Study on Ground Deformation Law of Small Spacing Shield Tunneling in Sand and Rock Composite Stratum

Abstract

The construction of shield tunnel often occurs in composite stratum, so it is of great significance to study the law of surface deformation under the working condition of composite stratum in order to ensure the safety of shield construction. Based on the actual tunnel engineering, the law of ground surface soil deformation caused by shield construction in the composite stratum of upper sand and lower rock is studied by using the method of field measurement. The results show that: The width coefficient of the surface settlement trough basically remains stable with the shield construction, and the stratum loss rate changes exponentially with the shield construction; Affected by the disturbance of the previous shield construction, the surface settlement trough caused by the subsequent shield construction is no longer on the top of the tunnel axis, and will move with the construction process, which is greatly affected by the shield attitude parameters; Taking into account the conditions of the center movement of the settlement trough of the subsequent tunnel, the total surface settlement caused by the successive shield constructions adopts the modified Mark-bolt formula to make the fitting parameters of the settlement trough more suitable for reality.

1 Introduction

With the rapid development of domestic urban rail transit construction, the stratum of tunnel crossing is complex and diverse, and the construction frequency of shield tunnel in composite stratum is getting higher and higher. Composite stratum is composed of two or more strata with different physical and mechanical parameters within the range of tunnel excavation surface and in the direction of tunnel excavation.

Due to the differences in the properties of different strata, the primary problems to be solved in the construction of shield tunnel in composite strata are mainly focused on shield type selection design, construction technical measures, construction parameter optimization, shield adaptability [1,2,3]. There is also a high degree of attention to the study of surrounding stratum disturbance, but the current research methods are mostly numerical simulation [4, 5] and theoretical analysis [6, 7]. Among them, the numerical simulation is generally based on the finite element calculation of the continuum [8, 9], the analysis of the field measured data is less, and there is little research on the sand layer [10].

The upper soft strata and lower hard strata are the more common composite strata. In the current field measurements, the upper soft and lower hard strata mostly refer to the upper clay and lower rock strata [11, 12], but there is less research and analysis on the field monitoring of the surrounding strata disturbance caused by the shield construction in the upper sand and lower rock strata, and there is even less research and analysis on the secondary disturbance of the soil caused by the construction of two tunnels one after another.

The analysis and prediction of surface settlement due to shield construction is mostly done using the Peck formula [13], as follows:

$$ S(x){ = }\frac{{V_{S} }}{{\sqrt {2\pi } i}} \cdot e^{{\left( { - \frac{{x^{2} }}{{2i^{2} }}} \right)}} $$

(1)

where S(x) is the surface settlement value at distance x from the tunnel axis, i is the width factor of the settlement trough, V_S is the amount of ground loss per unit length, V_S = πR²V_L, V_L is the rate of ground loss per unit length, and R is the radius of cutter excavation. Peck assumes that the soil does not drain during construction and that the ground loss is uniformly distributed along the entire tunnel length.

O'reilly [14] based on the actual monitoring data in London, it is concluded that there is a linear relationship between i and tunnel depth z₀:

$$ i = K \cdot z_{0} $$

(2)

where K is the width parameter of settlement trough and is dimensionless.

Peck formula is often used to predict and evaluate the surface subsidence caused by shield construction, but two key parameters i and V_S are generally difficult to be determined in advance and have low versatility due to the influence of stratum conditions, tunnel parameters and construction quality. Therefore, dimensionless parameters K and V_L are usually used for reference between surface subsidence caused by shield engineering in different areas, which is practical and empirical [15, 16].

According to the assumption of Peck formula, V_L (or V_S) has only one value in the average sense in the whole process of shield construction, and K (or i) has only one value in most shield projects. At present, there are the following deficiencies in the research of K and V_L: (1) the timing of inversion of K and V_L parameters in different projects is not uniform and the explanation is not clear, which leads to a wide range of empirical values, which brings difficulties for prediction and calculation; (2) limited by the monitoring frequency, the actual change of the shape characteristics of surface settlement trough in the process of shield construction is not clear.

