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Three-dimensional stress-transfer mechanism and soil arching evolution induced by shield tunneling in sandy ground
Tunnelling and Underground Space Technology 93 (2019) 103104
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Three-dimensional stress-transfer mechanism and soil arching evolution induced by shield tunneling in sandy ground
T
Xing-Tao Lin, Ren-Peng Chen , Huai-Na Wu, Hong-Zhan Cheng ⁎
Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education, Hunan University, Changsha 410082, China National Center for International Research Collaboration in Building Safety and Environment (NCIRCBSE), Hunan University, Changsha 410082, China College of Civil Engineering, Hunan University, Changsha 410082, China
ARTICLE INFO
ABSTRACT
Keywords: Earth pressure balance shield (EPBS) Numerical modeling Stress redistribution Soil arching effect
Tunnel excavation inevitably causes variations in stress and displacement fields in soil, which could affect the serviceability and safety of the adjacent underground structures. Change of the earth pressure acting on the existing structures is closely related to soil arching effect caused by a new tunnel excavation, but it is still lack of full understanding. In this study, a finite element method (FEM) model was first verified by field measurements based on a case history of Metro Line 2 construction in Changsha, China. Then, a series of simplified threedimensional (3D) FEM models were established to investigate the stress redistribution and the soil arching evolution induced by earth pressure balance shield (EPBS) tunneling. The changes of the earth pressure, the coefficient of lateral earth pressure, and the settlement of soil mass above the tunnel during tunneling were analyzed and the soil arching zone was determined. 3D stress-transfer mechanism in soil arching zone during tunneling was revealed. In addition, the influences of shield-driving parameters (i.e. support pressure, grouting pressure) on soil arching evolution were also investigated. The results show that the loosened zone extends to nearly 0.73D (D = tunnel diameter) above the tunnel crown in vertical direction. The height of the arch zone above the loosened zone is about 1.27D. The horizontal soil arching in front of EPBS occurs near the ground surface. With EPBS advancing, the horizontal soil arching gradually transforms into the vertical soil arching. After the installation of lining, the earth pressure is finally mainly transferred by vertical soil arching in the transverse section. The proper combination of shield-driving parameters for controlling the expansion of the loosened zone is support pressure of 0.6P1 − 2.2P1 and grouting pressure of 1.0P2 − 1.8P2, where P1 is initial horizontal stress at the tunnel axis and P2 = 1.2P1.
1. Introduction In the past few decades, EPBS tunneling technology has been widely used in the construction of the urban subway tunnel (Reilly, 1999; Chen et al., 2011c, 2019; Shen et al., 2014; Wu et al., 2015, 2018; Zhang et al., 2019). If the earth pressure in shield’s chamber is insufficient or the grouting pressure setting at tail is unreasonable, shield driving will easily cause disturbance in surrounding soils, which could induce safety problem of the adjacent underground structures. Changes in stress and displacement fields in soil are a reflection of the soil arching effect due to tunnel excavation. Thus, it is of great significance for ensuring existing underground structure safety to study the soil arching effect caused by tunnel excavation. The soil arching effect widely exists in the civil engineering (e.g., the tunnel, the piled embankment, the retaining wall and the
⁎
foundation pit etc.) (He and Zhang, 2015; Lai et al., 2018; Wang et al., 2018; Wang and Chen, 2019). For the soil arching around the tunnel, many researchers have performed much meaningful work in the theoretical analyses, model tests and numerical simulations. Based on the trapdoor tests, some theoretical researches have been conducted to study the variation of the earth pressure around tunnel (Terzaghi, 1943; Getzler et al., 1970; Li et al., 2013; Chen et al., 2015; Son, 2017). The laboratory tests were also frequently used to investigate the soil arching effect and stress redistribution caused by the tunnel excavation (Adachi et al., 2003; Berthoz et al., 2018; Chen et al., 2013, 2018b; Dewoolkar, 2007; Franza et al., 2018; Idinger et al., 2011; Kirsch, 2010; Lee et al., 2006a,b; Li et al., 2011; Liu et al., 2018; Murayama and Matsuoka, 1971; Nakai et al., 1997). Based on the trapdoor modeling tests, Terzaghi (1943) observed the changes of vertical stress distribution above the tunnel after excavation, as depicted in Fig. 1. The increasing
Corresponding author at: College of Civil Engineering, Hunan University, Changsha 410082, China. E-mail addresses: [email protected] (X.-T. Lin), [email protected] (R.-P. Chen), [email protected] (H.-N. Wu), [email protected] (H.-Z. Cheng).
