Study on the Deformation Induced by Vertical Two-Layer Large Diameter Pipe-Jacking in the Soil-Rock Composite Stratum

Abstract

Aiming at the features of deformation caused by large diameter vertical two-layer pipe jacking in the soil-rock composite stratum, on-site monitoring and numerical analysis has been done based on an electric power tunnel project constructed with the pipe jacking method, in which the upper tunnel is located in the soil layer and the lower tunnel is partially located in the rock layer. The research shows that: (1) During upper pipe jacking construction, the maximum transverse and longitudinal ground settlements are about three times those of the lower pipe jacking construction, and the maximum horizontal lateral displacement is about 3.3 times the lower pipe jacking construction. (2) Total ground settlement increases rapidly with the reduction of vertical clear spacing of the upper and lower pipe, and the superimposed effect should be taken into consideration during the vertical arranged pipe-jacking construction. (3) The Peck formula, which is used to estimate lateral surface subsidence distribution, is modified to make it more applicable in the soil–rock composite stratum to calculate the ground settlement induced by the construction of pipe-jacking.

1. Introduction

In recent years, with the rapid development of urban underground space, such as utility tunnel, underground station, and underground commercial space [1,2,3], pipe jacking technology has been widely applied to the construction of large diameter pipe, municipal pipe corridors and underground passages due to its advantages of small excavation amount and few impacts on the surrounding environment [4]. However, pipe jacking will have a certain impact on the ground; in particular, large section jacking construction in complex stratum will cause greater disturbance to the soil within the affected area [5,6]. Research concerning soil deformation features during pipe-jacking has received some attention. Peck [7] obtained the typically distributed land subsidence conclusions based on the analysis of the number of engineering measured data. The Peck formula for estimating the lateral ground settlement was proposed with the assumption that the soil is incompressible. Fang et al. [8] modified Peck’s formula for calculating ground surface settlement by conducting the on-site monitoring of large pipe jacking construction. By field tests and theoretical comparisons, Tang et al. [9] showed that the Peck formula is more accurate in predicting natural settlement within 1.5 times the width of the pipe jacking, and put forward suggestions for predicting ground settlement of large rectangular pipe jacking. Bing et al. [10] obtained the influence range of transverse and longitudinal surface deformation caused by circular pipe jacking construction based on simulating the actual working conditions. Ren et al. [11] put forward a calculation method of surface settlement during circular pipe jacking and carried out a case analysis. Wei et al. [12] proposed the soil disturbance zoning map through on-site monitoring. By three-dimensional numerical simulation, Yu [13] obtained the ground deformation features in the process of the construction of pipe jacking and finished construction. Jing et al. [14] modified the Loganathan soil deformation equation based on the Mindlin’s solution with improved clearance parameter g to derive the dynamic changes of the surface soil during jacking. Huang et al. [15] used the three-dimensional numerical analysis method to simulate the frontal thrust of the pipe jacking machine head, ground loss and grouting, etc., and studied the stress and surface displacement distribution of surrounding soil during pipe jacking. Using Mindlin’s displacement solution to analyze the formation deformation caused by additional stress and friction on excavation surface and soil loss during pipe jacking, Niu et al. [16] obtained the surface settlement model based on the random medium theory. By analyzing the interaction characteristics between the main components of the tunnel boring machine and complex geological conditions, Qi et al. [17] proposed a model to calculate the total thrust and torque.

The above are some studies on the deformation features of the soil induced by single pipe jacking construction. These scholars studied the single-layer pipe jacking construction through one or more methods, such as field monitoring, numerical simulation and theoretical analysis, and deeply analyzed the soil deformation mechanism and characteristics. The settlement, soil displacement and toppling force changes in the construction process are monitored through field monitoring. The monitoring method can provide reference for subsequent engineering monitoring. The data obtained can provide a realistic basis for subsequent research, and create a foundation for optimizing the construction process and intelligent information construction. Numerical simulation can simulate working conditions that are different from the actual engineering through software, which can solve the limitations of the single condition and special situation of the actual engineering, so as to study the general law and promote the results of the single engineering research. Theoretical analysis, on the basis of the existing theoretical studies, can be a more in-depth analysis of the soil change mechanism, and through the in-depth study of the formula, can be a more suitable calculation formula. In order to further save underground space in the important areas, the pipes are arranged vertically in two layers. However, there is less research on the deformation features of the soil induced by the construction of vertical two-layer pipe jacking. The main ones are Yang et al. [18], who studied the vertical deformation feature of silty clay caused by two-layer pipe jacking construction and the soil pipe crossing is relatively simple in this research. An et al. [19] also analyzed the sand layer ground settlement produced by the different construction sequences and pipe materials of two-layer pipe jacking. Nevertheless, the features of the deformation induced by two-layer pipe jacking are not clear, especially in the soil–rock composite stratum. Most of the Jinan area is soil–rock combination strata. Under the environment of accelerated urban development, more and more urban underground pipelines are arranged in the vertical double-layer layout, which means that the properties of the soil layer through which the upper layer and the lower layer are more different. With the rapid development of engineering construction, there is a serious lack of relevant research. Therefore, the study on soil deformation law of vertical double-layer pipe jacking construction in soil–rock combination stratum can effectively fill the research gap in this field, and it does not provide reference for subsequent related engineering and research.