In order to find out the variation law of the characteristic parameters of the surface settlement trough with the shield construction and its performance in the upper sand and lower rock composite strata, this paper relies on the actual tunnel engineering, through on-site intensive monitoring, this paper analyzes the deformation law of the surface soil caused by the shield construction and the morphological characteristics of the final settlement trough after the construction.

2 Background

2.1 Tunnel Condition

220 kV Shi**g-Huanxi Electric Power Tunnel (**wan Road ~ Shisha Road Section) is located in Baiyun District, Guangzhou City. It is constructed from north to south along Shikuan Road. Parallel to the power tunnel is the north extension of Guangzhou Metro Line 8, which is constructed from south to north.

The length of electric power tunnel shield machine is 9.62 m, the inner diameter of shield segment is 3.6 m, the outer diameter is 4.1 m, the diameter of cutter head is 4.35 m, and the length of segment is 1 m. The length of shield machine in subway tunnel is 10.29 m, the inner diameter of shield machine segment is 5.4 m, the outer diameter is 6.0 m, the diameter of cutter head is 6.28 m, and the length of segment is 1.5 m. The net distance between the two tunnels is about 3 m. In the monitoring area, the tunnel constructed first is subway, and the tunnel constructed later is electric power.

2.2 Survey Point Layout and Deformation Summary

The section where the monitoring section is located belongs to the upper sand and lower rock composite strata with karst development, and the stratigraphic distribution at the section is shown in Fig. 1. At the location of the monitoring section, nearly half of the sand layer is exposed on the construction surface of the subway tunnel, and the construction surface of the electric power tunnel is basically a full-section sand layer. The measuring points of surface deformation are set in the cross section, and the subway tunnel is located under the Shikuan Road, so the measuring points can not be arranged, and the positions of the measuring points are shown in Fig. 1. The front and rear 10 rings of the monitoring section belong to intensive monitoring, with monitoring points in each ring, and the other 5 rings are non-intensive monitoring, with one monitoring point in every other ring.

Fig. 1

Monitoring section stratigraphic distribution and measuring point arrangement

The surface deformation caused by subway and electric power tunnels construction is shown in Fig. 2 and Fig. 3 respectively. The more close to the tunnel, the greater the deformation. The maximum deformation caused by subway and electric power construction is CJ1 and CJ3, respectively, and the corresponding settlement is 15.24 and 23.31 mm. In addition, the settlement of each measuring point is stable with the shield construction.

Fig. 2

Ground surface deformation of subway shield construction

Fig. 3

Ground surface settlement of power shield construction

3 Monitoring and Analysis of Surface Subsidence

Considering the disturbance of the soil near the electric power tunnel caused by the subway tunnel construction, the disturbance degree of the soil on both sides of the electric power tunnel is different, and the excavation causes the center of the horizontal surface settlement trough to shift the tunnel axis, so it is necessary to modify the Peck formula. As follows:

$$ S(x){ = }\frac{{V_{S} }}{{\sqrt {2\pi } i}} \cdot e^{{\left( { - \frac{{(x - x_{c} )^{2} }}{{2i^{2} }}} \right)}} $$

(3)

Among them, x_c is the distance of the moving axis in the center of the settlement trough.

3.1 The Variation Process of Settlement Trough Parameters with Shield Construction

The curve fitting degree of settlement trough caused by subway and electric power tunnel construction is shown in Fig. 4. adj-R² reflects the curve fitting degree. The closer the value is, the higher the fitting degree is. It can be seen that the curve fitting degree is low when the cutterhead is at a certain distance from the monitoring section (all less than 80%). This is because the maximum surface fitting settlement values of subway and electric power tunnel cutterhead in front of the monitoring fault are 4.63 and 1.62 mm respectively, and the disturbance degree of soil mass is low at this stage. At the same time, non-construction factors such as monitoring errors account for a small proportion of the monitoring data in this stage. Therefore, the corresponding fitting parameters may not accurately reflect the shape of the settlement trough. According to the monitoring data of electric power tunnel, compared with the Peck formula, the curve fitting degree of the modified Peck formula can be increased by about 1.5 times when the cutter head reaches the monitoring surface, and the curve fitting degree can be increased by about 1.1 times when the shield tail comes off the monitoring surface. It can be seen that the modified Peck formula is more suitable for the situation of different degree of soil disturbance on the left and right sides of the shield tunnel.