https://doi.org/10.1016/j.tust.2019.103104 Received 29 March 2019; Received in revised form 12 July 2019; Accepted 27 August 2019 Available online 04 September 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
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economical method. Recently, the numerical simulation has played a significant role in studying shield tunneling. Numerous numerical models have been established to research the soil arching effect and stress redistribution ahead of the tunnel face or around tunnel (Vermeer et al., 2002; Ng and Lee, 2005; Gomes and Celestino, 2009; Chen et al., 2011a, 2011b; Jiang and Yin, 2012; Lin et al., 2018; Kong et al., 2018, 2019). Jiang and Yin (2012) analyzed the effect of the buried depth and tail gaps on the stress redistribution in soil and the earth pressure around the tunnel due to excavation by using two-dimensional (2D) discrete element method (DEM). It was found that the soil arching effects were slightly unaffected by the depth and tail gaps of the tunnel when those values were larger than certain values. Kong et al. (2018) built many 2D numerical models to investigate arching mechanism in rock mass, and defined the three characteristic lines of the pressure arch (i.e. the outer boundary line, the centroid line and the inner boundary line) based on the changes of horizontal and vertical stresses distributions of the rock around tunnel. However, the above analyses of arching effect were limited to 2D because these results were obtained under the condition of plane strain. Chen et al. (2011b) investigated the failure mechanism of a tunnel face in dry sandy ground by using 3D DEM. It was found that soil arching occurred in the upper part of the failure zone and the soil become loosened in the failure zone. Chen et al. (2011a) set up a series of 3D finite element models to research the vertical stress distribution variations above the tunnel roof during tunneling. Selecting the changes of inflection point at the σzz-depth curve act as the reliable indexes to reflect the development of the soil arching. However, the scope of arch zone is not given by Chen et al. (2011a). Yang et al. (2015) established a 3D numerical model to study arching mechanism in rock mass, and determined the inner and outer boundaries of the arch zone according to the variations of the maximum principle stress of the rock surrounding tunnel. It was found that as the span-to-height of tunnel increased, the shape of arch zone varied from a circular to a flat, meanwhile the arch zone opening also increased. Although the 3D numerical models were built in the above researches, there is the lack of full analyses in three directions stresses during tunnel excavation. So 3D soil arching effect is not clearly revealed. Moreover, the stress redistribution caused by EPBS tunneling is significantly affected by the shield-driving parameters. But the above researches mainly focus on the unlined tunnel, which was excavated using mining method in rock mass. To sum up, although many researches on the arching effect due to tunnel excavation have been made, there are still two problems: i) the 3D stress-transfer mechanism and evolution process of soil arching during the shield tunneling are not full revealed; ii) there is a lack of the understanding of the effects of the shield-driving parameters on soil arching effect around the tunnel. In this study, a 3D FEM model is first validated on a case history of Metro Line 2 construction in Changsha, China. Subsequently, a series of simplified 3D numerical analyses are conducted to investigate the soil arching evolution and stress redistribution caused by the shield tunneling. The changes of the three direction earth pressures, the coefficient of lateral earth pressure and the settlement of soil mass above the tunnel during EPBS tunneling are discussed. Additionally, the influence of shield-driving parameters on soil arching evolution is also investigated.
Fig. 1. Vertical stress profile at centerline after tunnel excavation: (a) shallow tunnel; (b) deep tunnel (Terzaghi, 1943).
trend of the vertical stress for the shallow tunnel gradually slows down with the increase of the depth, and then keeps constant when the depth reaches a certain value (see Fig. 1(a)). The vertical stress for the deep buried tunnel is equal to the self-weight stress as the depth increases, and then sharply decreases when the depth reaches a certain value (see Fig. 1(b)). Thus, Terzaghi (1943) thought that the soil arching effect occurs in the region below this depth. Adachi et al. (2003) carried out a series of 3D trapdoor experiments, which were simulated tunnel excavation. Based on the experimental results, it was found that the distribution of earth pressure was greatly affected by the process of the excavation. Lee et al. (2006a, b) investigated the tunnel stability and soil arching effects during tunneling in sandy soil and soft clayey soil by a series of centrifuge model tests. The boundaries of arch zone were determined according to the changes of earth pressure around the tunnel, and the positive and negative arch zones boundaries were also suggested. Chen et al. (2013) researched the evolution of soil arching during face failure by monitoring the redistribution of earth pressure in front of the face based on large-scale laboratory test. Then, a two-stage failure pattern was proposed based on the observation of earth pressure redistribution. These experimental studies improve the understanding of the interaction between the tunnel and the surrounding soils. However, the model tests are limited sometimes due to time consuming and cost expensive. The numerical analysis has been widely adopted in the investigation of tunnel excavation since it is an effective and
2. Case history and verification of the numerical model 2.1. Introduction of the case history To investigate soil arching effect around the tunnel during shield tunneling, a 3D FEM model was established. A case history of the construction of the left tunnel of Metro Line 2 in Changsha, China, near the Yingwanzhen station, is chosen as the research objective for validating the reliability of the numerical modeling method. The study area is located in the section between Yingwanzhen station and Juzizhou 2
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Table 1 Material properties of EPBS and tunnel lining.
EPBS Tunnel lining
Table 3 Parameters for soils constitutive models (data from Lin et al. (2019)).
Young’s modulus E (GPa)
Poisson’s ratio v
Volumetric weight γ (kN/m3)
230 31
0 0.1
120 25
Table 2 Soil basic physical property index (data from Lin et al. (2019)).
