the viscoplastic tests.
Specimenσn (kPa)s (kPa)R1-11000R1-22000R1-33000R1-44000R2-14000R2-240050R2-3400100R2-4400200R3-11000R3-210050R3-3100100


## 3. Results and Discussion

### 3.1. Viscoplastic Parameterβ Value

Based on the viscoplastic parameterβ related to the loading rate effect, proposed by Li (2012) [70], the viscoplasticity of reticulate red clay was analyzed in this study. Li (2012) [70] demonstrated that the stress change is always proportional to strain rate (Figure 3) as follows:(1)∆qaqa=qa2−qa1qa1=βlogεa2iṙεa1iṙ,where qa1, qa2, εa1iṙ, and εa2iṙ are the axial stresses and irreversible axial strain rates before and after a change in the strain rate, respectively, and β is the viscoplastic parameter.Figure 3
Method of obtaining∆qa, qa1, qa2, ε̇a1, and ε̇a2.Li (2012) [70] analyzed the experiment results and found that the total strain rate has the following relationship with the irreversible part:(2)εa1iṙεa2iṙ≅εa2̇εa1̇,where εa1̇ and εa2̇ are the total axial strain rates before and after a change in the strain rate.Theβ value was calculated using the following equation.(3)∆qaqa=qa2−qa1qa1=βlogεa2̇εa1̇.The specific method for obtaining∆qa, qa1, qa2, εa1̇, and εa2̇ is shown in Figure 3.


### 3.2. Analysis of Viscoplastic Test Results

From the viscoplastic test data of reticulate red clay, the relationship curves of the deviator stress (σ1-σ3) and the axial strain (εa) of the soil specimens at all levels of suction and net confining pressure were obtained as shown in Figures 4 and 5. Figure 6 shows the isokinetic viscosity diagram.Figure 4
(σ1-σ3)–εa summary curves (s=0kPa).Figure 5
(σ1-σ3)–εa summary curves (σn=400kPa).Figure 6
Isokinetic viscosity diagram.It is observed in Figures4 and 5 that under the triaxial test conditions, both the saturated and unsaturated remolded reticulate red clay specimens show obvious loading rate effects during loading. That is, the stress–strain curve mutates upward when the loading rate suddenly increases, and the stress–strain curve mutates downward when the loading rate suddenly decreases. In the test range, the stress–strain curves of reticulate red clay with different saturations are all in isotach. It is also observed that under the same matric suction level, the corresponding stiffness of reticulate red clay under the same strain was greater with greater net confining pressure. At the same net confining pressure level, the corresponding stiffness of reticulate red clay under the same strain was greater with greater matric suction. The stiffness of the specimen was evidently improved with increased matric suction. Thus, in the process of rainfall, the matric suction in reticulate red clay decreases, and the stiffness of the soil body decreases gradually, because reticulate red clay absorbs water and moves from an unsaturated state to a saturated state.Comparing the two areas indicated by the circles and rectangles in Figures4 and 5, the process of the strain rate is from 10ε̇⟶ε̇⟶0.1ε̇ (ε̇=0.005%/min) in the area covered by the circle, and the process of the strain rate is from 10ε̇⟶0.1ε̇ (ε̇=0.005%/min) in the area covered by the rectangle. It is found that the slope of the stress–strain curve corresponding to the strain rate 0.1ε̇ in the area covered by the circle is smaller than that in the area covered by the rectangle. The loading sequence has an effect on the stress–strain change process.As observed in Figure6, the stress–strain relationship mutates correspondingly when the strain rate of the specimen changes abruptly, and this mutation is permanent rather than instantaneous. As loading proceeds, the stress–strain relationship is closer to the stress–strain relationship of the strain rate after mutation, until the strain rate changes again. During testing, the stress–strain curves of specimens at different loading stages with the same strain rate can be normalized into the same curve. Thus, under monotonic loading, the effective stress can be indicated as a single-value function of the irrecoverable strain and its strain rate.


