# Research on Soft Rocks for the Construction of Roadbeds for High-Speed Railroad: Effect of Water Soaking Environment

Authors: Xiangdong Zhang; Jie Geng; Yuebo Xu; Zhongchao Zhou; Shuai Pang
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

The strength of the roadbed composed of soft rock decreases following water immersion. Cement slurry is mixed with a soft rock to strengthen the soft rock roadbed to address this problem. The uniaxial compressive strength was determined, and the triaxial compression tests were conducted to analyze muddy sandstones mixed with different amounts of the cement slurry of the same composition. Some of the cured samples were soaked in water, and the samples were analyzed. The results were compared with the results obtained by analyzing unsoaked samples. The MIDAS/GTS NX software was used to develop a three-dimensional finite model to simulate the settlement patterns of roadbeds developed in the presence of natural water, saturated water, and muddy sandstone reinforcements. The experimental results have been presented and discussed. (1) When the filling rate corresponding to the cement slurry is 32%, the uniaxial compressive strength of muddy sandstone containing natural water reaches 3.32 MPa, which is approximately 5 times higher than the strength of muddy sandstone devoid of cement slurry. (2) The water absorption energy of the reinforced muddy sandstone was analyzed from the perspective of saturated water content. The water plugging effect observed after the addition of the cement slurry was studied, and the equations defining uniaxial compressive strength, elastic modulus, and free saturated water content were established. (3) An increase in the content of the cement slurry admixture resulted in a change in the nature of the partial stress–strain curves generated for muddy sandstone. The curve change from strain-hardening to strain-softening type and the deformation modulus and extent of cohesion realized increased exponentially with an increase in the cement slurry filling rate. A positive linear correlation was observed between the internal friction angle and the cement slurry filling rate. (4) An increase in the cement slurry filling rate corresponding to the saturated muddy sandstone resulted in an exponential decrease in the settlement deformation value. The vertical displacement decreased to 0.3497 mm when the grouting rate reached 32% under conditions of saturation. The deformation tended to converge and stabilize, indicating that the introduction of the admixture consisting of the cement slurry could help in effectively controlling the property of settlement deformation observed in the fully weathered muddy sandstone roadbed. The results helped in the scientific evaluation of the reinforcement effect. The reported results also helped develop a theoretical basis for the development of soft foundation reinforcement.


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## Body

## 1. Introduction

Hydrophilic mineral components such as montmorillonite and illite are widely found in muddy sandstones. Expansion stress in rocks is induced when the mineral components absorb water. When the effect of expansion stress is greater than the effect of confining stress, the fissures present inside the rock gradually grow. The cracks expand and grow with the growth of the fissures. This eventually causes the rock to soften and disintegrate. Under these conditions, the mechanical properties of the rock significantly deteriorate. The long-term stability of the soft rock system forming the foundation of roadbeds for the high-speed railway is negatively affected as creep deformation is induced in rocks. The process of deformation is accelerated in the presence of water. This results in settlement of soft rocks forming the foundation of high-fill embankments. Yang et al. [1] and Wang et al. [2] reported that creep deformation in a rock mass could be induced, and the process could be accelerated in the presence of water, resulting in excessive settlement of soft rock subgrade found in high embankments. This significantly harms the long-term stability of the high-speed railway subgrade. Foundation reinforcements are being widely studied by researchers at present [3–6]. Rabab’Ah et al. [7] added glass fibers to the swelling foundation soil to improve the strength of the roadbed and reduce the free swelling value of the foundation soil. Jia et al. [8] found that after ramming, the moisture content, dry density, and specific penetration resistance of the topsoil improved significantly, and a significant reinforcement effect was exerted on the effective reinforcement zone. Huang et al. [9] developed a new type of gelled composite material that was characterized by a dense internal structure of roadbeds composed of cured saline soil. The extents of foundation displacements, accelerations, superstatic pore water pressures, and damage levels realized were significantly low. Ang [10] constructed a real-time monitoring system and information feedback system to study the slurry reinforcement process associated with the multiperformance high-speed railway roadbeds. They proposed new methods to realize the slurry injection process and confirmed that the information-based slurry reinforcement technology meets the settlement control standards of high-speed railway roadbeds. Zhang and Wu [11] carried out field tests to address the problem of settlement observed in high-speed railway roadbeds in operation to study the mechanism associated with grouting reinforcement. They also studied the mode, effect of the reinforcement tube location, and influence of pore water pressure. Lou [12] developed a method combining the rotary piling and cuff pipe grouting methods to address the problem of settlement associated with the use of the high-speed railroad. The effectiveness of the reinforcement technology was verified by analyzing the results obtained during the monitoring of the settlements. Fu et al. [13] conducted a field test on the composite structure of pile-rafts and studied the settlement deformation properties and mechanical characteristics of the pile-raft and foundations. The standards set for the ballastless track formed on soft-soil-based roadbeds were met using the reinforcement methods. Shang and Xu [14] analyzed the results obtained during the study of the cement-modified expanded-soil roadbed that was used in developing the beds in the Sanmenxia–Jingmen section of the Haolejian–Ji’an heavy-haul railroad and carried out field excitation tests (number of vibrations: ≥ 4 million). They reported that the improved expansion soil (containing 3–5% cement admixture) could be efficiently used as the sub-bed layer to form the embankment fill to meet the dynamic stability requirements.Based on the test results, the strength and deformation characteristics of the cement slurry-mixed muddy sandstone were quantitatively analyzed, and the evolution of the basic mechanical parameters associated with the reinforced muddy sandstone samples with an increase in the cement slurry filling rate was studied. The evolution equation was established, and a three-dimensional finite element model was built using MIDAS/GTS NX to simulate the settlement conditions for natural, saturated, and reinforced muddy sandstone. The results helped in the scientific evaluation of the reinforcement effect and the development of a theoretical basis for the development of soft foundation reinforcement.


## 2. Experimental Scheme

### 2.1. Raw Materials and Reagents

The muddy sandstone specimens used to conduct the test were obtained from the Niu Heliang High-Speed Railway Station. The relevant data on the muddy sandstone cores (after reworking) are listed in Table1.Table 1
Detailed data obtained for the reprocessed muddy sandstone cores.
Density (g/cm3)Natural watercontent (%)Saturated watercontent (%)Particle specificgravitySpecimen porosityratioSpecimen porosity (%)1.886.6814.242.650.5134The “Fuxin Yingshan” cement (standard: 42.5,ρc = 3.00 g/cm3) was used for the tests. The tests were carried out based on the guidelines presented in the Specification for Proportional Design of Cement Soil (JGJ/T233-2011) [15] and the standards specified for geotechnical tests (GB/T50123-2019) [16]. The test samples were prepared following the relevant guidelines, and the water-cement (W/C) ratio in the prepared cement slurry was set at 0.8 (ρc = 1.59 g/cm3). Depending on the porosity of the specimens, the cement slurry filling rates were set at 0%, 8%, 16%, 24%, and 32%. The cement mass ratios were 0%, 2.6%, 5.2%, 7.8%, and 10.4%, respectively. The detailed fitting ratios are listed in Table 2.Table 2
Detailed mix proportions of a single specimen.
Slurry filling rate (%)Cliff sample quality (g)Cement slurry quality (g)Total mass of specimen (g)0180.500mw = 0180.50mc = 08180.504.69mw = 2.08185.19mc = 2.6116180.509.39mw = 4.18189.89mc = 5.2124180.5014.08mw = 6.26194.58mc = 7.8232180.5018.77mw = 8.34199.27mc = 10.43


### 2.2. Sample Preparation

In order to maintain the homogeneity of the test results, the dry admixture of muddy sandstone was fixed at 1.88 g/cm3 when preparing the specimens, and the specimen size was 39.1 mm × 80 mm. During the process of sample preparation, to ensure the uniformity of the specimen, the specimens were prepared using a three-flap saturator. Muddy sandstone, water, and cement slurry were thoroughly mixed, and the mixture was loaded onto the saturator in 5 layers. Each layer was tamped 20 times, and each layer was scraped to form a flat surface after tamping. The specimens were prepared and stored for 1 d. Following this, the samples were stored at room temperature under humid conditions for 7 d. The specimen preparation process is shown in Figure 1. Subsequently, the specimens were removed from the molds and partially immersed in water for 48 h. The specimens devoid of cement paste were prepared as saturated specimens by directly adding water. The detailed test fits are listed in Table 3.Figure 1
Sample preparation process.Table 3
Specimen details.
Specimen numberSlurry filling rate (%)Size (mm)Quality (g)Density (g·cm−3)Natural moisture content (%)Saturated water content (%)S1039.1 × 79.6180.501.886.6814.24S2839.1 × 79.5185.191.936.6613.90S31639.1 × 79.9189.891.986.6713.18S42439.1 × 79.4194.582.036.6812.23S53239.1 × 79.8199.272.086.6411.20