Parameter type
Soil layers
Constitutive model
Backfill MC
Gravel MC
MCS HSS
φ′ Ψ c′ Eref
18.5 0 46 –
37.4 0 0 –
34 4 2 37,800
[°] [°] [kN/m2] [kN/m2]
–
–
37,800
[kN/m2]
–
–
113,500
[kN/m2]
4750 –
27,850 –
– 0.5
[kN/m2] [–]
–
–
189,200
[kN/m2]
–
–
10-4
[–]
– –
– –
100 0.2
[kN/m2] [–]
0.3 19 0.9
0.27 20 0.9
– 19.5 0.9
[–] [kN/m2] [–]
ref
50
Soil layer
Depth (m)
e0
γ (kN/m2)
w (%)
k (m/d)
E
oed
Fill Gravel Medium coarse sand
0–2.2 2.2–5.0 5.0–40
0.74 0.65 0.40
19.0 20.0 19.5
22.1 – 15.7
2.0 10.0 8.6
Eref
ur
E′ m
Note: e0 = void ratio; γ = soil unit weight; w = water content; k = hydraulic conductivity.
Gref γ0.7
station, and starts from the Yingwanzhen station until the end of 150 m from it. In the study area, the average burial depth of Metro Line 2 is about 9.0 m. The outer and inner diameters of tunnel are 6.0 m and 5.7 m, respectively. The length of each segmental ring is 1.5 m. Metro Line 2 was excavated using EPBS, with excavation diameter of 6250 mm, the length of 12.5 m, and the cutter opening ratio of 37%. The material parameters for the tunnel lining and EPBS are summarized in Table 1. The sub-soils in the construction site mainly consist of backfill, gravel and medium coarse sand. The distribution and physical properties of the soils are listed in Table 2. Metro Line 2 is located in the medium coarse sand layer. The groundwater level is about 2.0 m under the ground surface. The settlement of ground surface was measured during EPBS tunneling.
pref vur v γ Rf
0
Effective friction angle Dilatancy angle Effective cohesion Reference secant stiffness in triaxial test Reference tangent stiffness for oedometer loading Reference unloading/reloading stiffness Effective Young’s modulus Power that controls the stress dependency of stiffness Reference shear modulus at very small strains (ε < 1 0 −6) Shear strain at which Gs = 0.772G0 Reference stress Poisson ratio of unloading/ reloading Poisson ratio for MC model Soil unit weight Failure ratio
Unit
Note: MCS = medium coarse sand.
2.2.2. Material model and parameters The soil mass around the tunnel is subjected to complex forces (i.e support pressure, shield shell friction, grouting pressure, etc.) during EPBS tunneling. However, the simple elastic-perfectly plastic soil constitutive model is difficult to simulate the behavior of soil accurately. There are many advanced constitutive models in existing literature (Benz, 2007; Chang et al., 2010; Jin et al., 2016; Yin et al., 2010, 2016, 2018). To simulate the behavior of medium coarse sand around tunnel during excavation, an advanced elasto-plastic constitutive model, namely Hardening Soil model with Small Strain Stiffness (HSS) (Benz, 2007) used frequently in PLAXIS, was adopted in this study. Meanwhile, to save computational time and cost without affecting the numerical results, the Mohr-Coulomb model was employed to simulate the behavior of the fill and gravel. The parameters of soils models, which are from Lin et al. (2019), used in this study are shown in Table 3. The lining segments and EPBS were modeled as linear elastic, the parameters of which are listed in Table 1. Since the EPBS/lining and the surrounding soils have different roughness, the contact properties between EPBS and soils as well as lining and soils depend on the type of soil. In this paper, the interface elements have the same constitutive law
2.2. Three-dimensional numerical simulation 2.2.1. Numerical model The 3D FEM model was established to investigate EPBS tunneling using the geotechnical software PLAXIS 3D, as shown in Fig. 2. Considering the symmetry of the research object, the numerical model employed half of the domain. To eliminate the influence of boundary conditions on the results, the dimensions of the model are 150 m in length, 100 m in width, and 40 m in depth. The soil mass and lining were modeled as 10-node tetrahedral elements. The EPBS was modeled by 6-node plate elements. As for boundary conditions of model, the horizontal displacements of all vertical boundaries were fixed, but the vertical displacements were free. The displacements of the bottom plane were fully fixed in three directions. There was no displacement constraint on the top plane.
Fig. 2. Model geometry and schematic of EPBS tunneling details simulation. 3
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as the surrounding soil. Due to the tunnel locating in medium coarse sand in this paper, the soil-lining contact interface is roughness. Thus, the reduction factor, which reflects the reduction of the stiffness and shear strength of the interface elements, is set to be 1.0.
