# Study of the Indoor Model Test and CEL Simulation of Jacking Force in the Vertical Tunnelling Method

Authors: Xinjiang Wei; Shuyuan Zhang; Xiao Wang; Liangliang Lu; Zhi Ding
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

The jacking force is one of the important parameters affecting the construction process in the vertical tunnelling method. To study the dynamic changing process of jacking force with the jacked distance and the influencing factors of the maximum jacking force, both the indoor model test and numerical simulation were conducted. In the model test, we investigated the influence of the height of the soil and water content. The results indicated that the higher the overburden height was, the greater the jacking force. Moreover, the water content enhanced the compressibility of the soil and had little effect on the maximum jacking force. Additionally, the coupled Eulerian–Lagrangian (CEL) approach was used to simulate the vertical jacking construction. In the numerical simulation, we investigated two construction factors (jacking speed and the standpipe outer diameter) and four soil parameters (cohesion, internal friction angle, elastic modulus, and Poisson’s ratio). Before that, the CEL simulation results were compared with test data to prove the rationality of the CEL approach, and the two were in good agreement. The results showed that among the six influence parameters, according to the influence degree on the maximum jacking force from large to low, the outer diameter of the standpipe, internal friction angle, cohesion, elastic modulus, jacking speed, and Poisson’s ratio were ranked. In addition, the jacking speed of numerical analysis was suggested to be 0.2 m/s. The research results in this paper can provide a reference for the construction of the vertical tunnelling method.


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## Body

## 1. Introduction

With the development of the urban economy, numerous large thermal power plants and nuclear power plants have been widely constructed in coastal areas. Correspondingly, the demand for water intake and drainage projects is also increasing due to the growing demand for power generation. As a new trenchless technology, the vertical tunnelling method is widely used due to its advantages of small environmental impact, high economic efficiency, and safety [1, 2]. The process of the vertical tunnelling method is shown in Figure 1. The standpipe is lifted-up section by section with the help of jacking equipment such as jacks [1, 2]. In the process of construction, the determination of jacking force is particularly important, especially maximum jacking force. It is not only related to the feasibility of jacking but also associated with the design of the standpipe and the stability of the horizontal tunnel.Figure 1
Construction process of the vertical tunnelling method.Previous research has examined the jacking force for the vertical tunnelling method. Wang et al. [1] regarded the vertical construction process as inverse pile driving, and the jacking force was estimated by Meyerhof’s theory. However, Meyerhof’s bearing capacity theory might not be suitable for the opposite direction. Based on a project in Beihai, China, Wang et al. [3] used terminal jacking force to back analyse the average frictional coefficient and obtained the changing law of the jacking force. Wei et al. [4] employed discrete elements to simulate the jacking process and studied the influence of the height of the overburdened soil and the soil shear strength index on the maximum jacking force. However, the simulation method was completed in two dimensions instead of three dimensions. Wei et al. [5] constructed a prediction model of jacking force through two intelligent algorithms, ANN and GA-ANN, and three types of influencing factors (including ten parameters) were investigated. It was believed that the GA-ANN model could be better for predicting the jacking force, and the height of overlaying water, the jacking speed, and the geological condition were considered as parameters with the greatest impact affecting the jacking force.Similar to the vertical tunnelling methods, the upwards shield method was applied in Japan most early [6, 7], whose direction of construction was also bottom-up. There has been some research on the introduction of construction techniques and usages [3, 6, 7]. However, the jacking force was rarely considered.The model test is an important research method, especially in the case of insufficient research theory [8–11]. It can not only help us understand the construction of geotechnical engineering but can also obtain the jacking force in the process and the variation trend. Similarly, the finite element method also plays an important role in solving geotechnical problems [12, 13]. Therefore, solving engineering problems by model tests and numerical simulation has become a trend for many scholars to study problems [14]. A coupled Eulerian–Lagrangian (CEL) approach [15] based on an explicit time integration formulation has been widely used for solving large-deformation problems [16–19].In this study, the jacking force in the process of the vertical tunnelling method was analysed by means of a model test and numerical simulation. Four model tests taking into account different heights of overburdened soil and water conditions were designed. Moreover, the influences of jacking speed, the standpipe outer diameter, and soil parameters on jacking force were obtained by the CEL method in Abaqus. The research results can provide a reference for guiding similar engineering construction.


## 2. Model Test

The model test is explained in the following sections.


### 2.1. Similarity Principle and Simplifications of the Test

The similarity principle is the basic theory of the physical model test, which means that the physical features of the model need to meet a series of similarity requirements [20–22]. However, it is nearly impossible to meet all similar constants [23]. In this study, the geometric dimension similarity constant (CL) was determined to be 14, and the similarity constant for bulk weight was determined to be 1. The geometric values between the prototype and the model are shown in Table 1, and key similarity ratios are shown in Table 2. Moreover, considering the manoeuvrability and research emphasis, the horizontal tunnel was simplified as a complete semicylinder, ignoring the influence of the structure of the horizontal tunnel. Additionally, in practical projects, the standpipe is lifted up section by section, and the connection between one pipe section and the other pipe section is a welding or bolt. This test was simplified as a complete standpipe, and the standpipe was marked every 0.025 m, which represented one pipe section.Table 1
Geometric values between the prototype and the model.
Geometric valuesGeometric parameter ratioPrototype scale (m)Model scale (m)Model box length1 : 1416.81.20Model box width1 : 14141Model box height1 : 14141Horizontal tunnel outer diameter1 : 146.30.45Horizontal tunnel length1 : 14141Overburden soil height1 : 145.950.425Standpipe outer diameter1 : 141.820.13Table 2
Key similitude parameter.
Physical valuesSimilarity ratio symbolSimilitude parameterLengthCL1 : 14Bulk weightCγ1CohesionCc1Internal friction angleCφ1LoadCP1 : 143