### 2.3. Model Construction and Basic Parameters

The muddy sandstone in the roadbed was replaced with the cement slurry admixture during the construction of the model to study the effect of the settlement. The process was conducted following the construction of the muddy sandstone roadbed prepared using cement slurry admixtures. Numerical simulations were carried out to analyze the roadbed under conditions of different cement slurry filling rates. Assuming that each layer of soil is continuous and isotropic, the influence of permeability on the deformation property of the foundation soil is ignored. The upper structure adopts the Mohr–Coulomb primary structure [17], and the argillaceous sandstone adopts the Burgers creep primary structure [18]. The effects of static loads on the roadbed and viscous boundaries were considered during the simulation process. The size of the three-dimensional finite element model has been presented: the top width of the subgrade is 17.2 m, the maximum filling height is 16.0 m, the slope gradient is 1 : 1, and the thickness of the foundation bed is 2.70 m. The upper part of the bed consists of a concrete foundation, which is 1.67 m thick, and the thickness of graded crushed stone is 0.58 m. The bottom range of the foundation is filled with group AB soil (thickness: 0.45 m), and the bottom of the foundation bed is filled with group ABC soil. The base is filled with 8% cement-graded gravel. The mechanical parameters are listed in Table 4.Table 4
Material parameters corresponding to the subgrade model.
NameThickness (m)Bulk density (kN·m−3)Elastic modulus (MPa)Poisson’s ratioCohesion (kPa)Angle of internal friction (°)C35 concrete0.524.202.8 × 1040.2——C25 concrete1.1724.003.15 × 1040.2——Graded gravel0.5818.005000.35——Group AB soil0.4520.601600.343025Group ABC soil1019.801000.353530Group AB soil mixed with 8% cement3.321.403000.323226.5Fully weathered muddy sandstone1018.8042.060.3208.3926.87Muddy sandstone2021.501.05 × 1040.25896039.5The hexahedral mesh generation method was used to generate the two-dimensional mesh, and the mesh was expanded along theY-axis direction to form a three-dimensional system. The expanded length was 70 m. The cross section of the subgrade model is presented in Figure 2.Figure 2
Cross section of subgrade model.


### 2.4. Uniaxial Compressive Strength Test

The uniaxial compressive strengths of the completely weathered muddy sandstones were determined using a rock triaxial tester. The amount of deformation per unit time was controlled using the test system, and the deformation rate was set to 1 mm/min. The experiment was aborted once the specimen was damaged (Figure3), and the stress–strain curve was generated using the data acquisition system (Figure 4).Figure 3
Failure mode corresponding to the uniaxial compressive specimens.Figure 4
System used for the uniaxial compressive strength test.


### 2.5. Triaxial Compression Test

The triaxial compression test was carried out using the GDS triaxial testing machine. Only the damage characteristics of the specimen in the conventional triaxial case were considered. The applied circumferential pressure was 90 kPa, and the deformation control method was used for loading. The deformation rate was set at 0.5 mm/min. The experiment was stopped once the specimen was damaged (Figure5) or the axial strain exceeded 3% (the loading time was approximately 5 min). The bias stress–strain curve was generated using the data acquisition system integrated into the software (Figure 6).Figure 5
Failure state of the triaxial compression test specimen.Figure 6
Setup used for the triaxial compression test.


## 2.1. Raw Materials and Reagents

The muddy sandstone specimens used to conduct the test were obtained from the Niu Heliang High-Speed Railway Station. The relevant data on the muddy sandstone cores (after reworking) are listed in Table1.Table 1
Detailed data obtained for the reprocessed muddy sandstone cores.
Density (g/cm3)Natural watercontent (%)Saturated watercontent (%)Particle specificgravitySpecimen porosityratioSpecimen porosity (%)1.886.6814.242.650.5134The “Fuxin Yingshan” cement (standard: 42.5,ρc = 3.00 g/cm3) was used for the tests. The tests were carried out based on the guidelines presented in the Specification for Proportional Design of Cement Soil (JGJ/T233-2011) [15] and the standards specified for geotechnical tests (GB/T50123-2019) [16]. The test samples were prepared following the relevant guidelines, and the water-cement (W/C) ratio in the prepared cement slurry was set at 0.8 (ρc = 1.59 g/cm3). Depending on the porosity of the specimens, the cement slurry filling rates were set at 0%, 8%, 16%, 24%, and 32%. The cement mass ratios were 0%, 2.6%, 5.2%, 7.8%, and 10.4%, respectively. The detailed fitting ratios are listed in Table 2.Table 2
Detailed mix proportions of a single specimen.
Slurry filling rate (%)Cliff sample quality (g)Cement slurry quality (g)Total mass of specimen (g)0180.500mw = 0180.50mc = 08180.504.69mw = 2.08185.19mc = 2.6116180.509.39mw = 4.18189.89mc = 5.2124180.5014.08mw = 6.26194.58mc = 7.8232180.5018.77mw = 8.34199.27mc = 10.43


## 2.2. Sample Preparation

In order to maintain the homogeneity of the test results, the dry admixture of muddy sandstone was fixed at 1.88 g/cm3 when preparing the specimens, and the specimen size was 39.1 mm × 80 mm. During the process of sample preparation, to ensure the uniformity of the specimen, the specimens were prepared using a three-flap saturator. Muddy sandstone, water, and cement slurry were thoroughly mixed, and the mixture was loaded onto the saturator in 5 layers. Each layer was tamped 20 times, and each layer was scraped to form a flat surface after tamping. The specimens were prepared and stored for 1 d. Following this, the samples were stored at room temperature under humid conditions for 7 d. The specimen preparation process is shown in Figure 1. Subsequently, the specimens were removed from the molds and partially immersed in water for 48 h. The specimens devoid of cement paste were prepared as saturated specimens by directly adding water. The detailed test fits are listed in Table 3.Figure 1
Sample preparation process.Table 3
Specimen details.
Specimen numberSlurry filling rate (%)Size (mm)Quality (g)Density (g·cm−3)Natural moisture content (%)Saturated water content (%)S1039.1 × 79.6180.501.886.6814.24S2839.1 × 79.5185.191.936.6613.90S31639.1 × 79.9189.891.986.6713.18S42439.1 × 79.4194.582.036.6812.23S53239.1 × 79.8199.272.086.6411.20


## 2.3. Model Construction and Basic Parameters

The muddy sandstone in the roadbed was replaced with the cement slurry admixture during the construction of the model to study the effect of the settlement. The process was conducted following the construction of the muddy sandstone roadbed prepared using cement slurry admixtures. Numerical simulations were carried out to analyze the roadbed under conditions of different cement slurry filling rates. Assuming that each layer of soil is continuous and isotropic, the influence of permeability on the deformation property of the foundation soil is ignored. The upper structure adopts the Mohr–Coulomb primary structure [17], and the argillaceous sandstone adopts the Burgers creep primary structure [18]. The effects of static loads on the roadbed and viscous boundaries were considered during the simulation process. The size of the three-dimensional finite element model has been presented: the top width of the subgrade is 17.2 m, the maximum filling height is 16.0 m, the slope gradient is 1 : 1, and the thickness of the foundation bed is 2.70 m. The upper part of the bed consists of a concrete foundation, which is 1.67 m thick, and the thickness of graded crushed stone is 0.58 m. The bottom range of the foundation is filled with group AB soil (thickness: 0.45 m), and the bottom of the foundation bed is filled with group ABC soil. The base is filled with 8% cement-graded gravel. The mechanical parameters are listed in Table 4.Table 4
Material parameters corresponding to the subgrade model.
NameThickness (m)Bulk density (kN·m−3)Elastic modulus (MPa)Poisson’s ratioCohesion (kPa)Angle of internal friction (°)C35 concrete0.524.202.8 × 1040.2——C25 concrete1.1724.003.15 × 1040.2——Graded gravel0.5818.005000.35——Group AB soil0.4520.601600.343025Group ABC soil1019.801000.353530Group AB soil mixed with 8% cement3.321.403000.323226.5Fully weathered muddy sandstone1018.8042.060.3208.3926.87Muddy sandstone2021.501.05 × 1040.25896039.5The hexahedral mesh generation method was used to generate the two-dimensional mesh, and the mesh was expanded along theY-axis direction to form a three-dimensional system. The expanded length was 70 m. The cross section of the subgrade model is presented in Figure 2.Figure 2
Cross section of subgrade model.