Settlement (mm)
0
2.2.3. Numerical simulation process The width of single precast concrete lining segments in this project is equal to 1.5 m. Hence, EPBS advances 1.5 m in each step of the staged excavation. The length of EPBS is set to be 12 m, which is exactly equal to the sum of the width of 8 segments, as shown in Fig. 2. The front 10.5 m length region is employed to simulate the cone-shaped EPBS and the volume loss caused by tunneling, which has a linear contraction with a reference value of 0.4% (Cref) at tail with increment of −0.0381%/m (Cinc). The rest 1.5 m length region is adopted to simulate the tail of EPBS, which has a uniform contraction of 0.4%. The support pressure acting on the tunnel face is used to keep the stability of the soil ahead of the tunnel. Based on the measured data, the support pressure is 72.4 kPa at the crown of tunnel face, and with the depth increasing, the pressure increases linearly with a gradient of 9.2 kPa/m. The grouting pressure in the shield tail, which acts on the crown of tunnel, is 147.3 kN/m2 with pressure gradient of 9.2 kPa/m. The average jacking thrust is 1775 kN/m2. The transverse measurement section is 20 m from the Yingwanzhen station (see Fig. 2). To eliminate the influence of initial position of EPBS on the monitoring point and to reduce the number of advancing rings, the initial position of the tunnel face of EPBS is 18.5 m (almost 3 D) from point 1. The detailed tunnel excavation for a total number of 36 steps is simulated. The shield tunneling procedure is modeled in a step-wise manner (Meng et al., 2018; Lin et al., 2019). More detailed descriptions can refer to the above corresponding literature.
-2
Z
Y
Ground surface L<0
-4
EPBS
L
-6 -8
-10 -5
L>0
Measured L=-0.33D L=1.17D L=4.17D
Monitoring section
L=0.42D L=1.92D
Calculated L=-0.33D L=0.42D L=1.17D L=1.92D L=4.17D
Tunnel
-4 -3 -2 -1 0 Normalized distance from tunnel centerline (X/D)
(a)
Settlement (mm)
0 Measured Calculated
-2 -4 -6
2.3. Verification of the numerical model
-8
Fig. 3 presents comparison of measured and calculated settlements on ground surface during shield tunneling, where L stands for normalized distance between the tunnel face and the monitoring section. L < 0 indicates that the tunnel face doesn’t pass through the monitoring section. L > 0 shows that the tunnel face has passed through it (see Fig. 3). It can be seen that the calculated results of transverse settlement troughs for various tunnel face position are in good agreement with the measured data. Especially, the computed results of the settlement development at monitoring point 1 well match the measured data (see Fig. 3(b)). Therefore, the numerical modeling method adopted in this study is confirmed to be reliable.
-3
-2
-1 0 1 2 3 4 5 Normalized distance between tunnel face and monitoring point (Y/D)
6
(b) Fig. 3. Comparison of measured and calculated settlements on ground surface: development of (a) transverse settlement trough and (b) settlement at monitoring point 1 during EPBS tunneling.
3. Simplified numerical simulation 3.1. Numerical model To study the 3D stress-transfer mechanism and soil arching effect around the tunnel during shield tunneling, based on the example of Changsha Metro Line 2 project, a hypothetical EPBS tunneling in homogeneous dry medium coarse sand was modeled in this study. The diameter of the tunnel is taken as 6 m, and the burial depth is 12 m, as shown in Fig. 4. According to the previous investigation of Line 2 numerical model, the dimensions of the model are 90 m (length) × 30 m (width) × 40 m (depth). Numerical simulation process in this section is the same as Section 2.2.3, unless stated otherwise. The support pressure is assumed to be equal to the initial horizontal stress at the tunnel axis (i.e P1 = 128.7 kN/m2). The grouting pressure is generally recommended to be larger than the support pressure at the same depth. Thus, the value of grouting pressure in this study is assumed to be equal to 1.2 times of the support pressure (i.e P2 = 1.2 P1 = 154.4 kN/m2). The average jacking thrust (P3) is 2000 kN/m2. The monitoring section, located at Y = 37.5 m (see Fig. 4), is investigated during EPBS tunneling. Points A, B, C and D at the tunnel centerline of the monitoring
Fig. 4. Simplified numerical model and position of monitoring section.
4
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away from the monitoring point. Then the settlement becomes stable when the face passes 5D away. So the initial position of the excavation face of EPBS is 16.5 m (almost 2.8D) from the monitoring section. Then EPBS advances 1.5 m in each step of the staged excavation until the excavation face is 39 m (almost 6.5D) away from the monitoring section. The soil in this study is the medium coarse sand and parameters are presented in Table 3. The lining segments and EPBS were also modeled as linear elastic, the parameters of which are shown in Table 1.
Table 4 Analysis cases. Support pressure (P1)
Grouting pressure (P2)
Analysis case
0.2 0.6 1.0 1.4 1.8 2.2 2.6 3.6 1.0
1.0
1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 2-1 2-2 2-3 2-4 2-5
0.2 0.6 1.8 2.7 3.6
3.2. Analysis cases To investigate the influence of shield-driving parameters (i.e. support pressure, grouting pressure) on evolution of soil arching and stress redistribution, thirteen numerical models were established, as shown in Table 4. The support pressure is usually less than the initial horizontal stress at the depth of tunnel axis during EPBS tunneling. Therefore, the next section focuses on the analysis and discussion of case 1–1.