### 2.2. Model Test Apparatus

A schematic sketch of the model test is shown in Figure2. The whole test apparatus was mainly composed of four parts: a model box, loading system, data acquisition system, and standpipe. As shown in Figure 3, the model box was made of organic glass, with an external size of 1.2 m × 1 m × 1 m (length × width × height) and a thickness of 0.02 m. A horizontal tunnel with an outer diameter of 0.45 m and an internal diameter of 0.4 m was on the lower side of the model box. There was a hole with a diameter of 0.13 m to place the standpipe on the top of the horizontal tunnel. The loading system for load application was composed of an oil pump and hydraulic cylinder. The rated power of the oil pump was 0.75 kW, and the jacking speed was 4.4 mm/s. The diameter of the piston rod of the hydraulic cylinder was 65 mm, which was larger than the diameter of the pressure sensor. The stroke of the piston rod was 0.45 m. The data acquisition system for collecting the original data of the test consisted of the pressure sensor and digital display. The diameter and thickness of the pressure sensor were 56 mm and 20 mm in thickness. During the test, the pressure sensor was placed in the middle of the hydraulic cylinder and the standpipe. The standpipe used for jacking in the test was made of steel, with a diameter of 0.1 m and a length of 0.5 m. The top cover was hollow, with an outer diameter of 0.13 m and a height of 0.025 m. Four Earth pressure cells were fixed on the surface of the top cover to monitor the soil pressure in the jacking process. The total weight of the standpipe and the top cover was 8.7 kg.Figure 2
Schematic sketch of the indoor model test.Figure 3
Test apparatus.


### 2.3. Model Materials and Test Conditions

Sea sand was selected as the test material and dried before the test. The relevant physical parameters are shown in Table3.Table 3
Basic physical properties of sand.
MaterialDensity (kN/m3)Cohesion (kPa)Internal friction angle (°)Void ratioCompression modulus (MPa)Sea sand15031.90.4826.24The jacking force might be related to the height of overburdened soil and water conditions. Therefore, four model tests were designed. The specific test conditions are shown in Table4.Table 4
Test conditions.
Test no.Height of overburden soil (m)Jacking speed (mm/s)Water condition10.4254.4No20.3754.4No30.4754.4No40.4254.4Yes


### 2.4. Test Process

As shown in Figure4, the model test process was mainly summarised as follows:(1)
Before the test, the standpipe was marked every 0.025 m (see Figure4(a)). Then, the hydraulic cylinder was placed at the centre of the bottom of the model box and aligned with the centre of the pole of the hydraulic cylinder and the standpipe. Then, the jacking process was tested in a soilless environment to ensure that the standpipe would not touch the horizontal tunnel (see Figure 4(b)).(2)
The model box was filled to the specified height. In the process, the uniform distribution of fill should be ensured as much as possible (see Figures4(c) and 4(d)).(3)
The foaming adhesive was applied at the bottom of the horizontal tunnel to prevent sand leakage (see Figure4(e)). Then, the power supply of the oil pump was connected, and jacking was started (see Figure 4(f)).(4)
When the standpipe of 0.025 m was jacked, the power supply was turned off. The process was videotaped to record the maximum value displayed on the digital display. The value was seen as the jacking force for the jacking section (see. Figure4(g)).(5)
The above operation was repeated until the elevation was completed (see Figure4(h)).Figure 4
Test process. (a) Marking standpipe. (b) Jacking test. (c) Loading soil. (d) Landfilling soil. (e) Painting foaming adhesive. (f) Jacking standpipe. (g) Data recording. (h) Completing jacking.
(a)(b)(c)(d)(e)(f)(g)(h)


## 2.1. Similarity Principle and Simplifications of the Test

The similarity principle is the basic theory of the physical model test, which means that the physical features of the model need to meet a series of similarity requirements [20–22]. However, it is nearly impossible to meet all similar constants [23]. In this study, the geometric dimension similarity constant (CL) was determined to be 14, and the similarity constant for bulk weight was determined to be 1. The geometric values between the prototype and the model are shown in Table 1, and key similarity ratios are shown in Table 2. Moreover, considering the manoeuvrability and research emphasis, the horizontal tunnel was simplified as a complete semicylinder, ignoring the influence of the structure of the horizontal tunnel. Additionally, in practical projects, the standpipe is lifted up section by section, and the connection between one pipe section and the other pipe section is a welding or bolt. This test was simplified as a complete standpipe, and the standpipe was marked every 0.025 m, which represented one pipe section.Table 1
Geometric values between the prototype and the model.
Geometric valuesGeometric parameter ratioPrototype scale (m)Model scale (m)Model box length1 : 1416.81.20Model box width1 : 14141Model box height1 : 14141Horizontal tunnel outer diameter1 : 146.30.45Horizontal tunnel length1 : 14141Overburden soil height1 : 145.950.425Standpipe outer diameter1 : 141.820.13Table 2
Key similitude parameter.
Physical valuesSimilarity ratio symbolSimilitude parameterLengthCL1 : 14Bulk weightCγ1CohesionCc1Internal friction angleCφ1LoadCP1 : 143