## 2.4. Uniaxial Compressive Strength Test

The uniaxial compressive strengths of the completely weathered muddy sandstones were determined using a rock triaxial tester. The amount of deformation per unit time was controlled using the test system, and the deformation rate was set to 1 mm/min. The experiment was aborted once the specimen was damaged (Figure3), and the stress–strain curve was generated using the data acquisition system (Figure 4).Figure 3
Failure mode corresponding to the uniaxial compressive specimens.Figure 4
System used for the uniaxial compressive strength test.


## 2.5. Triaxial Compression Test

The triaxial compression test was carried out using the GDS triaxial testing machine. Only the damage characteristics of the specimen in the conventional triaxial case were considered. The applied circumferential pressure was 90 kPa, and the deformation control method was used for loading. The deformation rate was set at 0.5 mm/min. The experiment was stopped once the specimen was damaged (Figure5) or the axial strain exceeded 3% (the loading time was approximately 5 min). The bias stress–strain curve was generated using the data acquisition system integrated into the software (Figure 6).Figure 5
Failure state of the triaxial compression test specimen.Figure 6
Setup used for the triaxial compression test.


## 3. Results and Analysis

### 3.1. Uniaxial Compressive Strength Test: Results

The uniaxial compressive strength of the muddy sandstone sample was determined using a rock testing machine to obtain the stress–strain curves (Figure7).Figure 7
Stress–strain curve generated by analyzing the uniaxial compressive strength of argillaceous sandstone. (a) Natural water content; (b) saturated water content.
(a)(b)


#### 3.1.1. Relationship between the Cement Slurry Filling Rate and the Uniaxial Compressive Strength

Based on the stress–strain curves generated by conducting the uniaxial compressive strength tests (Figure7), the changes in the uniaxial compressive strength of the muddy sandstone samples were studied under conditions of varying cement slurry filling rates. The relationship between the cement slurry filling rate and the uniaxial compressive strength was plotted based on the test curve (Figure 8). The uniaxial compressive strengths of the rock specimens in the presence of natural water and under the saturated states are listed in Table 5.Figure 8
Relationship between the filling ratio and the uniaxial compressive strength.It can be seen from Table5 that the uniaxial compressive strength of the rock gradually increases with an increase in the content of the cement paste admixture. When the cement slurry filling rate reached 32%, the uniaxial compressive strength of muddy sandstone reached 3.32 MPa in the presence of natural water. This was approximately 5 times higher than the strength recorded in the absence of cement slurry. This indicated that the use of cement slurry could improve the peak strength of muddy sandstone. The uniaxial compressive strengths of muddy sandstone recorded under natural water-bearing and saturated states were compared, and it was observed that the degrees of loss of uniaxial compressive strength were different for these two states. The losses in strength were 38.23%, 24.06%, and 10.52% for 0%, 16%, and 32% cement slurry fillings, respectively. This indicated that an increase in the cement slurry content resulted in a deterioration of the softening effect of water on the rock. An increase in the content of the cement slurry admixture resulted in the production of hydration products that formed bonds with the sandstone particles, generating links between the particles present in the muddy sandstone samples. The pores in the rocks were filled with hydration products, the number of internal cracks decreased, and the density of the rock increased, resulting in improved strength.As shown in Table5, the variation in the uniaxial compressive strength with the cement filling rate can be expressed by a positive exponential relationship, and the functional form is expressed by (1) as follows:(1)R=A0eR0a+y00%≤a≤32%.Here,A0R0, and y0 represent the equation Parameters, a denotes the rock saturated water content (%), and R represents the uniaxial compressive strength of rocks (MPa).The test curves were fitted, and the results are shown in Figure9.Figure 9
Curves representing the relation between the filling ratio and the uniaxial compressive strength. (a) Natural water content; (b) saturated water content.
(a)(b)Analysis of the fitting results reveals that the positive exponential function can reflect the functional relationship between the cement slurry filling rate and the uniaxial compressive strength. The fitting degree was high, and the correlation coefficients (R2) were greater than 0.98. This reflected the accuracy of the relationship.


#### 3.1.2. Relationship between the Cement Slurry Filling Rate and the Saturated Water Content

The data presented in Table1 reveals that the saturated water content in muddy sandstone in the presence of natural water is 14.24%, and the saturated water content is 11.20% when the cement slurry filling rate is 32%. This indicated a gradual decrease in the rate of water absorption for cement slurry-mixed muddy sandstone. It was also observed that the saturated water content in the rock decreased, which indirectly indicated the significantly high levels of reinforcement and water plugging effects exerted on the samples. The hydration products obtained by mixing cement slurry with muddy sandstone particles and water undergo a series of physicochemical reactions, which enhance the cementing effect observed between the particles. Aggregates of dense muddy sandstones are formed, and the internal pores of the rocks are filled. The hydration products contain a large amount of hydrated calcium silicate particles that connect the rock particles to form a spatial network. The hydration reactions continue to progress to form a highly compact spatial network, microscopically playing a “reinforcing effect.”The relationship between the cement slurry filling rate and the saturated water content was analyzed, and it was observed that the saturated water content in the rock exhibited a negative exponential relationship with the cement slurry filling rate. (2) was used to fit the test data. The fitting results are presented in Figure 10.(2)ωsat=A1e−a/R1+y10%≤a≤32%.Figure 10
Curve representing the relation between the cement slurry filling rate and the saturated water content.Here,A1R1, and y1 represent the equation parameters, a denotes the rock saturated water content (%), and R represents the uniaxial compressive strength of rocks (MPa).Analysis of Figure10 and the fitted results reveal that the negative exponential function can effectively reflect the variation in the cement slurry filling rate and saturation water content. A good fitting effect was observed for the fitted curves, and the correlation coefficients (R2) were greater than 0.98. This confirmed the accuracy of the expression.The modulus of elasticity was determined based on the calculation method (presented in the Standard for test methods of engineering rock mass [19]; used to determine the average modulus of elasticity of rocks). The calculation results are presented in Table 6. The formula used for calculation is presented as follows:(3)E=ΔσaΔεa=σb−σaεvb−εva.Table 5
Uniaxial compressive strength of argillaceous sandstone.
Aqueous stateUniaxial compressive strength at different grout filling rates (MPa)0%8%16%24%32%Natural moisture content0.680.871.332.093.32Saturated water content0.420.651.011.842.97Here,E denotes the elastic modulus (MPa), σa and σb stand for stress values at point a and point b of the elastic phase section (MPa), and εva and εvb stand for the axial strain values corresponding to stresses σa and σb.The calculated elastic moduli (Table6) were analyzed to determine the changes occurring in the elastic modulus of the muddy sandstone with a change in the cement slurry filling rate under conditions of varying water contents. The corresponding plots were generated and fitted. The fitting results are shown in Figure 11.Figure 11
Curve representing the relationship between the elastic modulus and the cement slurry filling rate. (a) Natural water content; (b) saturated water content.
(a)(b)Analysis of the data presented in Table6 reveals that the higher the cement slurry admixture content in muddy sandstone, the higher the modulus of elasticity. Under these conditions, growth occurs exponentially. In the presence of natural moisture, the elastic modulus was 0.042 GPa at a = 0% and 0.507 GPa at a = 32%, indicating that the resistance to slip damage and deformation increases when muddy sandstone is mixed with cement slurry. However, the modulus of elasticity recorded under the saturated state decreased by different degrees, indicating that the water content influenced the modulus of elasticity of the muddy sandstone sample mixed with cement slurry. However, the extent of influence exerted was not significantly high.