Fig. 4

The change process of settlement trough fitting degree with shield construction

On the whole, the Peck formula is suitable for the upper sand and lower rock composite strata after karst cave reinforcement, and the fitting degree can basically reach 95%, which can meet the engineering requirements.

Since the Peck formula is based on the undrained assumption, we can refer to the method of Fang [17] to take the tail of the shield machine about 2–3 days after passing through the monitoring section as the boundary between drained and undrained soil. Therefore, for subway and electric power shield, it can be considered that the surface measuring points after the tail of the shield machine leaves the monitoring section of 10.94 and 15.09 m respectively are basically not affected by the disturbance of shield construction.

Based on this, the curve fitting parameters which are directly affected by the disturbance of shield construction and the degree of fitting is more than 95% are analyzed. The change of K during the construction of subway and electric power tunnels is shown in Fig. 5. It can be seen that K fluctuates near a certain value during normal construction and remains stable with the tunneling process. The linear fitting equations are respectively.

$$ K = - 1.07 \times 10^{ - 4} \cdot x + 0.45 $$

(4)

$$ K{ = }1.05 \times 10^{ - 3} \cdot x + 0.33 $$

(5)

Fig. 5

Change process of K with shield construction

The fitting line is basically a horizontal line. Therefore, the K values of shield construction in the exposed rock layer and the single sand layer are 0.45 and 0.33 respectively.

It can be seen that K is affected by formation conditions, and can not be excluded from the influence of tunnel conditions. Therefore, when the strata and tunnel conditions are known, when the shield construction produces a certain degree of disturbance to the survey point, the K (or i) obtained by monitoring and fitting by Peck formula can be used to predict the surface lateral influence range in the whole process of shield construction, and can also be used to approximately calculate the surface lateral influence range caused by shield tunnel construction with similar strata and tunnel conditions. And assess the safety of important structures within the scope of influence.

The change of V_L during subway and electric power tunnels construction is shown in Fig. 6. V_L increases with shield construction, but the growth rate gradually decreases, and finally tends to remain the same. The V_L caused by subway and electric power tunnels construction is about 1.1% and 1.6%.

Fig. 6

Change process of V_L with shield construction

In addition, there is an exponential relationship between V_L and the monitoring section distance from the cutter head to the measuring point, and the fitting equations are respectively.

$$ V_{L} = 1.830 - 1.449 \cdot e^{{\left( { - 0.032} \right)}} $$

(6)

$$ V_{L} = 1.821 - 2.060 \cdot e^{{\left( { - 0.092} \right)}} $$

(7)

The corresponding adj-R² is 98.9% and 98.8%, indicating that the index relationship can well reflect the changes of VL with the construction process. Therefore, the final stratum loss caused by shield construction under normal working conditions can be estimated by obtaining three data points through pre-monitoring.

3.2 Settlement trough Moves with the Construction of Electric Power Tunnel

Taking the monitoring data when the monitoring section is disturbed at the beginning of the electric power tunnel construction as the initial value, the translation of the center of the horizontal surface settlement trough during the construction is shown in Fig. 7. Combined with Fig. 4, Fig. 7 and Fig. 8, we can see that although the curve fitting degree of the settlement trough before the cutter head reaches the cross section is low, resulting in a certain discreteness of x_c, from the overall change trend, taking the axis of the electric power tunnel as the center, the center of the settlement tank moves from the left side to the right side (that is, from side A to side B), and finally remains stable, and the moving process mainly occurs during the shield machine passing through the monitoring section. Taking the average x_c of all the translation values after the tail of the shield machine is separated from the monitoring section, it can be known that the center of the surface settlement trough deviates from the axis about 0.5 m after the completion of the electric power tunnel construction.