Based on a real jacking project of a high-voltage power pipe corridor in Jinan city, on-site monitoring has been designed and carried out, and a large number of data of ground settlement and inner lateral displacement was obtained. Using Midas GTS NX 2021 finite element software, three-dimensional numerical simulation has been done to analyze the deformation of the soil–rock composite stratum. By comparison analysis, deformation features have been discussed and some useful conclusions are obtained. According to a new proposed theoretical model of the buried depth in rock formations of the pipe, the Peck formula has been studied and revised for calculating the ground settlement curve on the soil–rock composite stratum. By the calculation results comparison analysis of numerical and formula methods, the applicability of the revised Peck formula has been proved and can be used for the preliminary estimation of the ground settlement. This project is a vertical double-layer large-diameter pipe jacking construction of soil and rock combination stratum. The upper pipe jacking is located in the soil layer, and the lower pipe jacking is mostly located in the rock layer. The construction site is small, the scope of the construction influence is difficult to determine, and there is a lack of relevant engineering monitoring scheme for reference. Therefore, the layout and protection of site monitoring and measuring points are a great test for experimental research. In addition, during the derivation of the formula, the factors that caused the difference between the peck formula and the surface settlement caused by pipe jacking in the soil–rock combination stratum are not clear, which is a great challenge for the correction of the peck formula.

2. Project Overview

The total length of the circular electric power utility tunnel is about 1132 m, and the inner diameter is 3 m and the outer diameter is 3.6 m, which is divided into eight intervals and constructed using the pipe-jacking method. The length of a single segment of the circular tunnel is 2 m and prefabricated by reinforced concrete in the building component’s factory. Due to the increasing shortage of underground space in the important routes, the power utility tunnel is vertically arranged into two completely parallel layers and the clear distance between the upper and the lower reinforced concrete pipe is 3.6 m, which is 1.0 times the outer diameter of the pipe.

The layout of the working shafts and jacking construction route and vertical arrangement are shown in Figure 1. The jacking construction area from working shafts DGJ5 to DGJ6 is selected for the on-site monitoring and the jacking length is about 100 m. The average thickness of the soil covering the upper pipe is about 6.5 m and the lower pipe is partly buried in hard, moderately weathered rock mass. The pipe-jacking is divided into two stages, which is the lower pipe jacking that first uses the rock pipe jacking machine, and then the upper pipe uses the earth pressure balancing pipe jack.

3. On-Site Monitoring Arrangement

3.1. Layout of On-Site Monitoring Points

According to the site construction conditions, the plane layout of test monitoring points is shown in Figure 2. The numbers 1#–11# are the ground settlement monitoring points, among which 1#–6# are arranged along the jacking axis with an interval of 3 m, and 6#–11# are arranged perpendicular to the jacking axis with an interval of 1.5 m. The monitoring point 1# is 60 m away from the pipe-jacking operation shaft DGJ5. The cross section at the monitoring point 1# is the monitoring section I, and the cross section at the monitoring point 6# is the monitoring section II. L₁ and L₂ are, respectively, the distance from the excavation face to the monitoring section I and II. L₁ and L₂ are denoted as negative when the jacking machine arrived before the monitoring section, and the value is denoted as positive when the jacking machine passing the monitoring section.

In order to further explore the internal deformation of soil during pipe-jacking construction, the monitoring points of soil horizontal lateral displacement below the surface are arranged at section I on both sides of the power tunnel, numbered CX1–CX3 using inclinometers. The relative position relationship is shown in Figure 2 and Figure 3.