### 3.2. Triaxial Compression Test: Results

Triaxial compression tests were conducted to study the fully weathered muddy sandstone samples. The tests were conducted using the GDS triaxial testing machine to generate the partial stress–strain curves (Figure12).Figure 12
Deviatoric stress–strain curve generated for argillaceous sandstone under conditions of triaxial compression. (a) Natural water content; (b) saturated water content.
(a)(b)


#### 3.2.1. Deformation Characteristics: Analysis

The deformation characteristics of muddy sandstone under conditions of varying cement slurry filling rates were studied, and the results were compared with the results obtained by conducting triaxial compression tests.The test data curves were analyzed, and the slope of the tangent between the initial point and the point of 1/2 peak intensity in the partial stress–strain curve was considered as the representative value of the deformation modulus of muddy sandstone [20] (Table 7).Table 6
Elastic modulus of argillaceous sandstone.
Aqueous stateElastic modulus of argillaceous sandstone at different filling rates (GPa)0%8%16%24%32%Saturated water content0.0420.1070.1700.3190.507Saturated water content0.0340.0660.1170.2480.432The data presented in Table7 reveals that the deformation modulus of rocks formed under different states increased by approximately 9–10 times when the cement slurry filling rate was 32%. This indicated that the use of the cement slurry could effectively increase the deformation modulus of muddy sandstone. The increase can be attributed to the use of the cement slurry admixture. The use of the admixture improves the cementing ability of the particles, resulting in the relative deformation of the internal particles of muddy sandstone. Under these conditions, the overall structure increases, improving the deformation resistance. The results from deformation modulus tests conducted with the muddy sandstone under conditions of varying cement slurry filling rates were fitted to a nonlinear curve using Origin 2019b, and the results are shown in Figure 13.Figure 13
Fitting curve for deformation modulus of argillaceous sandstone. (a) Natural water content; (b) saturated water content.
(a)(b)The analysis of Figure13 reveals that the deformation modulus of muddy sandstone increases exponentially with an increase in the content of the cement slurry admixture. The correlation coefficients (R2) were greater than 0.98, indicating an exponential relationship between the deformation modulus and the cement slurry filling rate. A positive exponential correlation was recorded.


#### 3.2.2. Strength Properties

Based on the results of the original test, triaxial compression tests under different confining pressures were carried out. The Mohr–Coulomb criterion was used to draw the strength envelope and calculate the strength characteristics of argillaceous sandstone based on the analysis of the experimental data curve. The detailed calculation method is presented in the following section.The geometric relation obtained from the Mohr–Coulomb linear strength line can be expressed as follows:(4)sinφ=σ1−σ3/2c⋅cotφ+σ1+σ3/2=σ1−σ3σ1+σ3+2c⋅cotφ.Here,σ1 is the maximum principal stress (kPa), and σ3 denotes the minimum principal stress (kPa).The rectangular coordinate system was established by expressing the minimum principal stress on theX-axis and the maximum principal stress on the Y-axis. The strength envelope can be transformed using (4) as follows:(5)σ1=ξσ3+σcHere,ξ is the slope of the strength line in the coordinate, and σc is the theoretical uniaxial compressive strength (kPa).From equation (5),(6)ξ=1+sinφ1−sinφ⇒φ=arcsinξ−1ξ+1,σc=2ccosφ1−sinφ⇒c=σc2ξ,σc and ξ can be used to fit the data based on the results obtained from triaxial tests to obtain the slope and intercept of the straight line. The cohesion (c) and internal friction angle (φ) values were also calculated. The data obtained are presented in Table 8.Table 7
Deformation modulus of argillaceous sandstone.
Aqueous stateDeformation modulus of argillaceous sandstone at different filling rates (GPa)0%8%16%24%32%Natural water content state0.0360.0870.1330.2280.327Saturated water content0.0250.0430.0940.1500.249The analysis of the data presented in Table8 reveals that the cohesive force and the angle of internal friction increase with an increase in the filling rate of cement slurry under conditions of constant moisture content. Under conditions of a constant cement slurry filling rate, the values of c and φ decrease under the saturated state. This can be attributed to the expansion of the hydrophilic mineral components present in the water-adsorbed muddy sandstone system. This results in changes in the microstructure of the rock, resulting in the generation of swelling stress. When the strength of swelling stress exceeds the strength of the cementing force between the particles, the internal connection between the rocks is broken, and the cohesive force and internal friction angle decrease. The hydration product is produced when the sample is mixed with cement slurry. The process enhances the cementing ability of the particles. The enhancement effect increases, and the extent of decrease in the c and φ values decreases with an increase in the cement slurry filling rate.The degree of cohesion decreases by approximately 32% ata = 0 and 10% at a = 32%, indicating that the higher the cement slurry filling rate, the smaller the rate of decrease. The analysis of the experimental results reveals a positive exponential correlation between the cohesive force and the cement slurry filling rate. A positive linear correlation was observed between the internal friction angle and the cement slurry filling rate. Equations depicting the variations in the cohesion degree and the angle of internal friction with the variations in the cement slurry filling rate were studied, and the changes were further analyzed by plotting and fitting the c and φ values generated under varying test conditions. The cohesion test curves and fitting results obtained for the muddy sandstone samples obtained after reinforcement under different test conditions are shown in Figure 14.Figure 14
Curve representing the cohesive force observed in argillaceous sandstone. (a) Natural water content; (b) saturated water content.
(a)(b)The analysis of Figure14 reveals that the cohesive force generated by the reinforced muddy sandstone increases exponentially and positively. When the cement slurry filling rate is 32%, the cohesive force recorded for reinforced muddy sandstone containing natural water increases by 780.70 kPa, the cohesive force recorded for the reinforced muddy sandstone under the saturated state increases to 761.45 kPa, and the cohesive force recorded for the saturated state under free-water immersion conditions decreases by 95.89 kPa.The correlation coefficients (R2) were greater than 0.98, indicating that the control equation could effectively define the evolution characteristics of the cohesive force associated with the muddy sandstone samples mixed with cement slurry.The variation curve presenting the changes in the internal friction angle with the change in the filling rate of the filling rate of the mud slurry was generated after the mixing of the muddy sandstone with the cement slurry. The fitting results are shown in Figure15.Figure 15
Curve representing the changes in the internal friction angle corresponding to argillaceous sandstone. (a) Natural water content; (b) saturated water content.
(a)(b)The analysis of Figure15 reveals that the internal friction angle increases linearly following the reinforcement of the muddy sandstone samples. When the cement slurry filling rate reaches 32%, the internal friction angle increases by 1.55° in the presence of natural water. Under the saturated state, the angle increases by 2.32° (compared to the angle recorded for the unreinforced muddy sandstone sample). The maximum increase is recorded under the saturated state.