Note: P1 = initial horizontal stress at the tunnel axis; P2 = 1.2P1.
section are selected for detailed study. Point A is located on the ground, and the distance among points A, B and C is 4 m. The interval between points C and D is 3.5 m. Based on the results of Line 2 numerical model, the ground settlement begins to develop when the tunnel face is 2.5D
Fig. 5. Variation of σ-depth curves at tunnel centerline during tunneling: (a) σzz; (b) σxx; (c) σyy. 5
Tunnelling and Underground Space Technology 93 (2019) 103104
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200
35
Face passing
30
Ground surface A
25
Tail arriving Tail passing
160
2D
20
xx
15
yy
Tunnel
10
zz
Initial value of horizontal stress
-5 -4
-3
-2 -1 0 1 2 3 4 5 6 Normalized distance between tunnel face and monitoring section (Y/D)
100
40 -4
zz
Initial value of horizontal stress
-3
-2 -1 0 1 2 3 4 5 6 Normalized distance between tunnel face and monitoring section (Y/D)
100
225
1.33D
yy zz
Tunnel
80 60
Initial value of horizontal stress
20 -4
-3
-2 -1 0 1 2 3 4 5 6 Normalized distance between tunnel face and monitoring section (Y/D)
xx
175
yy
150 125 75 50
Tail passing
Face passing
200
D 0.08D Tunnel
zz
Initial value of horizontal stress
Tail arriving
Face passing
Tail passing
100
Tail arriving
40
Ground surface
250
B
Stress (kPa)
Stress (kPa)
275
Ground surface xx
7
(c)
160
120
Tail arriving Tail passing
Face passing
(a) 140
0.64D
Tunnel
yy
120
60
7
C xx
140
80
5 0
Ground surface
180
Stress (kPa)
Stress (kPa)
40
25 -4
7
(b)
-3
-2 -1 0 1 2 3 4 5 6 Normalized distance between tunnel face and monitoring section (Y/D)
7
(d)
Fig. 6. Variation of stresses (σxx, σyy, σzz) at the four monitoring points during tunneling: (a) point A; (b) point B; (c) point C; (d) point D.
4. Results and discussion
In order to reduce the development of deformation of soil, the soil arching is formed at the upper part of the loosened zone (Chen et al., 2011b). The arch foot acts on the soil mass ahead of the loosened zone, which is defined as the stability zone. Due to the stress transfer function of arch foot, the stresses of the stability zone increase. Therefore, the monitoring section may be located in the stability zone at this time. Phase III (L = −0.25D) The σzz-depth curve becomes obvious nonlinear and sharply decreases. Both σxx and σyy above the tunnel crown begin to increase, and the increment of σxx is larger than that of σyy. σxx in the range of the tunnel slightly increases, whereas σyy sharply decreases. This shows that the area in front of the tunnel face forms loosened zone because of the lack of the support pressure. The inflection points with marker in the σzz-depth curve are chosen as the characterize points of soil arching development (Terzaghi, 1943; Chen et al., 2011a; Lin et al., 2018). There are two inflection points on σzz-depth curve, which are represented by points a and b, respectively. With the increase of depth above point a, the vertical stress gradually reduces relative to the initial stress. This indicates that the vertical stress is transferred to surrounding soil mass through the soil arching. The vertical stress sharply decreases in the depth range of points a and b, which shows that the soil mass in this zone may be in the loosened state. The vertical stress begins to increase with the increase of depth below point b, and the increment is larger than that of the initial vertical stress (γΔH).
4.1. Soil arching effect A typical case 1–1 was analyzed. The variations of stresses and settlements in the monitoring section during tunneling were measured to investigate the evolution of soil arching and stress-transfer mechanism. 4.1.1. Variations of stresses (σxx, σyy, σzz) at the monitoring section The stresses of soil around the tunnel constantly change during EPBS tunneling. Fig. 5 presents variation of σ-depth curves at tunnel centerline during tunneling. Based on variation of σ-depth curves, the following five phases can be determined. Phase Ⅰ (L < −2.25D) The σ-depth curves are linear and equal to the initial earth stress (see Fig. 5(a)). The monitoring section is not affected by tunnel excavation. Phase Ⅱ (L = −0.75D) The σzz-depth curve becomes nonlinear in the range of tunnel (−3 < Z/D < −2) and σzz is larger than the initial earth stress (σzz = γH). σxx slightly increases in the whole region above the bottom of the tunnel, whereas σyy hardly change. This indicates that, due to over-excavation, the loosened zone emerges in front of the tunnel face. 6
Tunnelling and Underground Space Technology 93 (2019) 103104
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Ka= 0.28 K0= 0.44
Normalized depth (Z/D)
0.0 -0.5
L=-2.25D L=-0.25D L=0.5D L=2D
-1.0 -1.5 -2.0
L=-0.75D L= 0 L=1.25D L=3.25D
Crown of the tunnel
-2.5 -3.0
Bottom of the tunnel
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 x
(a) Ka= 0.28
K0= 0.44
Fig. 8. Variation of settlement-depth curve at tunnel centerline during tunneling.