3.2. Transverse Ground Settlement

According to the site monitoring arrangement, the 6#–11# measuring points at monitoring section II and is 75 m away from the operation shaft. The monitoring results of transverse ground settlement in the process of the two-layer pipe jacking are shown in Figure 4. In the Figure 4, L₂ = −10 m and L₂ = 10 m mean the cutterhead of jacking machine is 10 m for reaching or passing through the monitoring section II, respectively, and the L₂ = 0 m represents that the cutterhead is located on the right in section II.

It can be seen from Figure 4 that: (1) The ground settlement of lower pipe jacking in the soil–rock stratum is about 0.8 mm, and the ground settlement of the upper pipe is about 2.3 mm, which is almost 3.0 times that of the lower pipe; (2) the curve of the transverse ground settlement caused by the lower pipe jacking is approximately horizontal, while the transverse ground settlement decreases significantly from the middle to both sides of the upper pipe, and the horizontal influence range exceeds 2D (D is the outer diameter of the jacking tube).

3.3. Longitudinal Ground Settlement

The monitoring results of longitudinal ground settlement during the construction of two-layer pipe jacking are shown in Figure 5, in which the upper and lower layers are counted separately. The dots of the settlement curves represent the ground settlement data of measuring points when the cutterhead is pushed from 50 m to 85 m when the interval is 5 m.

It can be seen from Figure 5 that: (1) The five settlement curves of the lower and upper pipe in the figure are basically consistent, indicating that the monitoring results collected are reliable. (2) With the approach of the pipe jacking machine ahead, the longitudinal settlement of the ground caused by the lower pipe jacking changes more gently, while the upper pipe jacking changes more rapidly. (3) The cumulative settlement of the pipe jacking machine before reaching the monitoring section accounts for about 60–70%. The main reasons are the discontinuity of pipe jacking and the difficulty in accurately controlling the pressure on the excavation surface, which leads to the larger settlement that has already occurred before the machine reaches the monitoring section. After the machine passes the monitoring section, with the bentonite mud injection, the pipe segment voids are filled, and the settlement tends to stabilize. It can be seen that it is difficult to achieve the ideal balance control of soil pressure in front of the cutterhead, so engineering measures should be strengthened for under-crossing important facilities.

3.4. Horizontal Lateral Displacement of Deep Soil

Figure 6a shows the monitoring results of horizontal lateral deformation of CX1 at monitoring section I with different positions of the cutterhead. The distance between this inclinometer monitoring point and the jacking axis is 2.3 m. Figure 6b shows the results of three horizontal soil deformation monitoring points when the jacking distance is 66 m (i.e., L₁ = 6 m)

It can be seen from Figure 6a that: (1) The horizontal lateral deformation caused by the upper pipe jacking is more obvious, and all the deformation is toward the pipe jacking hole. The maximum deformation is located at the center of the pipe, and the maximum lateral displacement is about 3.3 times that of the lower pipe jacking, and the vertical distribution range is wider than the lower pipe. (2) Before and after the pipe jacking machine reaches an excavation face of 2 m, the soil deformation into the hole accounts for about 50% of the total deformation. The main reasons for soil deformation inward from the jacking hole are the diameter of the pipe being less than that of the jacking machine cutterhead, bentonite mud filling not being compact, and mud seepage loss, etc. Therefore, it is necessary to strictly control the construction gap of pipe jacking and to adopt a reasonable proportion of mud to fill the void in time. As can be seen from Figure 6b, (1) CX1 is closer to the pipe jacking axis, and the horizontal deformation of soil is larger during construction. As the distance away from the axis increases, the effect of construction on the horizontal deformation becomes less and less. (2) The maximum horizontal deformation occurs near the depth of the pipeline, but the depth of the maximum horizontal displacement during the construction of the lower pipe jacking is higher than the depth of the pipeline, because in most of the displaced rock layers of the lower pipe jacking, the disturbance of the rock layer is smaller during the construction.