## 2.2. Model Test Apparatus

A schematic sketch of the model test is shown in Figure2. The whole test apparatus was mainly composed of four parts: a model box, loading system, data acquisition system, and standpipe. As shown in Figure 3, the model box was made of organic glass, with an external size of 1.2 m × 1 m × 1 m (length × width × height) and a thickness of 0.02 m. A horizontal tunnel with an outer diameter of 0.45 m and an internal diameter of 0.4 m was on the lower side of the model box. There was a hole with a diameter of 0.13 m to place the standpipe on the top of the horizontal tunnel. The loading system for load application was composed of an oil pump and hydraulic cylinder. The rated power of the oil pump was 0.75 kW, and the jacking speed was 4.4 mm/s. The diameter of the piston rod of the hydraulic cylinder was 65 mm, which was larger than the diameter of the pressure sensor. The stroke of the piston rod was 0.45 m. The data acquisition system for collecting the original data of the test consisted of the pressure sensor and digital display. The diameter and thickness of the pressure sensor were 56 mm and 20 mm in thickness. During the test, the pressure sensor was placed in the middle of the hydraulic cylinder and the standpipe. The standpipe used for jacking in the test was made of steel, with a diameter of 0.1 m and a length of 0.5 m. The top cover was hollow, with an outer diameter of 0.13 m and a height of 0.025 m. Four Earth pressure cells were fixed on the surface of the top cover to monitor the soil pressure in the jacking process. The total weight of the standpipe and the top cover was 8.7 kg.Figure 2
Schematic sketch of the indoor model test.Figure 3
Test apparatus.


## 2.3. Model Materials and Test Conditions

Sea sand was selected as the test material and dried before the test. The relevant physical parameters are shown in Table3.Table 3
Basic physical properties of sand.
MaterialDensity (kN/m3)Cohesion (kPa)Internal friction angle (°)Void ratioCompression modulus (MPa)Sea sand15031.90.4826.24The jacking force might be related to the height of overburdened soil and water conditions. Therefore, four model tests were designed. The specific test conditions are shown in Table4.Table 4
Test conditions.
Test no.Height of overburden soil (m)Jacking speed (mm/s)Water condition10.4254.4No20.3754.4No30.4754.4No40.4254.4Yes


## 2.4. Test Process

As shown in Figure4, the model test process was mainly summarised as follows:(1)
Before the test, the standpipe was marked every 0.025 m (see Figure4(a)). Then, the hydraulic cylinder was placed at the centre of the bottom of the model box and aligned with the centre of the pole of the hydraulic cylinder and the standpipe. Then, the jacking process was tested in a soilless environment to ensure that the standpipe would not touch the horizontal tunnel (see Figure 4(b)).(2)
The model box was filled to the specified height. In the process, the uniform distribution of fill should be ensured as much as possible (see Figures4(c) and 4(d)).(3)
The foaming adhesive was applied at the bottom of the horizontal tunnel to prevent sand leakage (see Figure4(e)). Then, the power supply of the oil pump was connected, and jacking was started (see Figure 4(f)).(4)
When the standpipe of 0.025 m was jacked, the power supply was turned off. The process was videotaped to record the maximum value displayed on the digital display. The value was seen as the jacking force for the jacking section (see. Figure4(g)).(5)
The above operation was repeated until the elevation was completed (see Figure4(h)).Figure 4
Test process. (a) Marking standpipe. (b) Jacking test. (c) Loading soil. (d) Landfilling soil. (e) Painting foaming adhesive. (f) Jacking standpipe. (g) Data recording. (h) Completing jacking.
(a)(b)(c)(d)(e)(f)(g)(h)


## 3. Numerical Simulation

The numerical simulation is described in the following sections.


### 3.1. Numerical Model

The coupled Eulerian–Lagrangian (CEL) technique in Abaqus was employed to simulate the process of vertical jacking construction. Due to the symmetry of the model, only a quarter of the domain was modelled. As shown in Figure5, this model consists of two parts: standpipe and soil. The standpipe outer diameter (D) is 1.8 m, and the length is 8 m. To avoid large mesh distortions, the top 0.45 m of the standpipe is embedded in the soil [12]. Thus, the jacking height (H) is actually 7.55 m. The soil is (length by width by height) 18 m × 18 m × 16 m, which was divided into two layers of the same size: the soil layer and the void layer (see Figure 6). The void layer at the top of the soil model had zero strength and stiffness so that the soil was allowed free movement of the soil materials in the upward direction, whereas the soil layer had the typical value of strength and stiffness.Figure 5
Numerical model.Figure 6
Front view of the soil model.The standpipe was set as a rigid body and adopted as a Lagrangian domain. Hence, the mesh of the standpipe domains consisted of 8-node Lagrangian brick elements (C3D8R). The soil was considered an Eulerian domain, and its mesh consisted of 8-node Eulerian brick elements (EC3D8R). A fine mesh zone with a horizontal extension of 2.2 m (1.22D) was set near the standpipe, where the mesh size was 0.1D along the horizontal direction, and the rest was 0.4 m (0.22D). The mesh size was 0.2 m (approximately 0.1D) along the height direction. The total number of elements was 169840.In addition, the soil parameters used in the numerical simulations are depicted in Table5.Table 5
Setting table of soil parameters in standard conditions [24].
ParametersDensity (kN/m3)Cohesion (kPa)Internal friction angle (°)Poisson’s ratioElastic modulus (MPa)Value20.032140.3518


