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

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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 efciency, and safety [1,2].Te process of the vertical tunnelling method is shown in Figure 1.Te 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.
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 coefcient and obtained the changing law of the jacking force.Wei et al. [4] employed discrete elements to simulate the jacking process and studied the infuence 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 infuencing 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 afecting 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.Tere has been some research on the introduction of construction techniques and usages [3,6,7].However, the jacking force was rarely considered.
Te model test is an important research method, especially in the case of insufcient research theory [8][9][10][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 fnite element method also plays an important role in solving geotechnical problems [12,13].Terefore, 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][17][18][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 diferent heights of overburdened soil and water conditions were designed.Moreover, the infuences of jacking speed, the standpipe outer diameter, and soil parameters on jacking force were obtained by the CEL method in Abaqus.Te research results can provide a reference for guiding similar engineering construction.

Model Test
Te model test is explained in the following sections.

Similarity Principle and Simplifcations of the Test.
Te 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][21][22].However, it is nearly impossible to meet all similar constants [23].In this study, the geometric dimension similarity constant (C L ) was determined to be 14, and the similarity constant for bulk weight was determined to be 1.Te 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 simplifed as a complete semicylinder, ignoring the infuence 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.Tis test was simplifed as a complete standpipe, and the standpipe was marked every 0.025 m, which represented one pipe section.

Model Test Apparatus.
A schematic sketch of the model test is shown in Figure 2. Te 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.Tere was a hole with a diameter of 0.13 m to place the standpipe on the top of the horizontal tunnel.Te loading system for load application was composed of an oil pump and hydraulic cylinder.Te rated power of the oil pump was 0.75 kW, and the jacking speed was 4.4 mm/s.Te diameter of the piston rod of the hydraulic cylinder was 65 mm, which was larger than the diameter of the pressure sensor.Te stroke of the piston rod was 0.45 m.Te data acquisition system for collecting the original data of the test consisted of the pressure sensor and digital display.Te 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.Te 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.Te top cover was hollow, with an outer diameter of 0.13 m and a height of 0.025 m.Four Earth pressure cells were fxed on the surface of the top cover to monitor the soil pressure in the jacking process.Te total weight of the standpipe and the top cover was 8.7 kg.

Model Materials and Test Conditions.
Sea sand was selected as the test material and dried before the test.Te relevant physical parameters are shown in Table 3.
Te jacking force might be related to the height of overburdened soil and water conditions.Terefore, four model tests were designed.Te specifc test conditions are shown in Table 4. (2) Te model box was flled to the specifed height.In the process, the uniform distribution of fll should be ensured as much as possible (see Figures 4(c) and 4(d)).

Test Process. As shown in
(3) Te foaming adhesive was applied at the bottom of the horizontal tunnel to prevent sand leakage (see Figure 4(e)).Ten, the power supply of the oil pump was connected, and jacking was started (see Figure 4(f)).

Numerical Simulation
Te numerical simulation is described in the following sections.To avoid large mesh distortions, the top 0.45 m of the standpipe is embedded in the soil [12].Tus, the jacking height (H) is actually 7.55 m.Te 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).Te void layer at the top of the soil model had zero strength and stifness 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 stifness.Te 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).Te soil was considered an Eulerian domain, and its mesh consisted of 8-node Eulerian brick elements (EC3D8R).A fne 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).Te mesh size was 0.2 m (approximately 0.1D) along the height direction.Te total number of elements was 169840.
In addition, the soil parameters used in the numerical simulations are depicted in Table 5.

Numerical Simulation Procedure.
Te initial stress feld caused by the self-weight of the model is of great importance [25,26].Terefore, the geostatic stress was supposed to be imposed in a predefned step according to the self-weight of the material.
Mohr-Coulomb yield strength criterion was used in the CEL simulation, which was able to refect the engineering properties of geotechnical materials well.In addition, the self-contact algorithm was selected for the contact surfaces between the standpipe and soil.Te simulation process was mainly divided into two steps: the initial step and the penetration step.In the penetration step, jacking was realised by defning the end circle centre of the as the reference point.To keep the jacking speed at a constant value, the displacement load of the amplitude was defned 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.