4. Numerical Simulation

4.1. Model Establishment

The following assumptions are made for the finite element method calculation [20]: (1) The soil is a homogeneous isotropic body and an ideal elastic–plastic body; (2) the thrust force acting on the excavation surface soil is circular, uniformly distributed load; (3) pipe segment joints are not considered in the model calculation; (4) the friction resistance value of bentonite mud is equally distributed along the pipeline; and (5) the time effect of soil is not considered during pipe jacking. Through the boundary sensitivity analysis [21], it is determined that the transverse (X axis) length of this calculation model is 40 m, the length of the parallel pipe jacking (Y axis) is 40 m, and the soil burial depth (Z axis) is 30 m. The finite element software Midas GTS NX 2021 was used to establish the 3D numerical analysis model of the vertical double-layer tube. The software was developed by POSCO of South Korea, and the Chinese version was developed and maintained by Beijing Midas Technology Co., LTD. The model is divided into a total of 111,900 cells and 115,860 grid nodes.

In the numerical model, the soil and pipe and grouting layers are simulated by solid elements. Each entity is connected to each other through Boolean operation, and the mesh size is controlled during mesh partitioning to ensure the coupling of nodes between layers. The grouting layer can well simulate the interaction between pipe jacking and soil, and the mesh is divided by the mixed hexahedron mesh. Gravity loads are applied to the model and the boundary conditions are set by limiting the displacement. The boundary conditions are set as follows: The left and right side boundaries are fixed in the horizontal direction to limit the horizontal displacement in the X direction, and the horizontal displacement in the Y direction of the front and rear boundaries is limited. The ground is fixed with displacements in three directions, and no boundary conditions are set for other boundaries. The computational model grid is shown in Figure 7.

4.2. Construction Process Simulation Method

The passivation and activation of the elements are used to simulate the process of soil excavation and jacking machine pushing, and the soil was excavated and then the pipe section was put in at each step. In order to simulate the external expansion and over excavation construction of the pipe jacking machine, the excavation soil radius is 30 mm larger than that of the pipe jacking model when the model is established. In the construction simulation, the excavation soil model is first passivated, and the pipe jacking model is activated for grouting simulation. The corresponding parameters are given to make a certain space between the model and the pipes after excavation to release the stress. Then, the soil excavation and pipe jacking simulation of the second section were started until the end of the excavation. In the process of excavation, the lower layer of pipe jacking is first excavated and then the upper layer of pipe jacking is successively excavated. The construction process model of soil excavation and pipe-jacking are shown in Figure 8.

4.3. Constitutive Model and Calculation Parameters

Due to the heterogeneity and anisotropy of rock and soil media, the test results of soil are unstable and discrete. In order to determine the calculation parameters, the physical property parameters and compression coefficient in this engineering geological survey report are used and the average value is taken.

The modified Mohr-Coulomb constitutive model is used for soil material and grouting layer, and the linear elastic material model is used for the tunnel structure. The parameters required for model establishment are determined according to the geological survey report of the monitoring area and the relevant geotechnical experiment, and the specific values are shown in

Table 1. Soil layer materials and grouting layer parameters.

Soil Layer Classification	E/MPa	μ	γ (kN/m3)	c/kPa	$\mathit{\phi }$/°	${\mathit{E}}_0$
Plain fill soil	13.5	0.35	18	8	10	5.81
Loess-like silty clay	18	0.35	25	15	18	6.39
Silty clay	18.9	0.33	19.6	30	16	7
Stroke limestone	500	0.27	23	55	32	1170
Grouting layer	10	0.38	15	5	5	2.29
Tube segment	3000	0.17	24	-	-	-

. Where E (MPa) is the elastic modulus; μ is Poisson’s ratio; γ is bulk density; c is cohesion; $\phi$ is the internal friction angle; and E₀ is the deformation modulus. As the modified Mohr-Coulomb model needs to be supplemented with other parameters, Midas GTS NX 2021does not give the value rules for the Jinan area. Since the project site is mainly clayey soil, which is similar to the soil in Beijing, other parameters are set according to the value rules of Beijing in Midas GTS NX help manual, and the specific rules are shown in

Table 2. Empirical values of nonlinear stiffness parameters of the modified Mohr-Coulomb constitutive model.

Area	${\mathit{E}}_0$	${\mathit{E}}_{50}^{\mathit{r}\mathit{e}\mathit{f}}$	${\mathit{E}}_{\mathit{o}\mathit{e}\mathit{d}}^{\mathit{r}\mathit{e}\mathit{f}}$	${\mathit{E}}_{\mathit{u}}$	m
Beijing	β$E_s$	β$E_s$	(0.5–1.0)$E_{50}^{ref}$	(2–4)$E_{oed}^{ref}$	0.4–0.7

. Where E₀ is the deformation modulus; $E_{50}^{ref}$ for the standard drainage triaxial experiment of secant stiffness; $E_{oed}^{ref}$ primarily oedometer records of tangent stiffness; E_u is the unloading reloading stiffness; and m is the power function of stress correlation, 0.5 for soft soil and 1 for hard soil.