### 3.2. Numerical Simulation Procedure

The initial stress field caused by the self-weight of the model is of great importance [25, 26]. Therefore, the geostatic stress was supposed to be imposed in a predefined step according to the self-weight of the material.Mohr–Coulomb yield strength criterion was used in the CEL simulation, which was able to reflect the engineering properties of geotechnical materials well. In addition, the self-contact algorithm was selected for the contact surfaces between the standpipe and soil.The simulation process was mainly divided into two steps: the initial step and the penetration step. In the penetration step, jacking was realised by defining the end circle centre of the standpipe as the reference point. To keep the jacking speed at a constant value, the displacement load of the amplitude was defined as tabular. When the time was 0, the amplitude was set to 0, and when the time was the total step time, the amplitude was set to 1.


### 3.3. Comparison of the Test and Numerical Results

Before the numerical simulation of actual working conditions, numerical simulation research based on the model test was carried out, and the measured values of the test and numerical simulation values were compared to verify the validity of the CEL method. Figure7 shows that the two had the same trend with increasing jacked distance. Furthermore, the measured value and numerical simulation value of the maximum jacking force were 756 N and 803.6 N, respectively. The numerical simulation value was larger, with a difference of 6.3%. The measured value and numerical simulation value of the terminal jacking force were 223 N and 199.7 N, respectively. The numerical simulation value was small, with a difference of 10.4%. Overall, the two showed good agreement.Figure 7
Comparison of jacking force.


## 3.1. Numerical Model

The coupled Eulerian–Lagrangian (CEL) technique in Abaqus was employed to simulate the process of vertical jacking construction. Due to the symmetry of the model, only a quarter of the domain was modelled. As shown in Figure5, this model consists of two parts: standpipe and soil. The standpipe outer diameter (D) is 1.8 m, and the length is 8 m. To avoid large mesh distortions, the top 0.45 m of the standpipe is embedded in the soil [12]. Thus, the jacking height (H) is actually 7.55 m. The soil is (length by width by height) 18 m × 18 m × 16 m, which was divided into two layers of the same size: the soil layer and the void layer (see Figure 6). The void layer at the top of the soil model had zero strength and stiffness so that the soil was allowed free movement of the soil materials in the upward direction, whereas the soil layer had the typical value of strength and stiffness.Figure 5
Numerical model.Figure 6
Front view of the soil model.The standpipe was set as a rigid body and adopted as a Lagrangian domain. Hence, the mesh of the standpipe domains consisted of 8-node Lagrangian brick elements (C3D8R). The soil was considered an Eulerian domain, and its mesh consisted of 8-node Eulerian brick elements (EC3D8R). A fine mesh zone with a horizontal extension of 2.2 m (1.22D) was set near the standpipe, where the mesh size was 0.1D along the horizontal direction, and the rest was 0.4 m (0.22D). The mesh size was 0.2 m (approximately 0.1D) along the height direction. The total number of elements was 169840.In addition, the soil parameters used in the numerical simulations are depicted in Table5.Table 5
Setting table of soil parameters in standard conditions [24].
ParametersDensity (kN/m3)Cohesion (kPa)Internal friction angle (°)Poisson’s ratioElastic modulus (MPa)Value20.032140.3518


## 3.2. Numerical Simulation Procedure

The initial stress field caused by the self-weight of the model is of great importance [25, 26]. Therefore, the geostatic stress was supposed to be imposed in a predefined step according to the self-weight of the material.Mohr–Coulomb yield strength criterion was used in the CEL simulation, which was able to reflect the engineering properties of geotechnical materials well. In addition, the self-contact algorithm was selected for the contact surfaces between the standpipe and soil.The simulation process was mainly divided into two steps: the initial step and the penetration step. In the penetration step, jacking was realised by defining the end circle centre of the standpipe as the reference point. To keep the jacking speed at a constant value, the displacement load of the amplitude was defined as tabular. When the time was 0, the amplitude was set to 0, and when the time was the total step time, the amplitude was set to 1.


## 3.3. Comparison of the Test and Numerical Results

Before the numerical simulation of actual working conditions, numerical simulation research based on the model test was carried out, and the measured values of the test and numerical simulation values were compared to verify the validity of the CEL method. Figure7 shows that the two had the same trend with increasing jacked distance. Furthermore, the measured value and numerical simulation value of the maximum jacking force were 756 N and 803.6 N, respectively. The numerical simulation value was larger, with a difference of 6.3%. The measured value and numerical simulation value of the terminal jacking force were 223 N and 199.7 N, respectively. The numerical simulation value was small, with a difference of 10.4%. Overall, the two showed good agreement.Figure 7
Comparison of jacking force.