### 3.3. Calculation and Analysis of Viscoplastic Parameterβ

The viscoplastic parameterβ value of reticulate red clay in different net confining pressure and matric suction conditions is shown in Figures 7–9.Figure 7
β value of reticulate red clay with different net confining pressure (s=0kPa).Figure 8
β value of reticulate red clay with different matric suction (σn=400kPa).Figure 9
β value of reticulate red clay with different matric suction (σn=100kPa).It is observed from Figures7, 8, and 9 that even under different test conditions, there is a linear relationship between (qa2-qa1)/qa1~log (εa2̇/εa1̇) in the process of testing. This shows that the solution of the viscosity parameter β of reticulate red clay in different test conditions is satisfied in Eq. (3). In addition, it is observed in Figure 7 that under the same water content and saturation conditions, the viscoplastic parameter β value of the saturated specimen increases with increasing net confining pressure; that is, the viscoplasticity of reticulate red clay under the condition of high net confining pressure is stronger than under low net confining pressure. It is also observed from Figures 8 and 9 that under the condition of constant net confining pressure, the viscoplastic parameter β value of the specimen is greater when a greater matric suction is applied to the specimen, indicating that reticulate red clay has a more obvious viscoplasticity when the matric suction is greater.According to Eq. (3) and the extraction method for each parameter in Figure 3, the viscoplastic parameter β value of reticulate red clay and the corresponding linear regression coefficient under different test conditions are shown in Table 3. From Table 3, the change in the viscoplastic parameter β in each group test can be understood more readily. The conditions of each test are different, but the linear regression coefficients of the viscoplastic parameter β values for each test are high, further illustrating that Eq. (3) is suitable for solving the viscoplastic parameter β of reticulate red clay under different experimental conditions.Table 3
Viscoplastic parameterβ values under different test conditions.
No.σn (kPa)s (kPa)Viscoplastic parameterβRegression coefficientsR1-110000.0880.941R1-220000.0980.920R1-330000.1050.928R1-440000.1150.945R2-140000.1150.945R2-2400500.1220.929R2-34001000.1290.991R2-44002000.1430.966R3-110000.0880.941R3-2100500.0910.967R3-31001000.0970.950The relationship between theβ value of reticulate red clay, net confining pressure, and matric suction are shown in Figures 10 and 11.Figure 10
Relationship betweenβ value of reticulate red clay and net confining pressureFigure 11
Relationship betweenβ value of reticulate red clay and matric suction.Figure10 shows that there is a linear relationship between the viscoplastic parameter β of reticulate red clay and the net confining pressure. The fitting equation for the net confining pressure and viscoplastic parameter β can be obtained from Figure 10.Whens=0kPa,(4)β=8.823×10−5×σ3−μa+0.07936.Figure11 shows that the viscoplastic parameter β of unsaturated reticulate red clay increases with increasing net confining pressure. There is a linear relationship between the viscoplastic parameter β of reticulate red clay and the matric suction. The fitting equation for the matric suction and viscoplastic parameter β can be obtained from Figure 11.Whenσn=100kPa,(5)β=8.54×10−5×s+0.08765.Whenσn=400kPa,(6)β=1.3953×10−4×s+0.115.To verify these conclusions, the R2-2, R2-3, R3-2, and R3-3 test data were processed. We can obtain the relationship (qa2-qa1)/qa1~log (εa2̇/εa1̇) as shown in Figures 12 and 13.Figure 12
β value of reticulate red clay with different confining pressure (s=50kPa).Figure 13
β value of reticulate red clay with different confining pressure (s=100kPa).It is observed in Figures12 and 13 that under constant matric suction, the β value of the specimen increases with increasing net confining pressure. In other words, the viscoplasticity of reticulate red clay under the condition of high net confining pressure is stronger than under low net confining pressure, thus validating the test results.


## 3.1. Viscoplastic Parameterβ Value

Based on the viscoplastic parameterβ related to the loading rate effect, proposed by Li (2012) [70], the viscoplasticity of reticulate red clay was analyzed in this study. Li (2012) [70] demonstrated that the stress change is always proportional to strain rate (Figure 3) as follows:(1)∆qaqa=qa2−qa1qa1=βlogεa2iṙεa1iṙ,where qa1, qa2, εa1iṙ, and εa2iṙ are the axial stresses and irreversible axial strain rates before and after a change in the strain rate, respectively, and β is the viscoplastic parameter.Figure 3
Method of obtaining∆qa, qa1, qa2, ε̇a1, and ε̇a2.Li (2012) [70] analyzed the experiment results and found that the total strain rate has the following relationship with the irreversible part:(2)εa1iṙεa2iṙ≅εa2̇εa1̇,where εa1̇ and εa2̇ are the total axial strain rates before and after a change in the strain rate.Theβ value was calculated using the following equation.(3)∆qaqa=qa2−qa1qa1=βlogεa2̇εa1̇.The specific method for obtaining∆qa, qa1, qa2, εa1̇, and εa2̇ is shown in Figure 3.