Fig. 7

The change process of settlement trough center with power shield construction

Fig. 8

Diagram of center movement of settlement trough

As can be seen from Fig. 7 and Fig. 8, the center of the settlement trough is located on side A when the shield of the electric power tunnel is about to reach the monitoring section, because after the completion of the subway tunnel construction, the degree of disturbance of the soil is greater on the A side than on the B side. Subsequently, when the electric power tunnel gradually disturbs the monitoring point, the soil on the A side is located in the superimposed area of the disturbance range of the subway and power shield construction, so that the center of the settlement trough is located on the A side at the beginning. After the subway construction, the subway tunnel construction grouting and karst cave grouting strengthen the soil layer, which makes the structure with high stiffness buried in the soil on the A side, and then the sand layer becomes denser after the disturbance of the electric power tunnel construction. The degree of disturbance of the soil is that the B side is greater than the A side, so that the center of the settlement trough gradually moves from side A to side B, after the tail of the shield machine leaves the monitoring section. The monitoring point is gradually out of the disturbance range, and the central position of the settlement trough remains stable. In addition, compared with the main construction parameters such as cutter head pressure and grouting pressure, the attitude parameters of shield machine have more influence on the center position of settlement trough.

3.3 Settlement trough Shape Caused by Shield Construction of Two Tunnels Successively

As mentioned earlier, after the tail of the shield machine leaves the monitoring Section 10.94 m, it is considered that the soil deformation is basically not affected by the shield disturbance, and the initial value of the shield monitoring of the electric power tunnel can be used to calculate the soil deformation value caused by the non-shield disturbance between the two monitoring. During this period, karst cave grouting treatment occurred near the monitoring section, because it only aims at the deep rock and soil, so the surface monitoring point mainly measures the consolidation deformation of the soil itself.

For double-line parallel tunnels, Liu Bo et al. [18] assume that the shield construction of two successive tunnels will not affect each other, and the surface settlement caused by the two tunnels is the same. With the help of superposition principle, two Peck formulas with the same parameters are used to calculate the final surface settlement. Ma Ke-Shuan [19] (Abbreviated as MKS) put forward the hypergeometric method, considering the influence of the later tunnel on the first tunnel, the Peck formula for superposition calculation has two different sets of calculation parameters, the calculation formula is as follows, but the parameters of the settlement trough of the latter tunnel are not specific.

$$ \begin{aligned} S(x) = & \frac{{V_{{S1}} }}{{\sqrt {2\pi } \cdot i_{1} }} \cdot e^{{\left( { - \frac{{(x + {L \mathord{\left/ {\vphantom {L 2}} \right. \kern-\nulldelimiterspace} 2})^{2} }}{{2i_{1} ^{2} }}} \right)}} \\ & + \frac{{V_{{S2}} }}{{\sqrt {2\pi } \cdot i_{2} }} \cdot e^{{\left( { - \frac{{(x - {L \mathord{\left/ {\vphantom {L 2}} \right. \kern-\nulldelimiterspace} 2})^{2} }}{{2i_{2} ^{2} }}} \right)}} \\ \end{aligned} $$

(8)

where L is the horizontal distance between the axes of the two tunnels.

Considering the translation of the center of the settlement trough caused by the rear tunnel shield, the MKS formula is modified as follows:

$$ \begin{aligned} S(x) = & \frac{{V_{{S1}} }}{{\sqrt {2\pi } \cdot i_{1} }} \cdot e^{{\left( { - \frac{{(x + {L \mathord{\left/ {\vphantom {L 2}} \right. \kern-\nulldelimiterspace} 2})^{2} }}{{2i_{1} ^{2} }}} \right)}} \\ & + \frac{{V_{{S2}} }}{{\sqrt {2\pi } \cdot i_{2} }} \cdot e^{{\left( { - \frac{{(x - {L \mathord{\left/ {\vphantom {L 2}} \right. \kern-\nulldelimiterspace} 2} - x_{c} )^{2} }}{{2i_{2} ^{2} }}} \right)}} \\ \end{aligned} $$

(9)

For this project, subscript 1 and 2 represent subway tunnel and electric power tunnel respectively.

Only consider the soil deformation caused by the shield construction of subway tunnel and electric power tunnel, and the total amount of surface settlement during the monitoring period. If the MKS formula and the modified MKS formula are used to fit the total settlement caused by successive shield construction, the unknown parameters are 4 and 5 respectively, and there are many possibilities of permutation and combination of parameters that satisfy a certain degree of fitting. and the physical meaning of the fitting parameters may not necessarily accord with the reality.