## 4. Discussion

The discussion of the study is described in the following sections.


### 4.1. Analysis of CEL Numerical Simulation Results

The analysis of CEL numerical simulation results is explained in the following sections.


#### 4.1.1. Influence of Jacking Speed

In actual working engineering, the jacking speed of the vertical tunnelling method is generally 5 ∼ 10 mm/min. However, in the finite element simulation, the jacking speed should not be set too small. Otherwise, the calculation speed is significantly reduced, and the efficiency is reduced. Additionally, the jacking speed should not be set too large. Otherwise, it will lead to a lack of computational accuracy. Referred to work by Hu et al. [27] and Dai et al. [28], the numerical simulation was set to be 0.1 m/s, 0.2 m/s, 0.4 m/s, and 1 m/s.Figure8 shows the influence of jacking speed on jacking force; the multiple of jacking speed in Figure 8(b) equals the quotient of the actual jacking speed divided by the minimum jacking speed, the same as below. We know that the greater the jacking speed was, the greater the maximum jacking force, and the smaller the terminal jacking force. However, the effect of jacking speed on the maximum jacking force was limited. Moreover, the influence on the position where the maximum jacking force occurs was not obvious, which was approximately 0.83 m (0.11H). Figure 8(b) shows that when the jacking speed was 0.2 m/s, the maximum jacking force was 3543 kN, while the maximum jacking force was 3470.2 kN when the jacking speed was 0.1 m/s. The difference was 2.1%, while the software running time increased by 367%. The operation time was significantly enhanced. Therefore, the jacking speed was suggested to be 0.2 m/s for simulation. Furthermore, there was a nonlinear positive correlation between jacking speed and maximum jacking force, and the effect was small.Figure 8
Influence of jacking speed on jacking force. (a) Influence of jacking speed on jacking force. (b) Relationship between jacking speed and maximum jacking force and software running time.
(a)(b)


#### 4.1.2. Influence of the Standpipe Outer Diameter

Figure9 shows the influence of the standpipe outer diameter on the jacking force. We know that the greater the standpipe outer diameter was, the greater the jacking force, and the position where the maximum jacking force occurs was advanced. When the outer diameter was 1 m, the position was 1.66 m (0.22H). When the outer diameter was 1.8 m, the position was 0.83 m (0.11H), which was a great increase. If 80% ∼ 100% Fmax in the construction process was defined as a large jacking force, the working area of a large jacking force was negatively correlated with the outer diameter. When the outer diameter was 1 m, the distance of the working area was 0.4H. When the outer diameter was 1.8 m, the distance was 0.256H. Based on the above research, it is necessary to pay attention to the influence of the maximum jacking force earlier when the outer diameter is large. Additionally, the effect of a large jacking force still needs to be prepared at all times when the outer diameter is small. Furthermore, Figure 9(b) shows that there was an approximate linear positive correlation between the standpipe outer diameter and maximum jacking force, and the effect was large.Figure 9
Influence of the standpipe outer diameter on jacking force. (a) Influence of the standpipe outer diameter on jacking force. (b) Relationship between the standpipe outer diameter and maximum jacking force.
(a)(b)


#### 4.1.3. Influence of Soil Conditions

Figure10 shows the influence of different soil conditions (including cohesion, internal friction angle, elastic modulus, and Poisson’s ratio) on jacking force. Figure 11 shows the relationship between different soil conditions and the maximum jacking force.Figure 10
Influence of soil conditions on jacking force. (a) Cohesion. (b) Internal friction. (c) Elastic modulus. (d) Poisson’s ratio.
(a)(b)(c)(d)Figure 11
Influence of soil conditions on maximum jacking force. (a) Cohesion. (b) Internal friction. (c) Elastic modulus. (d) Poisson’s ratio.
(a)(b)(c)(d)Figure10 shows that when the other conditions were the same, the greater the cohesion was, the greater the jacking force. The greater the internal friction angle and elastic modulus were, the greater the maximum jacking force, and the smaller the terminal jacking force. There was little effect on the jacking force for Poisson’s ratio. However, when Poisson’s ratio was increased to 0.49, the maximum jacking force increased. In addition, there was little relationship between the position where the maximum jacking force occurs and cohesion or internal friction angle. In contrast, the position was related to the elastic modulus. When the elastic modulus was increased from 6 MPa to 24 MPa, the position was advanced from 0.197H to 0.095H, and when Poisson’s ratio was increased to 0.49, the position also advanced slightly. Moreover, the working area of a large jacking force had little to do with cohesion and Poisson’s ratio, which was negatively correlated with the internal friction angle and elastic modulus. When the internal friction angle was increased from 10° to 22°, the working distance decreased from 0.366H to 0.195H, and when the elastic modulus was increased from 6 MPa to 24 MPa, the working distance decreased from 0.36H to 0.245H. Moreover, the terminal jacking force was positively correlated with cohesion and negatively correlated with the internal friction angle, elastic modulus, and Poisson’s ratio.Figure11 shows that the maximum jacking force was linearly and positively correlated with cohesion, internal friction angle, and Poisson’s ratio and was nonlinearly and positively correlated with elastic modulus. Among the four parameters, cohesion and internal friction angle had the greatest impact, followed by elastic modulus and Poisson’s ratio.Among the above two construction parameters and four soil conditions, the influence degree on the maximum jacking force from large to small was the outer diameter, internal friction angle, cohesion, elastic modulus, jacking speed, and Poisson’s ratio.