## 3.2. Analysis of Viscoplastic Test Results

From the viscoplastic test data of reticulate red clay, the relationship curves of the deviator stress (σ1-σ3) and the axial strain (εa) of the soil specimens at all levels of suction and net confining pressure were obtained as shown in Figures 4 and 5. Figure 6 shows the isokinetic viscosity diagram.Figure 4
(σ1-σ3)–εa summary curves (s=0kPa).Figure 5
(σ1-σ3)–εa summary curves (σn=400kPa).Figure 6
Isokinetic viscosity diagram.It is observed in Figures4 and 5 that under the triaxial test conditions, both the saturated and unsaturated remolded reticulate red clay specimens show obvious loading rate effects during loading. That is, the stress–strain curve mutates upward when the loading rate suddenly increases, and the stress–strain curve mutates downward when the loading rate suddenly decreases. In the test range, the stress–strain curves of reticulate red clay with different saturations are all in isotach. It is also observed that under the same matric suction level, the corresponding stiffness of reticulate red clay under the same strain was greater with greater net confining pressure. At the same net confining pressure level, the corresponding stiffness of reticulate red clay under the same strain was greater with greater matric suction. The stiffness of the specimen was evidently improved with increased matric suction. Thus, in the process of rainfall, the matric suction in reticulate red clay decreases, and the stiffness of the soil body decreases gradually, because reticulate red clay absorbs water and moves from an unsaturated state to a saturated state.Comparing the two areas indicated by the circles and rectangles in Figures4 and 5, the process of the strain rate is from 10ε̇⟶ε̇⟶0.1ε̇ (ε̇=0.005%/min) in the area covered by the circle, and the process of the strain rate is from 10ε̇⟶0.1ε̇ (ε̇=0.005%/min) in the area covered by the rectangle. It is found that the slope of the stress–strain curve corresponding to the strain rate 0.1ε̇ in the area covered by the circle is smaller than that in the area covered by the rectangle. The loading sequence has an effect on the stress–strain change process.As observed in Figure6, the stress–strain relationship mutates correspondingly when the strain rate of the specimen changes abruptly, and this mutation is permanent rather than instantaneous. As loading proceeds, the stress–strain relationship is closer to the stress–strain relationship of the strain rate after mutation, until the strain rate changes again. During testing, the stress–strain curves of specimens at different loading stages with the same strain rate can be normalized into the same curve. Thus, under monotonic loading, the effective stress can be indicated as a single-value function of the irrecoverable strain and its strain rate.