### 3.3. Analysis of Roadbed Settlement under Conditions of Static Load: Results

The simulation results obtained under different cement slurry filling conditions are presented in Figure16. Table 9 summarizes the data obtained by analyzing the field measurement monitoring points (Figures 16(a)–16(e)) under natural conditions and the data obtained by analyzing the monitoring points (Figures 16(a)–16(e)) under different water content states. Software-based simulation methods were followed. A comparison between the data obtained under the natural state is presented in Figure 17. (Table 9)Figure 16
Nephogram presenting the maximum displacement in theZ-direction under conditions of natural water content. (a) Natural water content, (b) saturated water content, (c) saturated-cement slurry fill rate 8%, (d) saturated-cement slurry fill rate 16%, (e) saturated-cement slurry fill rate 24%, (f) saturated-cement slurry fill rate 32%.
(a)(b)(c)(d)(e)(f)Table 8
Parameters representing the strength characteristics of argillaceous sandstone.
Rock nameSlurry filling rate (%)Natural water content stateSaturated water content stateCohesion (kPa)Internal friction angle (°)Cohesion (kPa)Internal friction angle (°)Argillaceous sandstone0208.8826.87132.2425.59Argillaceous sandstone8265.0227.33202.6726.12Argillaceous sandstone16403.3527.54310.4626.79Argillaceous sandstone24628.4227.97560.9027.29Argillaceous sandstone32989.5828.42893.6927.91Figure 17
Comparison of the field monitoring data and the model prediction monitoring data under natural conditions.Table 9
Deformation values recorded for each monitoring node recorded under different water content states and cement slurry filling rates.
NameMonitoring the deformation of nodes (mm)ABCDEField measurement of natural state−0.1408−0.5234−1.5154−0.7295−2.9453Natural water content state−0.1392−0.4992−1.4765−0.7417−2.8088Saturated state−0.1562−0.5098−1.7217−0.8545−3.2724Saturated-cement slurry fill rate 8%−0.0851−0.3039−0.9185−0.4676−1.8734Saturated-cement slurry fill rate 16%−0.0559−0.1972−0.5274−0.2769−1.1302Saturated-cement slurry fill rate 24%−0.0297−0.0956−0.2505−0.1383−0.5651Saturated-cement slurry fill rate 32%−0.0210−0.0654−0.1566−0.0903−0.3497The analysis of the field measured data reveals that the maximum settlement recorded for the subgrade is 2.9453 mm, which is 0.1365 mm higher than the predicted value of 2.8088 mm. The difference ratio was 4.63%, and the deviation was within the allowable error range [21].The analysis of the data presented in Table9 reveals that the settlement deformation at point A is 0.1392 mm under conditions of natural water content and 0.1562 mm under conditions of saturation. The deformation increased by 0.0170 mm after water saturation. Under conditions of saturation, the settlement deformation was reduced to 0.0210 mm when the cement slurry filling rate was 32%. It was observed that point A was not significantly affected by the self-weight of the track slab and embankment. Significantly higher levels of settlement deformation did not occur under these conditions. Point B presents the contact point between the embankment and the ground. The settlement deformation realized under conditions of the natural state was 0.4992 mm, the settlement deformation under conditions of the saturated state was 0.5098 mm, and the settlement difference was 0.0106 mm. Under conditions of the same state, the displacement recorded for point C was greater than the displacement recorded for point D. Point E was located directly below the embankment and could represent the extent of settlement deformation and the extent of deformation realized for the roadbed after the process of water immersion. The displacement produced under conditions of the saturated state was 16.51% higher than the displacement produced under conditions of the natural state. Different degrees of settlement deformation were observed at different monitoring nodes (at saturation conditions under immersion conditions). As the grouting rate corresponding to the muddy sandstone exposed to saturated conditions increases, the vertical displacement achieved for the roadbed gradually decreases. When the cement slurry filling rate reaches 32%, the extent of vertical displacement achieved decreases. Under these conditions, the rate of deformation gradually decreases and eventually reaches a plateau. This indicates that the admixture can effectively control the post-work settlement deformation observed in fully weathered muddy sandstone samples used for the development of high-fill roadbeds.


## 3.1. Uniaxial Compressive Strength Test: Results

The uniaxial compressive strength of the muddy sandstone sample was determined using a rock testing machine to obtain the stress–strain curves (Figure7).Figure 7
Stress–strain curve generated by analyzing the uniaxial compressive strength of argillaceous sandstone. (a) Natural water content; (b) saturated water content.
(a)(b)


### 3.1.1. Relationship between the Cement Slurry Filling Rate and the Uniaxial Compressive Strength

Based on the stress–strain curves generated by conducting the uniaxial compressive strength tests (Figure7), the changes in the uniaxial compressive strength of the muddy sandstone samples were studied under conditions of varying cement slurry filling rates. The relationship between the cement slurry filling rate and the uniaxial compressive strength was plotted based on the test curve (Figure 8). The uniaxial compressive strengths of the rock specimens in the presence of natural water and under the saturated states are listed in Table 5.Figure 8
Relationship between the filling ratio and the uniaxial compressive strength.It can be seen from Table5 that the uniaxial compressive strength of the rock gradually increases with an increase in the content of the cement paste admixture. When the cement slurry filling rate reached 32%, the uniaxial compressive strength of muddy sandstone reached 3.32 MPa in the presence of natural water. This was approximately 5 times higher than the strength recorded in the absence of cement slurry. This indicated that the use of cement slurry could improve the peak strength of muddy sandstone. The uniaxial compressive strengths of muddy sandstone recorded under natural water-bearing and saturated states were compared, and it was observed that the degrees of loss of uniaxial compressive strength were different for these two states. The losses in strength were 38.23%, 24.06%, and 10.52% for 0%, 16%, and 32% cement slurry fillings, respectively. This indicated that an increase in the cement slurry content resulted in a deterioration of the softening effect of water on the rock. An increase in the content of the cement slurry admixture resulted in the production of hydration products that formed bonds with the sandstone particles, generating links between the particles present in the muddy sandstone samples. The pores in the rocks were filled with hydration products, the number of internal cracks decreased, and the density of the rock increased, resulting in improved strength.As shown in Table5, the variation in the uniaxial compressive strength with the cement filling rate can be expressed by a positive exponential relationship, and the functional form is expressed by (1) as follows:(1)R=A0eR0a+y00%≤a≤32%.Here,A0R0, and y0 represent the equation Parameters, a denotes the rock saturated water content (%), and R represents the uniaxial compressive strength of rocks (MPa).The test curves were fitted, and the results are shown in Figure9.Figure 9
Curves representing the relation between the filling ratio and the uniaxial compressive strength. (a) Natural water content; (b) saturated water content.
(a)(b)Analysis of the fitting results reveals that the positive exponential function can reflect the functional relationship between the cement slurry filling rate and the uniaxial compressive strength. The fitting degree was high, and the correlation coefficients (R2) were greater than 0.98. This reflected the accuracy of the relationship.


### 3.1.2. Relationship between the Cement Slurry Filling Rate and the Saturated Water Content

The data presented in Table1 reveals that the saturated water content in muddy sandstone in the presence of natural water is 14.24%, and the saturated water content is 11.20% when the cement slurry filling rate is 32%. This indicated a gradual decrease in the rate of water absorption for cement slurry-mixed muddy sandstone. It was also observed that the saturated water content in the rock decreased, which indirectly indicated the significantly high levels of reinforcement and water plugging effects exerted on the samples. The hydration products obtained by mixing cement slurry with muddy sandstone particles and water undergo a series of physicochemical reactions, which enhance the cementing effect observed between the particles. Aggregates of dense muddy sandstones are formed, and the internal pores of the rocks are filled. The hydration products contain a large amount of hydrated calcium silicate particles that connect the rock particles to form a spatial network. The hydration reactions continue to progress to form a highly compact spatial network, microscopically playing a “reinforcing effect.”The relationship between the cement slurry filling rate and the saturated water content was analyzed, and it was observed that the saturated water content in the rock exhibited a negative exponential relationship with the cement slurry filling rate. (2) was used to fit the test data. The fitting results are presented in Figure 10.(2)ωsat=A1e−a/R1+y10%≤a≤32%.Figure 10
Curve representing the relation between the cement slurry filling rate and the saturated water content.Here,A1R1, and y1 represent the equation parameters, a denotes the rock saturated water content (%), and R represents the uniaxial compressive strength of rocks (MPa).Analysis of Figure10 and the fitted results reveal that the negative exponential function can effectively reflect the variation in the cement slurry filling rate and saturation water content. A good fitting effect was observed for the fitted curves, and the correlation coefficients (R2) were greater than 0.98. This confirmed the accuracy of the expression.The modulus of elasticity was determined based on the calculation method (presented in the Standard for test methods of engineering rock mass [19]; used to determine the average modulus of elasticity of rocks). The calculation results are presented in Table 6. The formula used for calculation is presented as follows:(3)E=ΔσaΔεa=σb−σaεvb−εva.Table 5
Uniaxial compressive strength of argillaceous sandstone.
Aqueous stateUniaxial compressive strength at different grout filling rates (MPa)0%8%16%24%32%Natural moisture content0.680.871.332.093.32Saturated water content0.420.651.011.842.97Here,E denotes the elastic modulus (MPa), σa and σb stand for stress values at point a and point b of the elastic phase section (MPa), and εva and εvb stand for the axial strain values corresponding to stresses σa and σb.The calculated elastic moduli (Table6) were analyzed to determine the changes occurring in the elastic modulus of the muddy sandstone with a change in the cement slurry filling rate under conditions of varying water contents. The corresponding plots were generated and fitted. The fitting results are shown in Figure 11.Figure 11
Curve representing the relationship between the elastic modulus and the cement slurry filling rate. (a) Natural water content; (b) saturated water content.
(a)(b)Analysis of the data presented in Table6 reveals that the higher the cement slurry admixture content in muddy sandstone, the higher the modulus of elasticity. Under these conditions, growth occurs exponentially. In the presence of natural moisture, the elastic modulus was 0.042 GPa at a = 0% and 0.507 GPa at a = 32%, indicating that the resistance to slip damage and deformation increases when muddy sandstone is mixed with cement slurry. However, the modulus of elasticity recorded under the saturated state decreased by different degrees, indicating that the water content influenced the modulus of elasticity of the muddy sandstone sample mixed with cement slurry. However, the extent of influence exerted was not significantly high.