### 4.2. Analysis of Model Test Results

The analysis of model test results is explained in the following sections.


#### 4.2.1. Influence of Height of Overburden Soil

Based on Section2.3, Figure 12 shows that when other conditions were the same, the higher the height of the overburden soil was, the greater the jacking force was. When the height was 0.375 m, 0.425 m, and 0.475 m, the maximum jacking forces were 607 N, 756 N, and 1014 N, respectively, and the terminal jacking forces were 198 N, 223 N, and 326 N, respectively. The height of overburdened soil had a great influence on the jacking force.Figure 12
Influence of height of overburden soil on jacking force.


#### 4.2.2. Influence of Water Conditions on Jacking Force

Based on 2.3, after adding water, the soil weight was increased from 15 kN/m3 to 16.3 kN/m3, so the water content was 8.67% in this test. Figure 13 shows that the compressibility of the soil was enhanced after adding water. Different from the declining trend, the jacking force with increasing jacked distance first increased and then decreased. In addition, adding water had little effect on the maximum jacking force.Figure 13
Influence of water conditions on jacking force.


## 4.1. Analysis of CEL Numerical Simulation Results

The analysis of CEL numerical simulation results is explained in the following sections.


### 4.1.1. Influence of Jacking Speed

In actual working engineering, the jacking speed of the vertical tunnelling method is generally 5 ∼ 10 mm/min. However, in the finite element simulation, the jacking speed should not be set too small. Otherwise, the calculation speed is significantly reduced, and the efficiency is reduced. Additionally, the jacking speed should not be set too large. Otherwise, it will lead to a lack of computational accuracy. Referred to work by Hu et al. [27] and Dai et al. [28], the numerical simulation was set to be 0.1 m/s, 0.2 m/s, 0.4 m/s, and 1 m/s.Figure8 shows the influence of jacking speed on jacking force; the multiple of jacking speed in Figure 8(b) equals the quotient of the actual jacking speed divided by the minimum jacking speed, the same as below. We know that the greater the jacking speed was, the greater the maximum jacking force, and the smaller the terminal jacking force. However, the effect of jacking speed on the maximum jacking force was limited. Moreover, the influence on the position where the maximum jacking force occurs was not obvious, which was approximately 0.83 m (0.11H). Figure 8(b) shows that when the jacking speed was 0.2 m/s, the maximum jacking force was 3543 kN, while the maximum jacking force was 3470.2 kN when the jacking speed was 0.1 m/s. The difference was 2.1%, while the software running time increased by 367%. The operation time was significantly enhanced. Therefore, the jacking speed was suggested to be 0.2 m/s for simulation. Furthermore, there was a nonlinear positive correlation between jacking speed and maximum jacking force, and the effect was small.Figure 8
Influence of jacking speed on jacking force. (a) Influence of jacking speed on jacking force. (b) Relationship between jacking speed and maximum jacking force and software running time.
(a)(b)


### 4.1.2. Influence of the Standpipe Outer Diameter

Figure9 shows the influence of the standpipe outer diameter on the jacking force. We know that the greater the standpipe outer diameter was, the greater the jacking force, and the position where the maximum jacking force occurs was advanced. When the outer diameter was 1 m, the position was 1.66 m (0.22H). When the outer diameter was 1.8 m, the position was 0.83 m (0.11H), which was a great increase. If 80% ∼ 100% Fmax in the construction process was defined as a large jacking force, the working area of a large jacking force was negatively correlated with the outer diameter. When the outer diameter was 1 m, the distance of the working area was 0.4H. When the outer diameter was 1.8 m, the distance was 0.256H. Based on the above research, it is necessary to pay attention to the influence of the maximum jacking force earlier when the outer diameter is large. Additionally, the effect of a large jacking force still needs to be prepared at all times when the outer diameter is small. Furthermore, Figure 9(b) shows that there was an approximate linear positive correlation between the standpipe outer diameter and maximum jacking force, and the effect was large.Figure 9
Influence of the standpipe outer diameter on jacking force. (a) Influence of the standpipe outer diameter on jacking force. (b) Relationship between the standpipe outer diameter and maximum jacking force.
(a)(b)