As mentioned earlier, the parameters K and V_L can be obtained by fitting the surface subsidence with Peck formula. Therefore, it is known that the settlement trough parameters caused by single-line shield construction, K or V_L in the MKS formula is artificially set (modified) to be equal to the single-line fitting value, the deviation degree between the other fitting parameters and the known values is observed, and the engineering practicability of (modified) MKS formula is evaluated.

For the modified MKS formula, the moving distance of the center of the settlement trough in the power tunnel is known, and the x_c value is temporarily set to 0.44 m.

The K values of single and double lines are equal to the known values, and the V_L values of subway tunnel and electric power tunnel and their standard deviation (degree of deviation) are obtained by fitting. TheV_L control value corresponding to subway tunnel and electric power tunnel construction is 1.09% and 1.55% respectively. Without considering different control conditions, the percentage of V_L value deviated from the control value obtained by different formulas shows that there is little difference in the standard deviation of VL value between the two shield tunnels under different control conditions, and the VL fitted by the modified MKS formula is closer to the control value.

The V_L value of the single line is equal to the known value, and the K value and its standard deviation of subway tunnel and electric power tunnel are obtained by fitting. The K control value for subway tunnel and electric power tunnel construction is 0.45 and 0.32 respectively. Without considering different control conditions, the percentage of K value deviated from the control value obtained by different formulas can be known. The standard deviation of K value caused by shield construction of subway tunnel and electric power tunnel is similar, the former is larger than the latter, and the K fitted by the modified MKS formula is closer to the control value.

From the analysis, it can be concluded that whether or not to control the K or V_L of single or double lines has little influence on the results of other fitting parameters, and the modified MKS formula is better to fit the total surface settlement caused by shield construction of two successive tunnels, but its use premise is that the center displacement of settlement trough caused by shield construction of the second tunnel is known. If the total surface settlement value and single-line settlement tank parameters caused by shield construction of two tunnels are known, the settlement trough parameters caused by another shield construction can be inverted by (modified) MKS formula.

The K or V_L of the double line is set to a known value to evaluate the influence of different degrees of x_c deviation on the fitting parameters. When the percentage of x_c deviation is-100%, the modified MKS formula is changed into the MKS formula, that is, the center of the settlement trough is located above the axis of the electric power tunnel. Therefore, when it is not clear which side of the tunnel the center of the settlement trough is caused by the backward shield construction, the MKS formula can be used. Although the fitting parameter value deviates from the reality to a certain extent, it will not cause too much error.

The fitting curve of the (modified) MKS formula for controlling V_L1 is drawn as shown in Fig. 9, which shows that the two settlement curves are highly consistent with the measured data, but there are differences in the physical meanings of the two corresponding parameters. As shown in Fig. 9, when the surface settlement values caused by subway tunnel and electric power tunnel construction are known, they can be fitted by Peck formula and modified Peck formula respectively, and then the final surface settlement curve can be obtained according to the linear superposition principle. At this time, the superposition curve can also fit the measured values well, but its use premise is that the measured data of surface subsidence caused by the construction of two tunnels are known.

Fig. 9

Curve of transverse settlement trough caused by shield

4 Conclusions

Through the field measurement method, this paper studied the deformation law of surface soil mass caused by the construction of two tunnels successively in the upper sand and lower rock composite strata, and drew the following conclusions:

• (1) The width coefficient (parameter) of the surface settlement trough is basically stable with the shield construction, and the lateral influence range of the surface does not change much with the construction, which can be used to evaluate the safety degree of the important structures in the influence area.

• (2) The formation loss rate changes exponentially with the shield construction.

• (3) Affected by the disturbance of the shield construction of the first tunnel, the surface settlement trough caused by the shield construction of the second tunnel is no longer located at the top of the tunnel axis, but will move with the construction process, which is greatly affected by the attitude parameters of the shield.

• (4) The total surface settlement caused by the successive construction of the two tunnels is well fitted by the modified MKS formula considering the movement of the center of the settlement trough.

• (5) for the total surface settlement caused by shield construction of two successive tunnels, under the condition that the surface settlement trough parameters V_L or K of the first or second tunnel are known, the surface settlement trough parameters of the second or first tunnel can be obtained by using MKS formula. Considering the movement of the center of the settlement trough of the back tunnel, the fitted settlement trough parameters will be more practical.