## 3.1.1. Relationship between the Cement Slurry Filling Rate and the Uniaxial Compressive Strength

Based on the stress–strain curves generated by conducting the uniaxial compressive strength tests (Figure7), the changes in the uniaxial compressive strength of the muddy sandstone samples were studied under conditions of varying cement slurry filling rates. The relationship between the cement slurry filling rate and the uniaxial compressive strength was plotted based on the test curve (Figure 8). The uniaxial compressive strengths of the rock specimens in the presence of natural water and under the saturated states are listed in Table 5.Figure 8
Relationship between the filling ratio and the uniaxial compressive strength.It can be seen from Table5 that the uniaxial compressive strength of the rock gradually increases with an increase in the content of the cement paste admixture. When the cement slurry filling rate reached 32%, the uniaxial compressive strength of muddy sandstone reached 3.32 MPa in the presence of natural water. This was approximately 5 times higher than the strength recorded in the absence of cement slurry. This indicated that the use of cement slurry could improve the peak strength of muddy sandstone. The uniaxial compressive strengths of muddy sandstone recorded under natural water-bearing and saturated states were compared, and it was observed that the degrees of loss of uniaxial compressive strength were different for these two states. The losses in strength were 38.23%, 24.06%, and 10.52% for 0%, 16%, and 32% cement slurry fillings, respectively. This indicated that an increase in the cement slurry content resulted in a deterioration of the softening effect of water on the rock. An increase in the content of the cement slurry admixture resulted in the production of hydration products that formed bonds with the sandstone particles, generating links between the particles present in the muddy sandstone samples. The pores in the rocks were filled with hydration products, the number of internal cracks decreased, and the density of the rock increased, resulting in improved strength.As shown in Table5, the variation in the uniaxial compressive strength with the cement filling rate can be expressed by a positive exponential relationship, and the functional form is expressed by (1) as follows:(1)R=A0eR0a+y00%≤a≤32%.Here,A0R0, and y0 represent the equation Parameters, a denotes the rock saturated water content (%), and R represents the uniaxial compressive strength of rocks (MPa).The test curves were fitted, and the results are shown in Figure9.Figure 9
Curves representing the relation between the filling ratio and the uniaxial compressive strength. (a) Natural water content; (b) saturated water content.
(a)(b)Analysis of the fitting results reveals that the positive exponential function can reflect the functional relationship between the cement slurry filling rate and the uniaxial compressive strength. The fitting degree was high, and the correlation coefficients (R2) were greater than 0.98. This reflected the accuracy of the relationship.


## 3.1.2. Relationship between the Cement Slurry Filling Rate and the Saturated Water Content

The data presented in Table1 reveals that the saturated water content in muddy sandstone in the presence of natural water is 14.24%, and the saturated water content is 11.20% when the cement slurry filling rate is 32%. This indicated a gradual decrease in the rate of water absorption for cement slurry-mixed muddy sandstone. It was also observed that the saturated water content in the rock decreased, which indirectly indicated the significantly high levels of reinforcement and water plugging effects exerted on the samples. The hydration products obtained by mixing cement slurry with muddy sandstone particles and water undergo a series of physicochemical reactions, which enhance the cementing effect observed between the particles. Aggregates of dense muddy sandstones are formed, and the internal pores of the rocks are filled. The hydration products contain a large amount of hydrated calcium silicate particles that connect the rock particles to form a spatial network. The hydration reactions continue to progress to form a highly compact spatial network, microscopically playing a “reinforcing effect.”The relationship between the cement slurry filling rate and the saturated water content was analyzed, and it was observed that the saturated water content in the rock exhibited a negative exponential relationship with the cement slurry filling rate. (2) was used to fit the test data. The fitting results are presented in Figure 10.(2)ωsat=A1e−a/R1+y10%≤a≤32%.Figure 10
Curve representing the relation between the cement slurry filling rate and the saturated water content.Here,A1R1, and y1 represent the equation parameters, a denotes the rock saturated water content (%), and R represents the uniaxial compressive strength of rocks (MPa).Analysis of Figure10 and the fitted results reveal that the negative exponential function can effectively reflect the variation in the cement slurry filling rate and saturation water content. A good fitting effect was observed for the fitted curves, and the correlation coefficients (R2) were greater than 0.98. This confirmed the accuracy of the expression.The modulus of elasticity was determined based on the calculation method (presented in the Standard for test methods of engineering rock mass [19]; used to determine the average modulus of elasticity of rocks). The calculation results are presented in Table 6. The formula used for calculation is presented as follows:(3)E=ΔσaΔεa=σb−σaεvb−εva.Table 5
Uniaxial compressive strength of argillaceous sandstone.
Aqueous stateUniaxial compressive strength at different grout filling rates (MPa)0%8%16%24%32%Natural moisture content0.680.871.332.093.32Saturated water content0.420.651.011.842.97Here,E denotes the elastic modulus (MPa), σa and σb stand for stress values at point a and point b of the elastic phase section (MPa), and εva and εvb stand for the axial strain values corresponding to stresses σa and σb.The calculated elastic moduli (Table6) were analyzed to determine the changes occurring in the elastic modulus of the muddy sandstone with a change in the cement slurry filling rate under conditions of varying water contents. The corresponding plots were generated and fitted. The fitting results are shown in Figure 11.Figure 11
Curve representing the relationship between the elastic modulus and the cement slurry filling rate. (a) Natural water content; (b) saturated water content.
(a)(b)Analysis of the data presented in Table6 reveals that the higher the cement slurry admixture content in muddy sandstone, the higher the modulus of elasticity. Under these conditions, growth occurs exponentially. In the presence of natural moisture, the elastic modulus was 0.042 GPa at a = 0% and 0.507 GPa at a = 32%, indicating that the resistance to slip damage and deformation increases when muddy sandstone is mixed with cement slurry. However, the modulus of elasticity recorded under the saturated state decreased by different degrees, indicating that the water content influenced the modulus of elasticity of the muddy sandstone sample mixed with cement slurry. However, the extent of influence exerted was not significantly high.


## 3.2. Triaxial Compression Test: Results

Triaxial compression tests were conducted to study the fully weathered muddy sandstone samples. The tests were conducted using the GDS triaxial testing machine to generate the partial stress–strain curves (Figure12).Figure 12
Deviatoric stress–strain curve generated for argillaceous sandstone under conditions of triaxial compression. (a) Natural water content; (b) saturated water content.
(a)(b)


### 3.2.1. Deformation Characteristics: Analysis

The deformation characteristics of muddy sandstone under conditions of varying cement slurry filling rates were studied, and the results were compared with the results obtained by conducting triaxial compression tests.The test data curves were analyzed, and the slope of the tangent between the initial point and the point of 1/2 peak intensity in the partial stress–strain curve was considered as the representative value of the deformation modulus of muddy sandstone [20] (Table 7).Table 6
Elastic modulus of argillaceous sandstone.
Aqueous stateElastic modulus of argillaceous sandstone at different filling rates (GPa)0%8%16%24%32%Saturated water content0.0420.1070.1700.3190.507Saturated water content0.0340.0660.1170.2480.432The data presented in Table7 reveals that the deformation modulus of rocks formed under different states increased by approximately 9–10 times when the cement slurry filling rate was 32%. This indicated that the use of the cement slurry could effectively increase the deformation modulus of muddy sandstone. The increase can be attributed to the use of the cement slurry admixture. The use of the admixture improves the cementing ability of the particles, resulting in the relative deformation of the internal particles of muddy sandstone. Under these conditions, the overall structure increases, improving the deformation resistance. The results from deformation modulus tests conducted with the muddy sandstone under conditions of varying cement slurry filling rates were fitted to a nonlinear curve using Origin 2019b, and the results are shown in Figure 13.Figure 13
Fitting curve for deformation modulus of argillaceous sandstone. (a) Natural water content; (b) saturated water content.
(a)(b)The analysis of Figure13 reveals that the deformation modulus of muddy sandstone increases exponentially with an increase in the content of the cement slurry admixture. The correlation coefficients (R2) were greater than 0.98, indicating an exponential relationship between the deformation modulus and the cement slurry filling rate. A positive exponential correlation was recorded.