### 4.1.3. Influence of Soil Conditions

Figure10 shows the influence of different soil conditions (including cohesion, internal friction angle, elastic modulus, and Poisson’s ratio) on jacking force. Figure 11 shows the relationship between different soil conditions and the maximum jacking force.Figure 10
Influence of soil conditions on jacking force. (a) Cohesion. (b) Internal friction. (c) Elastic modulus. (d) Poisson’s ratio.
(a)(b)(c)(d)Figure 11
Influence of soil conditions on maximum jacking force. (a) Cohesion. (b) Internal friction. (c) Elastic modulus. (d) Poisson’s ratio.
(a)(b)(c)(d)Figure10 shows that when the other conditions were the same, the greater the cohesion was, the greater the jacking force. The greater the internal friction angle and elastic modulus were, the greater the maximum jacking force, and the smaller the terminal jacking force. There was little effect on the jacking force for Poisson’s ratio. However, when Poisson’s ratio was increased to 0.49, the maximum jacking force increased. In addition, there was little relationship between the position where the maximum jacking force occurs and cohesion or internal friction angle. In contrast, the position was related to the elastic modulus. When the elastic modulus was increased from 6 MPa to 24 MPa, the position was advanced from 0.197H to 0.095H, and when Poisson’s ratio was increased to 0.49, the position also advanced slightly. Moreover, the working area of a large jacking force had little to do with cohesion and Poisson’s ratio, which was negatively correlated with the internal friction angle and elastic modulus. When the internal friction angle was increased from 10° to 22°, the working distance decreased from 0.366H to 0.195H, and when the elastic modulus was increased from 6 MPa to 24 MPa, the working distance decreased from 0.36H to 0.245H. Moreover, the terminal jacking force was positively correlated with cohesion and negatively correlated with the internal friction angle, elastic modulus, and Poisson’s ratio.Figure11 shows that the maximum jacking force was linearly and positively correlated with cohesion, internal friction angle, and Poisson’s ratio and was nonlinearly and positively correlated with elastic modulus. Among the four parameters, cohesion and internal friction angle had the greatest impact, followed by elastic modulus and Poisson’s ratio.Among the above two construction parameters and four soil conditions, the influence degree on the maximum jacking force from large to small was the outer diameter, internal friction angle, cohesion, elastic modulus, jacking speed, and Poisson’s ratio.


## 4.1.1. Influence of Jacking Speed

In actual working engineering, the jacking speed of the vertical tunnelling method is generally 5 ∼ 10 mm/min. However, in the finite element simulation, the jacking speed should not be set too small. Otherwise, the calculation speed is significantly reduced, and the efficiency is reduced. Additionally, the jacking speed should not be set too large. Otherwise, it will lead to a lack of computational accuracy. Referred to work by Hu et al. [27] and Dai et al. [28], the numerical simulation was set to be 0.1 m/s, 0.2 m/s, 0.4 m/s, and 1 m/s.Figure8 shows the influence of jacking speed on jacking force; the multiple of jacking speed in Figure 8(b) equals the quotient of the actual jacking speed divided by the minimum jacking speed, the same as below. We know that the greater the jacking speed was, the greater the maximum jacking force, and the smaller the terminal jacking force. However, the effect of jacking speed on the maximum jacking force was limited. Moreover, the influence on the position where the maximum jacking force occurs was not obvious, which was approximately 0.83 m (0.11H). Figure 8(b) shows that when the jacking speed was 0.2 m/s, the maximum jacking force was 3543 kN, while the maximum jacking force was 3470.2 kN when the jacking speed was 0.1 m/s. The difference was 2.1%, while the software running time increased by 367%. The operation time was significantly enhanced. Therefore, the jacking speed was suggested to be 0.2 m/s for simulation. Furthermore, there was a nonlinear positive correlation between jacking speed and maximum jacking force, and the effect was small.Figure 8
Influence of jacking speed on jacking force. (a) Influence of jacking speed on jacking force. (b) Relationship between jacking speed and maximum jacking force and software running time.
(a)(b)


## 4.1.2. Influence of the Standpipe Outer Diameter

Figure9 shows the influence of the standpipe outer diameter on the jacking force. We know that the greater the standpipe outer diameter was, the greater the jacking force, and the position where the maximum jacking force occurs was advanced. When the outer diameter was 1 m, the position was 1.66 m (0.22H). When the outer diameter was 1.8 m, the position was 0.83 m (0.11H), which was a great increase. If 80% ∼ 100% Fmax in the construction process was defined as a large jacking force, the working area of a large jacking force was negatively correlated with the outer diameter. When the outer diameter was 1 m, the distance of the working area was 0.4H. When the outer diameter was 1.8 m, the distance was 0.256H. Based on the above research, it is necessary to pay attention to the influence of the maximum jacking force earlier when the outer diameter is large. Additionally, the effect of a large jacking force still needs to be prepared at all times when the outer diameter is small. Furthermore, Figure 9(b) shows that there was an approximate linear positive correlation between the standpipe outer diameter and maximum jacking force, and the effect was large.Figure 9
Influence of the standpipe outer diameter on jacking force. (a) Influence of the standpipe outer diameter on jacking force. (b) Relationship between the standpipe outer diameter and maximum jacking force.
(a)(b)