## 3.3. Calculation and Analysis of Viscoplastic Parameterβ

The viscoplastic parameterβ value of reticulate red clay in different net confining pressure and matric suction conditions is shown in Figures 7–9.Figure 7
β value of reticulate red clay with different net confining pressure (s=0kPa).Figure 8
β value of reticulate red clay with different matric suction (σn=400kPa).Figure 9
β value of reticulate red clay with different matric suction (σn=100kPa).It is observed from Figures7, 8, and 9 that even under different test conditions, there is a linear relationship between (qa2-qa1)/qa1~log (εa2̇/εa1̇) in the process of testing. This shows that the solution of the viscosity parameter β of reticulate red clay in different test conditions is satisfied in Eq. (3). In addition, it is observed in Figure 7 that under the same water content and saturation conditions, the viscoplastic parameter β value of the saturated specimen increases with increasing net confining pressure; that is, the viscoplasticity of reticulate red clay under the condition of high net confining pressure is stronger than under low net confining pressure. It is also observed from Figures 8 and 9 that under the condition of constant net confining pressure, the viscoplastic parameter β value of the specimen is greater when a greater matric suction is applied to the specimen, indicating that reticulate red clay has a more obvious viscoplasticity when the matric suction is greater.According to Eq. (3) and the extraction method for each parameter in Figure 3, the viscoplastic parameter β value of reticulate red clay and the corresponding linear regression coefficient under different test conditions are shown in Table 3. From Table 3, the change in the viscoplastic parameter β in each group test can be understood more readily. The conditions of each test are different, but the linear regression coefficients of the viscoplastic parameter β values for each test are high, further illustrating that Eq. (3) is suitable for solving the viscoplastic parameter β of reticulate red clay under different experimental conditions.Table 3
Viscoplastic parameterβ values under different test conditions.
No.σn (kPa)s (kPa)Viscoplastic parameterβRegression coefficientsR1-110000.0880.941R1-220000.0980.920R1-330000.1050.928R1-440000.1150.945R2-140000.1150.945R2-2400500.1220.929R2-34001000.1290.991R2-44002000.1430.966R3-110000.0880.941R3-2100500.0910.967R3-31001000.0970.950The relationship between theβ value of reticulate red clay, net confining pressure, and matric suction are shown in Figures 10 and 11.Figure 10
Relationship betweenβ value of reticulate red clay and net confining pressureFigure 11
Relationship betweenβ value of reticulate red clay and matric suction.Figure10 shows that there is a linear relationship between the viscoplastic parameter β of reticulate red clay and the net confining pressure. The fitting equation for the net confining pressure and viscoplastic parameter β can be obtained from Figure 10.Whens=0kPa,(4)β=8.823×10−5×σ3−μa+0.07936.Figure11 shows that the viscoplastic parameter β of unsaturated reticulate red clay increases with increasing net confining pressure. There is a linear relationship between the viscoplastic parameter β of reticulate red clay and the matric suction. The fitting equation for the matric suction and viscoplastic parameter β can be obtained from Figure 11.Whenσn=100kPa,(5)β=8.54×10−5×s+0.08765.Whenσn=400kPa,(6)β=1.3953×10−4×s+0.115.To verify these conclusions, the R2-2, R2-3, R3-2, and R3-3 test data were processed. We can obtain the relationship (qa2-qa1)/qa1~log (εa2̇/εa1̇) as shown in Figures 12 and 13.Figure 12
β value of reticulate red clay with different confining pressure (s=50kPa).Figure 13
β value of reticulate red clay with different confining pressure (s=100kPa).It is observed in Figures12 and 13 that under constant matric suction, the β value of the specimen increases with increasing net confining pressure. In other words, the viscoplasticity of reticulate red clay under the condition of high net confining pressure is stronger than under low net confining pressure, thus validating the test results.


## 4. Conclusions

Owing to their low permeability, self-healing by swelling, low cost, and high adsorption capacity, clays such as red clay can be used in seepage control systems in contaminated sites. Triaxial experiments were performed on a reticulate red clay in this study. It was found that unsaturated reticulate red clay has an evident viscoplastic nature, which is affected by the matric suction and net confining pressure. The following are the conclusions of this study.Saturated and unsaturated reticulate red clay specimens show an obvious loading rate effect during loading under the triaxial test conditions. This study demonstrated that reticulate red clay under different saturation and different net confining pressure has similar viscoplasticity during loading. The stress–strain curves were isochronic. For the same matric suction level, the corresponding stiffness of reticulate red clay under the same strain was greater with greater net confining pressure. For the same net confining pressure level, the corresponding stiffness of reticulate red clay under the same strain was greater with greater matric suction. In the loading tests with variable strain rates, the stress–strain relationships of reticulate red clay with different saturations were affected by the changing loading sequence. Based on the obtainedβ value of reticulate red clay and the corresponding linear regression coefficient, Eq. (3) is suitable for obtaining the β values of reticulate red clay under different experimental conditions. The viscoplastic parameter β of the specimens increases with increasing net confining pressure under the same water content and saturation conditions. There is a linear relationship between the viscoplastic parameter β and the net confining pressure. The viscoplastic parameter β of the specimens increases with increasing matric suction under the condition of constant net confining pressure. There is also a linear relationship between the viscoplastic parameter β and the matric suction. Thus, the research provides significant insights for analyzing the effect of loading rate on the viscoplasticity of unsaturated reticulate red clay. These results may be beneficial in the design of compacted clay barriers in landfills.



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