### 3.2.2. Strength Properties

Based on the results of the original test, triaxial compression tests under different confining pressures were carried out. The Mohr–Coulomb criterion was used to draw the strength envelope and calculate the strength characteristics of argillaceous sandstone based on the analysis of the experimental data curve. The detailed calculation method is presented in the following section.The geometric relation obtained from the Mohr–Coulomb linear strength line can be expressed as follows:(4)sinφ=σ1−σ3/2c⋅cotφ+σ1+σ3/2=σ1−σ3σ1+σ3+2c⋅cotφ.Here,σ1 is the maximum principal stress (kPa), and σ3 denotes the minimum principal stress (kPa).The rectangular coordinate system was established by expressing the minimum principal stress on theX-axis and the maximum principal stress on the Y-axis. The strength envelope can be transformed using (4) as follows:(5)σ1=ξσ3+σcHere,ξ is the slope of the strength line in the coordinate, and σc is the theoretical uniaxial compressive strength (kPa).From equation (5),(6)ξ=1+sinφ1−sinφ⇒φ=arcsinξ−1ξ+1,σc=2ccosφ1−sinφ⇒c=σc2ξ,σc and ξ can be used to fit the data based on the results obtained from triaxial tests to obtain the slope and intercept of the straight line. The cohesion (c) and internal friction angle (φ) values were also calculated. The data obtained are presented in Table 8.Table 7
Deformation modulus of argillaceous sandstone.
Aqueous stateDeformation modulus of argillaceous sandstone at different filling rates (GPa)0%8%16%24%32%Natural water content state0.0360.0870.1330.2280.327Saturated water content0.0250.0430.0940.1500.249The analysis of the data presented in Table8 reveals that the cohesive force and the angle of internal friction increase with an increase in the filling rate of cement slurry under conditions of constant moisture content. Under conditions of a constant cement slurry filling rate, the values of c and φ decrease under the saturated state. This can be attributed to the expansion of the hydrophilic mineral components present in the water-adsorbed muddy sandstone system. This results in changes in the microstructure of the rock, resulting in the generation of swelling stress. When the strength of swelling stress exceeds the strength of the cementing force between the particles, the internal connection between the rocks is broken, and the cohesive force and internal friction angle decrease. The hydration product is produced when the sample is mixed with cement slurry. The process enhances the cementing ability of the particles. The enhancement effect increases, and the extent of decrease in the c and φ values decreases with an increase in the cement slurry filling rate.The degree of cohesion decreases by approximately 32% ata = 0 and 10% at a = 32%, indicating that the higher the cement slurry filling rate, the smaller the rate of decrease. The analysis of the experimental results reveals a positive exponential correlation between the cohesive force and the cement slurry filling rate. A positive linear correlation was observed between the internal friction angle and the cement slurry filling rate. Equations depicting the variations in the cohesion degree and the angle of internal friction with the variations in the cement slurry filling rate were studied, and the changes were further analyzed by plotting and fitting the c and φ values generated under varying test conditions. The cohesion test curves and fitting results obtained for the muddy sandstone samples obtained after reinforcement under different test conditions are shown in Figure 14.Figure 14
Curve representing the cohesive force observed in argillaceous sandstone. (a) Natural water content; (b) saturated water content.
(a)(b)The analysis of Figure14 reveals that the cohesive force generated by the reinforced muddy sandstone increases exponentially and positively. When the cement slurry filling rate is 32%, the cohesive force recorded for reinforced muddy sandstone containing natural water increases by 780.70 kPa, the cohesive force recorded for the reinforced muddy sandstone under the saturated state increases to 761.45 kPa, and the cohesive force recorded for the saturated state under free-water immersion conditions decreases by 95.89 kPa.The correlation coefficients (R2) were greater than 0.98, indicating that the control equation could effectively define the evolution characteristics of the cohesive force associated with the muddy sandstone samples mixed with cement slurry.The variation curve presenting the changes in the internal friction angle with the change in the filling rate of the filling rate of the mud slurry was generated after the mixing of the muddy sandstone with the cement slurry. The fitting results are shown in Figure15.Figure 15
Curve representing the changes in the internal friction angle corresponding to argillaceous sandstone. (a) Natural water content; (b) saturated water content.
(a)(b)The analysis of Figure15 reveals that the internal friction angle increases linearly following the reinforcement of the muddy sandstone samples. When the cement slurry filling rate reaches 32%, the internal friction angle increases by 1.55° in the presence of natural water. Under the saturated state, the angle increases by 2.32° (compared to the angle recorded for the unreinforced muddy sandstone sample). The maximum increase is recorded under the saturated state.


## 3.2.1. Deformation Characteristics: Analysis

The deformation characteristics of muddy sandstone under conditions of varying cement slurry filling rates were studied, and the results were compared with the results obtained by conducting triaxial compression tests.The test data curves were analyzed, and the slope of the tangent between the initial point and the point of 1/2 peak intensity in the partial stress–strain curve was considered as the representative value of the deformation modulus of muddy sandstone [20] (Table 7).Table 6
Elastic modulus of argillaceous sandstone.
Aqueous stateElastic modulus of argillaceous sandstone at different filling rates (GPa)0%8%16%24%32%Saturated water content0.0420.1070.1700.3190.507Saturated water content0.0340.0660.1170.2480.432The data presented in Table7 reveals that the deformation modulus of rocks formed under different states increased by approximately 9–10 times when the cement slurry filling rate was 32%. This indicated that the use of the cement slurry could effectively increase the deformation modulus of muddy sandstone. The increase can be attributed to the use of the cement slurry admixture. The use of the admixture improves the cementing ability of the particles, resulting in the relative deformation of the internal particles of muddy sandstone. Under these conditions, the overall structure increases, improving the deformation resistance. The results from deformation modulus tests conducted with the muddy sandstone under conditions of varying cement slurry filling rates were fitted to a nonlinear curve using Origin 2019b, and the results are shown in Figure 13.Figure 13
Fitting curve for deformation modulus of argillaceous sandstone. (a) Natural water content; (b) saturated water content.
(a)(b)The analysis of Figure13 reveals that the deformation modulus of muddy sandstone increases exponentially with an increase in the content of the cement slurry admixture. The correlation coefficients (R2) were greater than 0.98, indicating an exponential relationship between the deformation modulus and the cement slurry filling rate. A positive exponential correlation was recorded.