## 4.1.3. Influence of Soil Conditions

Figure10 shows the influence of different soil conditions (including cohesion, internal friction angle, elastic modulus, and Poisson’s ratio) on jacking force. Figure 11 shows the relationship between different soil conditions and the maximum jacking force.Figure 10
Influence of soil conditions on jacking force. (a) Cohesion. (b) Internal friction. (c) Elastic modulus. (d) Poisson’s ratio.
(a)(b)(c)(d)Figure 11
Influence of soil conditions on maximum jacking force. (a) Cohesion. (b) Internal friction. (c) Elastic modulus. (d) Poisson’s ratio.
(a)(b)(c)(d)Figure10 shows that when the other conditions were the same, the greater the cohesion was, the greater the jacking force. The greater the internal friction angle and elastic modulus were, the greater the maximum jacking force, and the smaller the terminal jacking force. There was little effect on the jacking force for Poisson’s ratio. However, when Poisson’s ratio was increased to 0.49, the maximum jacking force increased. In addition, there was little relationship between the position where the maximum jacking force occurs and cohesion or internal friction angle. In contrast, the position was related to the elastic modulus. When the elastic modulus was increased from 6 MPa to 24 MPa, the position was advanced from 0.197H to 0.095H, and when Poisson’s ratio was increased to 0.49, the position also advanced slightly. Moreover, the working area of a large jacking force had little to do with cohesion and Poisson’s ratio, which was negatively correlated with the internal friction angle and elastic modulus. When the internal friction angle was increased from 10° to 22°, the working distance decreased from 0.366H to 0.195H, and when the elastic modulus was increased from 6 MPa to 24 MPa, the working distance decreased from 0.36H to 0.245H. Moreover, the terminal jacking force was positively correlated with cohesion and negatively correlated with the internal friction angle, elastic modulus, and Poisson’s ratio.Figure11 shows that the maximum jacking force was linearly and positively correlated with cohesion, internal friction angle, and Poisson’s ratio and was nonlinearly and positively correlated with elastic modulus. Among the four parameters, cohesion and internal friction angle had the greatest impact, followed by elastic modulus and Poisson’s ratio.Among the above two construction parameters and four soil conditions, the influence degree on the maximum jacking force from large to small was the outer diameter, internal friction angle, cohesion, elastic modulus, jacking speed, and Poisson’s ratio.


## 4.2. Analysis of Model Test Results

The analysis of model test results is explained in the following sections.


### 4.2.1. Influence of Height of Overburden Soil

Based on Section2.3, Figure 12 shows that when other conditions were the same, the higher the height of the overburden soil was, the greater the jacking force was. When the height was 0.375 m, 0.425 m, and 0.475 m, the maximum jacking forces were 607 N, 756 N, and 1014 N, respectively, and the terminal jacking forces were 198 N, 223 N, and 326 N, respectively. The height of overburdened soil had a great influence on the jacking force.Figure 12
Influence of height of overburden soil on jacking force.


### 4.2.2. Influence of Water Conditions on Jacking Force

Based on 2.3, after adding water, the soil weight was increased from 15 kN/m3 to 16.3 kN/m3, so the water content was 8.67% in this test. Figure 13 shows that the compressibility of the soil was enhanced after adding water. Different from the declining trend, the jacking force with increasing jacked distance first increased and then decreased. In addition, adding water had little effect on the maximum jacking force.Figure 13
Influence of water conditions on jacking force.


## 4.2.1. Influence of Height of Overburden Soil

Based on Section2.3, Figure 12 shows that when other conditions were the same, the higher the height of the overburden soil was, the greater the jacking force was. When the height was 0.375 m, 0.425 m, and 0.475 m, the maximum jacking forces were 607 N, 756 N, and 1014 N, respectively, and the terminal jacking forces were 198 N, 223 N, and 326 N, respectively. The height of overburdened soil had a great influence on the jacking force.Figure 12
Influence of height of overburden soil on jacking force.


## 4.2.2. Influence of Water Conditions on Jacking Force

Based on 2.3, after adding water, the soil weight was increased from 15 kN/m3 to 16.3 kN/m3, so the water content was 8.67% in this test. Figure 13 shows that the compressibility of the soil was enhanced after adding water. Different from the declining trend, the jacking force with increasing jacked distance first increased and then decreased. In addition, adding water had little effect on the maximum jacking force.Figure 13
Influence of water conditions on jacking force.


## 5. Conclusion

In this study, the jacking force in the process of the vertical tunnelling method was analysed by model tests and numerical simulations. The main conclusions were as follows:(1)
The results from the CEL method based on the model test were in good agreement with the measured value of the test. In addition, the jacking speed was suggested to be 0.2 m/s for the analysis of the numerical simulation.(2)
The numerical results showed that the position where the maximum jacking force occurs had little to do with the cohesion and internal friction angle and was negatively correlated with the outer diameter of the standpipe and elastic modulus instead. Especially when Poisson’s ratio was increased to 0.49, the position was slightly advanced.(3)
The numerical results showed that the working area of a large jacking force had little to do with jacking speed, cohesion, and Poisson’s ratio and was negatively correlated with the outer diameter of the standpipe, internal friction angle, and elastic modulus.(4)
The numerical results showed that the maximum jacking force was linearly and positively correlated with the standpipe outer diameter, cohesion, internal friction angle, and Poisson’s ratio. Moreover, it was nonlinearly and positively correlated with the elastic modulus and jacking speed. Among the above two construction parameters and four soil conditions, the influence degree on the maximum jacking force from large to small was the outer diameter, internal friction angle, cohesion, elastic modulus, jacking speed, and Poisson’s ratio.(5)
The test results showed that when other conditions were the same, the higher the height of the overburden soil was, the greater the jacking force was. The effect was strong. Additionally, adding water could enhance the compressibility of the soil but had little effect on the maximum jacking force.



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*Source: 3046621-2022-12-15.xml*