0.0
2 L=-2.25D L=-0.25D L=0.5D L=2D
-1.0 -1.5
L=-0.75D L= 0 L=1.25D L=3.25D
-2.5 -3.0
Ground surface A 0.67D B 0.67D C 0.58D D
-2
Crown of the tunnel
-2.0
-0.75D
0 Settlement (mm)
Normalized depth (Z/D)
-0.5
-4 -6
Point A Point B Point C Point D
-8
-10
Bottom of the tunnel
-12
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Face passing
-14
y
(b)
-3
Fig. 7. Variation of coefficients of lateral earth pressure at tunnel centerline during tunneling: (a) Kx; (b) Ky.
Tunnel
-2
Tail arriving Tail passing
-1 0 1 2 3 4 5 6 Normalized distance between tunnel face and monitoring section (Y/D)
7
Fig. 9. Development of settlement at the four monitoring points during tunneling.
Phase Ⅳ (0 < L < 2D) The vertical stress (σzz) gradually decreases in this stage. The horizontal stresses (σxx, σyy) continue to increase. At this time, EPBS is passing through the monitoring section. These inflection points in the σzz-depth curve gradually moves up since the volume loss increases, which implies the expansion of the loosened zone. Phase Ⅴ (L > 2D) The grouting zone passes through the monitoring section first, and then the lining segments are installed, and the σzz-depth curve only slightly changes. This shows that the loosened zone is not upward development. Final vertical stress distribution above the tunnel is similar to the result of Terzaghi’s plane strain condition. Meanwhile, the horizontal stresses (σxx, σyy) near the crown of tunnel undergo complicated variations before and after the shield tail passing due to the shield friction, grouting pressure and segments installation. The area above the inflection point is defined the zone Ⅰ (i.e. Arch zone), and the area between the inflection point and the tunnel crown is defined the zone Ⅱ (i.e. Loosened zone). The height of zones Ⅰ and Ⅱ is 1.27D and 0.73D, respectively. Fig. 6 presents variation of stresses (i.e σxx, σyy, σzz) at the four monitoring points (i.e. A, B, C and D) during tunneling. The locations of
the four points can be referred to Fig. 4. At the points A and B (see Fig. 6(a) and (b)), when the tunnel face approaches the monitoring section, σxx gradually increases, σyy decreases, and σzz remains constant. It shows that the horizontal soil arching occurs in the X-Y plane in the depth range of 0.67D below the ground surface. σyy is transferred to the soil mass on both sides of settlement trough via the horizontal soil arching (as shown in Fig. 13(a)), the stress-transfer mechanism of which is similar to that of arch dam in water conservancy projects. As the tunnel face continues to approach the monitoring section until the shield tail reaches it, σyy begins to increase and σxx continues to increase. Moreover, σxx is always greater than σyy. σzz slightly decreases at point B. This indicates that the vertical soil arching occurs in the Y-Z and X-Z planes (i.e. the horizontal soil arching gradually transforms into the vertical soil arching, as shown in Fig. 13(b)), and the soil arching effect in the X-Z plane is more obvious than that in the Y-Z plane. As the shield tail passes through the monitoring section, σxx and σzz almost keep constant, but σyy begins to decrease and finally stay constant. This shows that the earth pressure above the tunnel is finally mainly transferred by means of vertical soil arching in the X-Z plane, as 7
Tunnelling and Underground Space Technology 93 (2019) 103104
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0
0
-2
1
γs (10-3)
6.00
Ground surface
Ground surface
-4
0.67D
-6
0.67D L=-0.75D 0.58D
1-1 2-2 3-3 4-4
Tunnel
Monitoring section
-10 -12
2-2 3-3 4-4
EPBS
-8
1-1
Normalized depth (Z/D)
Settlement (mm)
5.47
Possible shear surface
3.89
3.36
3
2.30 1.78 1.25
5
0.72
-5 -4 -3 -2 -1 Normalized distance from tunnel centerline (X/D)
0.19
6
0
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zz
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Fig. 11. (a) Shear strain contour at transversal section; (b) σzz-depth curves of the different distances from tunnel centerline.
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of horizontal stresses (σxx, σyy) at point C is the same as that of points A and B. Whereas the variations of the horizontal stresses (σxx, σyy) at point D are complex and are different from other points. σzz at point C and D sharply decreases when the tunnel face is −0.5D from the monitoring section. As a result of grouting pressure at the shield tail, σzz at point D steeply increases during the shield tail passing through the monitoring section. The stresses at points C and D keep constant after EPBS completely passing.
Ground surface Monitoring section L=3.25D
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-5 -4 -3 -2 -1 Normalized distance from tunnel centerline (X/D)
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4.1.2. Variations of coefficients of lateral earth pressure (Kx, Ky) The coefficient of lateral earth pressure, K, is equal to the horizontal stress divided by corresponding the vertical stress (i. e. Kx = σxx/σzz; Ky = σyy/σzz). Therefore, the coefficient of lateral earth pressure at various excavation stages is calculated by adopting the data of Fig. 5, as shown in Fig. 6, where the coefficient of lateral earth pressure at rest is taken as K0 = 1 − sinφ = 1 − sin34° ≈ 0.44, and the active coefficient of lateral earth pressure is calculated using the formula as follows: Ka = tan2(45° − φ/2) = tan2(45° − 34°/2) ≈ 0.28. When L = −2.25D, the theoretical value of K0 is close to the value obtained from the numerical simulation (see Fig. 7). Similar to the horizontal stress, the coefficients of lateral earth pressure of soil above the tunnel
Fig. 10. Comparison between transverse settlement troughs of different depths at the monitoring section: (a) L = −0.75D; (b) L = 0; (c) L = 3.25D.