5. Analysis of Numerical Simulation Results

5.1. Analysis of Ground Settlement

Figure 9 shows the vertical displacement cloud diagram of calculated model during pipe jacking. It can be seen that lower pipe jacking generates surface settlement although the pipe mostly located in the rock strata, and the surface settlement further aggravated after the completion of the upper pipe jacking. Figure 10 shows the comparison between the monitoring data and simulated ground settlement curves. The simulated results are basically consistent with the monitoring results. As can be seen from Figure 10, numerical calculation shows that the influence range of the transverse surface settlement is about six times the outer diameter of the pipe.

5.2. Analysis of Horizontal Lateral Displacement

Figure 11 shows the horizontal lateral displacement curve after the construction of the lower pipe is completed. It can be seen that the numerical simulation results are basically consistent with the on-site monitoring data. The farther the inclinometer pipe is from the pipe jacking axis, the smaller the lateral deformation, and the position of the maximum lateral displacement gradually moves up. Figure 11 shows the horizontal lateral displacement curve after the construction of the pipe is completed. The numerical simulation results are basically consistent with the on-site monitoring data. It can be seen that: (1) The farther the inclinometer pipe is from the pipe jacking axis, the smaller the lateral deformation. This is because, in the process of pipe jacking construction, the surrounding soil is disturbed, and the closer to the pipe, the greater the disturbance is. (2) The maximum lateral deformation occurs near the pipeline, because most of the lower pipeline is located in the rock stratum, the rock stratum disturbance is small during construction, and the deformation on both sides of the pipeline is small. The soil mass near the upper part of the lower pipe is disturbed greatly, so the maximum lateral deformation occurs above the pipe during the construction of the lower pipe jacking. (3) The farther the inclinometer pipe is from the pipe jacking axis, the position of the maximum lateral displacement gradually moves up.

5.3. Influence Analysis of Vertical Spacing between Pipes

Based on the established model, the influence of vertical clear spacing were explored. The clear spacing between two pipes is 0.5 D and 2 D, respectively (D is the outer diameter of the jacking tube). Figure 12a shows the position of lower pipe jacking when the spacing is changed. Figure 12b shows the comparison of the ground settlement caused by pipe jacking with different vertical spacing.

Table 3. Ground settlements at different vertical clear distances.

	0.5 D/mm	1 D/mm	2 D/mm
Lower pipe jacking (SL)	2.64	0.75	0.09
Upper pipe jacking (SU)	4.00	2.21	1.59
Total ground settlement (ST)	6.64	2.96	1.68
SL/ST	39.8%	25.3%	5.4%

shows the value of ground settlement caused by pipe jacking under different vertical clear spacing. It can be seen that, with the larger of pipe vertical distance, the buried depth of the lower pipe in the rock layer was increased, the influence of the lower pipe jacking on the ground settlement was decreased, and the total ground settlement decreases obviously. When the vertical clear spacing is 0.5 D, the total ground settlement is 6.6 mm, which is about four times the ground settlement when the spacing is 2.0 D.

5.4. Ground Settlement Prediction for Pipe Jacking in the Soil-Rock Composite Stratum

According to the results comparison between on-site monitoring and Peck formula calculation [7,19,22,23,24], the estimation formula of lateral land subsidence distribution in Peck is as follows:

$$S\left(x\right)=\frac{V_1}{\sqrt{2\pi }i}\exp \left(-\frac{x^2}{2i^2}\right),$$

(1)

$$i=z/\left[\sqrt{2\pi }\tan \left({45}^{°}-\phi /2\right)\right],$$

(2)

where S(x) is the land surface settlement (mm); x is the distance (m) from a point on the surface to the center line; V₁ is the formation loss per unit length (m³/m); i is the width coefficient of settling tank (m); z is the distance between the pipe jacking axis and the ground; and φ is the internal friction Angle (°) of the soil.

According to the construction site situation, assuming that the stratum loss rate is 0.5%, the maximum ground settlement S(x) = 2.7 mm, after the completion of the lower pipe jacking construction is calculated, which is significantly different from the field data of 0.8 mm. Therefore, the applicability of the Peck formula used for predicted settlement is poor when the pipe jacking in the soil–rock composite layer.