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.Figure 7 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.Te numerical simulation value was larger, with a diference of 6.3%.Te measured value and numerical simulation value of the terminal jacking force were 223 N and 199.7 N, respectively.Te numerical simulation value was small, with a diference of 10.4%.Overall, the two showed good agreement.

Discussion
Te discussion of the study is described in the following sections.

Analysis of CEL Numerical Simulation Results
. Te analysis of CEL numerical simulation results is explained in the following sections.

Infuence of Jacking Speed.
In actual working engineering, the jacking speed of the vertical tunnelling method is generally 5 ∼ 10 mm/min.However, in the fnite element simulation, the jacking speed should not be set too small.Otherwise, the calculation speed is signifcantly reduced, and the efciency 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.
Figure 8 shows the infuence 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 efect of jacking speed on the maximum jacking force was limited.Moreover, the infuence 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.Te diference was 2.1%, while the software running time increased by 367%.Te operation time was signifcantly enhanced.Terefore, 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 efect was small.

Infuence of the Standpipe Outer Diameter.
Figure 9 shows the infuence 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% F max in the construction process was defned 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 infuence of the maximum jacking force   Advances in Civil Engineering earlier when the outer diameter is large.Additionally, the efect 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 between the standpipe outer diameter and maximum jacking force, and the efect was large.

Infuence of Soil Conditions.
Figure 10 shows the infuence of diferent soil conditions (including cohesion, internal friction angle, elastic modulus, and Poisson's ratio) on jacking force.Figure 11 shows the relationship between diferent soil conditions and the maximum jacking force.
Figure 10 shows that when the other conditions were the same, the greater the cohesion was, the greater the jacking force.Te greater the internal friction angle and elastic modulus were, the greater the maximum jacking force, and the smaller the terminal jacking force.Tere was little efect on the jacking force for Poisson's ratio.However, when Poisson's ratio was increased to 0.49, the maximum jacking    Advances in Civil Engineering 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.
Figure 11 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 infuence 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.

Analysis of Model Test Results
. Te analysis of model test results is explained in the following sections.

Infuence of Height of Overburden Soil.
Based on Section 2.3, 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.Te height of overburdened soil had a great infuence on the jacking force.

Infuence of Water Conditions on Jacking Force.
Based on 2.3, after adding water, the soil weight was increased from 15 kN/m 3 to 16.3 kN/m 3 , so the water content was 8.67% in this test.Figure 13 shows that the compressibility of the soil was enhanced after adding water.Diferent from the declining trend, the jacking force with increasing jacked distance frst increased and then decreased.In addition, adding water had little efect on the maximum jacking force.

Conclusion
In this study, the jacking force in the process of the vertical tunnelling method was analysed by model tests and numerical simulations.Te main conclusions were as follows: (1) Te 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) Te 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) Te 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) Te 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 infuence 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) Te 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.Te efect was strong.Additionally, adding water could enhance the compressibility of the soil but had little efect on the maximum jacking force.

Figure 1 :
Figure 1: Construction process of the vertical tunnelling method.

Figure 2 :Figure 3 :
Figure 2: Schematic sketch of the indoor model test.
3.1.Numerical Model.Te 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 Figure 5, this model consists of two parts: standpipe and soil.Te standpipe outer diameter (D) is 1.8 m, and the length is 8 m.

Figure 9 :
Figure 9: Infuence of the standpipe outer diameter on jacking force.(a) Infuence of the standpipe outer diameter on jacking force.(b) Relationship between the standpipe outer diameter and maximum jacking force.

Figure 8 :
Figure 8: Infuence of jacking speed on jacking force.(a) Infuence of jacking speed on jacking force.(b) Relationship between jacking speed and maximum jacking force and software running time.

Table 1 :
Geometric values between the prototype and the model.

Table 3 :
Basic physical properties of sand.