shown in Fig. 13(b). With the tunnel face approaching the monitoring section, σzz at points C and D increases and reaches the maximum when the tunnel face is about −1.25D and -D from the monitoring section, respectively. But σxx and σyy change little. As the tunnel face continues to approach the monitoring section until the shield tail reaches it, the change trend 8
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(a)
Z
Y
yy
xx
X
BS
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Arch zone Loosened zone
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Fig. 12. Porosity ratio contour after tunnel excavation: (a) transversal section; (b) longitudinal section.
crown increase with EPBS tunneling, and the increment of Kx is larger than that of Ky. When L = −0.25D, Kx and Ky in the range of tunnel are increased and decreased, respectively. This is because σxx changes little (see Fig. 5(b)), but both σzz and σyy significantly decrease (see Fig. 5(a) and (c)), and the decrement of σyy is larger than that of σzz. After EPBS passing, the coefficients of lateral earth pressure along the depth above the tunnel crown are C-shaped distribution, and the maximum coefficient of lateral earth pressure appears near the ground surface. This is because, near the ground surface, the increased horizontal stresses coupled with the relatively unaffected vertical stress result in the maximum coefficients of lateral earth pressure.
(b) Fig. 13. Schematic diagram of three-dimensional soil arching zone: (a) horizontal soil arching near the ground surface; (b) vertical soil arching above EPBS and tunnel.
zone, and an important index to evaluate the influence of shield tunneling on surrounding environment. Fig. 9 shows development of settlement at the four monitoring points (i.e. A, B, C and D) during tunneling. The locations of the four points are depicted in Fig. 4. When the tunnel face is about −2.5D from the monitoring section, the four points begin to settle continuously. However, before the tunnel face reaches the position of about −0.75D from the monitoring section, the settlement rate of the point A is larger than that of other points, and the settlement rate decreases with the depth. The transverse settlement troughs corresponding to the depth locations of points A, B, C, and D are shown in Fig. 10. When the tunnel face is −2.5D from the monitoring section, the settlement of point A is largest, and that of point D is smallest (see Fig. 10(a)). As the tunnel face continues to approach the monitoring section, the settlement rates at the four points gradually increase, and point D increases the fastest, whereas points A, B and C are relatively close. At this time, the point D may be located in the loosened zone, whereas the points A, B and C may be located in the soil arching zone. When the tunnel face arrives at the monitoring section, the settlements of points A and D are larger than or
4.1.3. Variations of settlements at the monitoring section The inflection points in the σzz-depth curves are depicted in the corresponding settlement-depth curves, as shown in Fig. 8. It can be seen that the settlement of soil in zone Ⅰ is almost constant along the depth after the tunnel excavation. This indicates that the whole settlement occurs in soil mass of zone Ⅰ. However, the settlement of soil in zone Ⅱ sharply increases with the depth. This shows that soil mass in zone Ⅱ is in the loosened state due to the separation between soils. So it is reasonable that zone Ⅱ is called the loosened zone. It can be found from the above analysis that the soil in the zone Ⅱ may be in the limit state, while the shear strength of the soil in the zone Ⅰ may not be fully played. So the height of inflection point in the σzz-depth curves can be used as the boundary between the loosened zone and the soil arching 9
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Fig. 14. Development of arch zone and loosened zone during shield tunneling.
Ground surface
Normalized depth (Z/D)
0.0 -0.5
case1-1 case1-3 case1-5 case1-8
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-2.0 -2.5
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-3.0 Fig. 15. Comparison of arch zone and loosened zone at different cross-sections during shield tunneling.
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(a)
equal to those of points B and C (see Fig. 10(b)). During shield passing through the monitoring section, the settlements at four points continue to increase. When the grouting zone passes through the monitoring section, the increment of settlement at point D begins to decrease. However, the settlements of other points are less affected. When the tunnel face is 3.25D from the monitoring section, as shown in Figs. 9 and 10 (c), the settlement of point D is maximum. The settlements of points A, B and C are close.
Normalized height of loosened zone above tunnel crown (Z/D)
1.0
4.1.4. Soil arching zone The relative displacement between soil masses produces the shear stress. The load of the yielded soil is transferred to the adjacent parts by the shear stress. This load transfer mechanism is so-called the soil arching effect. The shear surface generally occurs where shear strains are large. One side of the shear surface is elastic soil which is defined as the stability zone. The other side is the yielded part which is defined as the arch zone. The contour of shear strain at transversal section after tunnel excavation is shown in Fig. 11(a). The maximum shear strain extends from the springline of the tunnel along inclined line to the ground surface, indicating that this area may form a shear surface, which is defined as the outer boundary of the soil arching. The lower boundary of the soil arching zone is determined by the inflection points of vertical stress at different positions of the cross-section, as shown in Fig. 11(b). The boundary where the horizontal stress increases by more than 5% is defined as the upper boundary of the arch zone. Fig. 12 shows the porosity ratio contours at the cross-section and longitudinal section after tunnel excavation. The upper, lower and outer boundaries of the soil arching are depicted in the porosity ratio contours. It can be seen that the porosity ratio of the soil arching zone and the stability zone are smaller than that of the other zone, indicating that these zones are compacted. The porosity ratio of the loosened zone increases. This shows that the soil swelling occurs in this zone. According to the above method of determining the soil arching
0.8 0.6 0.4 0.2 0.0
0.0
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1.0
1.5
2.0
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Surpport pressure (P1)
(b) Fig. 16. Distribution of soil arching zone and loosened zone above tunnel crown in longitudinal section with different support pressures; (b) variation of height of loosened zone with different support pressures.