The peck formula is widely used in the prediction of land surface subsidence in various projects due to its simple calculation. However, due to the differences in geological characteristics in different areas, there is a certain gap between the predicted value of the peck formula and the measured data. Many scholars have adapted the peck formula for different strata [8,9,25,26,27]. There is still a lack of modified peck formulas for sore–rock composite strata in many studies. Therefore, referring to the modification method of previous scholars, the compensation formula is adaptively modified for this project. According to the numerical results, with the increase in the vertical pipe jacking spacing, the depth of the lower pipe jacking embedded in the rock layer gradually increases, and the surface settlement caused by the lower pipe jacking construction gradually decreases. Therefore, the main reason for this difference is the depth of the pipe jacking embedded in the rock layer. In order to better study the specific relationship between such differences, the thickness of the pipe jacking embedded in the rock layer is represented by h, and the influence of the surface settlement on the change of h is shown in Figure 13.

It can be seen from Figure 13 that the surface subsidence is obviously affected by the change of h. In order to further study the relationship between surface subsidence and h, the parameter k(h) is introduced to modify the peck formula. k(h) varies with the depth h of the pipeline embedded in the rock stratum. Through a large number of formula trial calculations and inversions, the relationship between k(h) and h is finally obtained, as shown in Equation (4). Therefore, the modified calculation formula is shown in Equations (3) and (4), as shown in the equation: S’(x) is the land surface settlement after correction (mm), D is the outer diameter of pipe jacking, h is the distance from the bottom of the jacking pipe to the soil and rock strata interface, which is the thickness of the rock layer the pipe is embedded in the buried depth in the rock layer.

$$S^{\prime }\left(x\right)=k\left(h\right)·S\left(x\right) ,$$

(3)

$$k\left(h\right)=\left\{\begin{array}{c}\frac{D}{D+h^2 } , 0\le h<D\\ \frac{D}{D+h^3} , h\ge D\end{array}\right\} ,$$

(4)

In order to verify the applicability of the modified peck formula for pipe jacking in the soil–rock composite stratum, the numerical simulation results were compared with the calculation results of the modified peck formula, as shown in Figure 14. Using three examples, as shown in Figure 12, the corresponding parameters of h are 0.8 m, 2.6 m and 6.2 m, respectively. Figure 14 shows that the two methods have good consistency. Since Equations (3) and (4) are modifications of the maximum value of the settlement, the consistency of the influence range of the settlement width is guaranteed. It can be seen from Figure 14a that, when the depth of the pipeline embedded in the rock layer is small, the maximum settlement value at the axis of the pipeline obtained by the modified formula is basically consistent with the numerical simulation results, but the surface settlement on both sides of the axis is slightly larger than the simulation value. When the depth of the pipeline embedded in the rock layer is large, the maximum value is slightly different, but the settlement value on both sides of the axis is basically the same. Figure 14b shows the comparison between the prediction results of the modified peck formula in this paper and the prediction results of the modified peck formula proposed in reference [27]. It is worth noting that the reference is also the modified peck formula proposed for soil–rock composite strata. It can be seen from the figure that the upper and lower limit values obtained from the formula settlement in reference [27] are far from those in this paper. Therefore, the modified Peck formula can be used to estimate the lateral distribution of ground settlement caused by pipe jacking in the strata of the soil–rock combination.

6. Conclusions

By on-site testing and numerical analysis, the surrounding soil deformation features caused by the vertical two-layer pipe jacking in the soil–rock composite stratum are discussed. The main conclusions are as follows:

(1)

The cumulative settlement of the pipe jacking machine before reaching the monitoring section accounts for about 60–70%, and 30–40% settlement can still be generated when the pipe jacking machine is far away from the monitoring section.

(2)

The maximum transverse and longitudinal ground settlements caused by the upper pipe are about three times those of the lower pipe. The maximum horizontal lateral displacement of the upper pipe jacking is about 3.3 times the lower pipe jacking construction.

(3)

In the construction of two-layer pipe jacking, total ground settlement increases with the reduction of vertical clear spacing between the upper and lower pipe. When the vertical clear spacing increased from half of the pipe diameter to 2.0 times pipe diameter, the total ground settlement is reduced by 75%.

(4)

The peck formula, which is used to estimate the lateral land subsidence distribution by tunnel construction, is modified to make it more applicable in the soil–rock composite stratum to calculate the ground settlement induced by pipe jacking.