## 3.2.2. Strength Properties

Based on the results of the original test, triaxial compression tests under different confining pressures were carried out. The Mohr–Coulomb criterion was used to draw the strength envelope and calculate the strength characteristics of argillaceous sandstone based on the analysis of the experimental data curve. The detailed calculation method is presented in the following section.The geometric relation obtained from the Mohr–Coulomb linear strength line can be expressed as follows:(4)sinφ=σ1−σ3/2c⋅cotφ+σ1+σ3/2=σ1−σ3σ1+σ3+2c⋅cotφ.Here,σ1 is the maximum principal stress (kPa), and σ3 denotes the minimum principal stress (kPa).The rectangular coordinate system was established by expressing the minimum principal stress on theX-axis and the maximum principal stress on the Y-axis. The strength envelope can be transformed using (4) as follows:(5)σ1=ξσ3+σcHere,ξ is the slope of the strength line in the coordinate, and σc is the theoretical uniaxial compressive strength (kPa).From equation (5),(6)ξ=1+sinφ1−sinφ⇒φ=arcsinξ−1ξ+1,σc=2ccosφ1−sinφ⇒c=σc2ξ,σc and ξ can be used to fit the data based on the results obtained from triaxial tests to obtain the slope and intercept of the straight line. The cohesion (c) and internal friction angle (φ) values were also calculated. The data obtained are presented in Table 8.Table 7
Deformation modulus of argillaceous sandstone.
Aqueous stateDeformation modulus of argillaceous sandstone at different filling rates (GPa)0%8%16%24%32%Natural water content state0.0360.0870.1330.2280.327Saturated water content0.0250.0430.0940.1500.249The analysis of the data presented in Table8 reveals that the cohesive force and the angle of internal friction increase with an increase in the filling rate of cement slurry under conditions of constant moisture content. Under conditions of a constant cement slurry filling rate, the values of c and φ decrease under the saturated state. This can be attributed to the expansion of the hydrophilic mineral components present in the water-adsorbed muddy sandstone system. This results in changes in the microstructure of the rock, resulting in the generation of swelling stress. When the strength of swelling stress exceeds the strength of the cementing force between the particles, the internal connection between the rocks is broken, and the cohesive force and internal friction angle decrease. The hydration product is produced when the sample is mixed with cement slurry. The process enhances the cementing ability of the particles. The enhancement effect increases, and the extent of decrease in the c and φ values decreases with an increase in the cement slurry filling rate.The degree of cohesion decreases by approximately 32% ata = 0 and 10% at a = 32%, indicating that the higher the cement slurry filling rate, the smaller the rate of decrease. The analysis of the experimental results reveals a positive exponential correlation between the cohesive force and the cement slurry filling rate. A positive linear correlation was observed between the internal friction angle and the cement slurry filling rate. Equations depicting the variations in the cohesion degree and the angle of internal friction with the variations in the cement slurry filling rate were studied, and the changes were further analyzed by plotting and fitting the c and φ values generated under varying test conditions. The cohesion test curves and fitting results obtained for the muddy sandstone samples obtained after reinforcement under different test conditions are shown in Figure 14.Figure 14
Curve representing the cohesive force observed in argillaceous sandstone. (a) Natural water content; (b) saturated water content.
(a)(b)The analysis of Figure14 reveals that the cohesive force generated by the reinforced muddy sandstone increases exponentially and positively. When the cement slurry filling rate is 32%, the cohesive force recorded for reinforced muddy sandstone containing natural water increases by 780.70 kPa, the cohesive force recorded for the reinforced muddy sandstone under the saturated state increases to 761.45 kPa, and the cohesive force recorded for the saturated state under free-water immersion conditions decreases by 95.89 kPa.The correlation coefficients (R2) were greater than 0.98, indicating that the control equation could effectively define the evolution characteristics of the cohesive force associated with the muddy sandstone samples mixed with cement slurry.The variation curve presenting the changes in the internal friction angle with the change in the filling rate of the filling rate of the mud slurry was generated after the mixing of the muddy sandstone with the cement slurry. The fitting results are shown in Figure15.Figure 15
Curve representing the changes in the internal friction angle corresponding to argillaceous sandstone. (a) Natural water content; (b) saturated water content.
(a)(b)The analysis of Figure15 reveals that the internal friction angle increases linearly following the reinforcement of the muddy sandstone samples. When the cement slurry filling rate reaches 32%, the internal friction angle increases by 1.55° in the presence of natural water. Under the saturated state, the angle increases by 2.32° (compared to the angle recorded for the unreinforced muddy sandstone sample). The maximum increase is recorded under the saturated state.


## 3.3. Analysis of Roadbed Settlement under Conditions of Static Load: Results

The simulation results obtained under different cement slurry filling conditions are presented in Figure16. Table 9 summarizes the data obtained by analyzing the field measurement monitoring points (Figures 16(a)–16(e)) under natural conditions and the data obtained by analyzing the monitoring points (Figures 16(a)–16(e)) under different water content states. Software-based simulation methods were followed. A comparison between the data obtained under the natural state is presented in Figure 17. (Table 9)Figure 16
Nephogram presenting the maximum displacement in theZ-direction under conditions of natural water content. (a) Natural water content, (b) saturated water content, (c) saturated-cement slurry fill rate 8%, (d) saturated-cement slurry fill rate 16%, (e) saturated-cement slurry fill rate 24%, (f) saturated-cement slurry fill rate 32%.
(a)(b)(c)(d)(e)(f)Table 8
Parameters representing the strength characteristics of argillaceous sandstone.
Rock nameSlurry filling rate (%)Natural water content stateSaturated water content stateCohesion (kPa)Internal friction angle (°)Cohesion (kPa)Internal friction angle (°)Argillaceous sandstone0208.8826.87132.2425.59Argillaceous sandstone8265.0227.33202.6726.12Argillaceous sandstone16403.3527.54310.4626.79Argillaceous sandstone24628.4227.97560.9027.29Argillaceous sandstone32989.5828.42893.6927.91Figure 17
Comparison of the field monitoring data and the model prediction monitoring data under natural conditions.Table 9
Deformation values recorded for each monitoring node recorded under different water content states and cement slurry filling rates.
NameMonitoring the deformation of nodes (mm)ABCDEField measurement of natural state−0.1408−0.5234−1.5154−0.7295−2.9453Natural water content state−0.1392−0.4992−1.4765−0.7417−2.8088Saturated state−0.1562−0.5098−1.7217−0.8545−3.2724Saturated-cement slurry fill rate 8%−0.0851−0.3039−0.9185−0.4676−1.8734Saturated-cement slurry fill rate 16%−0.0559−0.1972−0.5274−0.2769−1.1302Saturated-cement slurry fill rate 24%−0.0297−0.0956−0.2505−0.1383−0.5651Saturated-cement slurry fill rate 32%−0.0210−0.0654−0.1566−0.0903−0.3497The analysis of the field measured data reveals that the maximum settlement recorded for the subgrade is 2.9453 mm, which is 0.1365 mm higher than the predicted value of 2.8088 mm. The difference ratio was 4.63%, and the deviation was within the allowable error range [21].The analysis of the data presented in Table9 reveals that the settlement deformation at point A is 0.1392 mm under conditions of natural water content and 0.1562 mm under conditions of saturation. The deformation increased by 0.0170 mm after water saturation. Under conditions of saturation, the settlement deformation was reduced to 0.0210 mm when the cement slurry filling rate was 32%. It was observed that point A was not significantly affected by the self-weight of the track slab and embankment. Significantly higher levels of settlement deformation did not occur under these conditions. Point B presents the contact point between the embankment and the ground. The settlement deformation realized under conditions of the natural state was 0.4992 mm, the settlement deformation under conditions of the saturated state was 0.5098 mm, and the settlement difference was 0.0106 mm. Under conditions of the same state, the displacement recorded for point C was greater than the displacement recorded for point D. Point E was located directly below the embankment and could represent the extent of settlement deformation and the extent of deformation realized for the roadbed after the process of water immersion. The displacement produced under conditions of the saturated state was 16.51% higher than the displacement produced under conditions of the natural state. Different degrees of settlement deformation were observed at different monitoring nodes (at saturation conditions under immersion conditions). As the grouting rate corresponding to the muddy sandstone exposed to saturated conditions increases, the vertical displacement achieved for the roadbed gradually decreases. When the cement slurry filling rate reaches 32%, the extent of vertical displacement achieved decreases. Under these conditions, the rate of deformation gradually decreases and eventually reaches a plateau. This indicates that the admixture can effectively control the post-work settlement deformation observed in fully weathered muddy sandstone samples used for the development of high-fill roadbeds.


## 4. Conclusions

Uniaxial compressive strength and triaxial compression tests were conducted under different test conditions to study the mechanical properties of the reinforced muddy sandstone systems. A three-dimensional finite element model was developed using MIDAS/GTS NX to simulate the settlement patterns under natural, saturated, and consolidated muddy sandstone conditions. The primary conclusions drawn have been presented as follows:(1)
When the cement slurry filling rate was 32%, the uniaxial compressive strength of the muddy sandstone treated with cement slurry was 3.32 MPa. This was approximately 5 times higher than the strength of the muddy sandstone devoid of cement slurry. This indicates that the use of cement slurry can significantly improve the uniaxial compressive strength of the muddy sandstone sample.(2)
The water absorption ability of the reinforced muddy sandstone sample was analyzed from the perspective of saturated water content, and the water plugging effect of the process of cement slurry filling was studied and verified. The controlling equations for determining the uniaxial compressive strength, elastic modulus, and free saturated water content (for the reinforced muddy sandstone samples; under conditions of varying cement slurry filling rates) were established.(3)
As the content of the cement slurry admixture increased, the nature of the bias stress–strain curve (generated for muddy sandstone) transformed from the strain-hardening type to the strain-softening type. The modulus of deformation and degree of cohesion increase exponentially with an increase in the cement slurry filling rate. The internal friction angle correlates linearly and positively with the cement slurry filling rate. The experimental data were fitted, and the correlation coefficient was found to be greater than 0.97. A high degree of fit was achieved for the curves. The accuracy of the equations relating the modulus of deformation, cohesive force, and angle of internal friction to the cement slurry filling rate was determined.(4)
The monitoring nodes corresponding to the muddy sandstone-based roadbed were characterized by varying degrees of settlement deformation after water saturation. The maximum settlement displacement (for the monitoring node at the center of the roadbed under conditions of water saturation) was calculated to be 3.2724 mm. It was observed that the value of settlement deformation decreased exponentially (under conditions of saturation) with an increase in the grouting rate [21].



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*Source: 7070119-2022-08-17.xml*