zone, the schematic diagram of 3D soil arching zone is shown in Fig. 13. Meanwhile, the stress-transfer mechanism in soil arching zone previously revealed is also depicted in Fig. 13. To better present the evolution of soil arching zone during EPBS tunneling, three typical sections were selected before and after tunneling from Fig. 13, as shown in Fig. 14. It demonstrates that with EPBS tunneling, the loosened zone gradually expands upward, meanwhile, the arch zone also expands upward and outward (see Fig. 15). Finally, the loosened zone extends to nearly 0.73D above the tunnel crown in vertical direction and 0.33D 10
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Normalized depth (Z/D)
4.2.1. Effect of support pressure To study the effect of support pressure on the soil arching, seven numerical models were built with support pressures of 0.6P1, 1.0P1, 1.4P1, 1.8P1, 2.2P1, 2.6P1 and 3.6P1, respectively (see Table 4). The modeling procedure is the same as that presented in Section 2.2. Based on the height of inflection point in σzz-depth curve, the boundary between soil arching and loosened zones above the tunnel for cases 1–1, 1–3, 1–5 and 1–8 was determined, as shown in Fig. 16(a). It can be found that both the boundaries for cases 1–3 and 1–5 are almost identical during tunneling. This is because the limited increase of support pressure only affects the soil in the range of tunnel in front of the face, and the soil in this area is excavated in the next step. When the support pressure largely decreases or increases (e.g. cases 1–1 and 1–8), the support pressure not only affects the soil in the tunnel range, but affects the soil above the tunnel. Therefore, the boundaries for cases 1–1 and 1–8 are higher than those for cases 1–3 and 1–5. As presented in Fig. 16(b), when the support pressure increases from 0.6P1 to 2.2P1, the variation of loosened zone height is small (from 0.33D to 0.38D). However, when the support pressure is 0.2P1 or more than equal to 2.6P1, the loosened zone height sharply increases from about 0.3D to 0.7D.
Ground surface
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case 2-1 case 1-3 case 2-3
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(a)
Normalized height of loosened zone above tunnel crown (Z/D)
1.0 0.8
4.2.2. Effect of grouting pressure To investigate the impact of grouting pressure on the soil arching, five numerical models were established with grouting pressures of 0.2P2, 0.6P2, 1.8P2, 2.7P2 and 3.6P2, respectively (see Table 4). According to the height of inflection point in σzz-depth curve, the boundary between soil arching and loosened zones above the tunnel for cases 2–1, 1–3 and 2–3 were determined, as presented in Fig. 17(a). It can be seen that the heights of loosened zone above EPBS for these three cases are the same. However, there are significant changes in these boundaries above the grouting zone. For the case 2–1, the height of loosened zone obviously increases after the grouting zone passing, but the height for the cases 1–3 and 2–3 slightly decreases. After the segment installed, the final height of loosened zone for the case 2–1 is about 0.52D higher than these of the cases 1–2 and 2–3. From the above analysis, we can see that small grouting pressure causes further upward expansion of the loosened zone, and then threatens the safety of surrounding underground existing structures. As shown in Fig. 17(b), the height of loosened zone decreases with the increase of the grouting pressure, and when the grouting pressure is more than 1.8P2, the height of loosened zone is little change. The height of loosened zone above the tunnel crown can be use as an important index to evaluate the influence of shield tunneling on the surrounding environment. From above analysis of shield-driving parameters, we can find that the proper combination of the parameters for controlling the expansion of the loosened zone is support pressure of 0.6P1 − 2.2P1 and grouting pressure of 1.0P2 − 1.8P2.
0.6 0.4 0.2 0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Grouting pressure (P2)
(b) Fig. 17. (a) Distribution of soil arching zone and loosened zone above tunnel crown in longitudinal section with different grouting pressures; (b) variation of height of loosened zone with different grouting pressures.
beyond the tunnel springline in horizontal direction. The height of the arch zone is about 1.27D above the loosened zone in vertical direction and the width is about D beyond the loosened zone in horizontal direction. The determinations of the soil arching zone and the loosened zone are helpful to understand the influences of tunnel excavation on surrounding existing structures. For example, for the project of the new tunnel construction beneath the existing structures (e.g., pipeline and tunnel) (Wang et al., 2011; Ng et al., 2013; Li et al., 2016; Chen et al., 2018a; Lin et al., 2019), if the vertical distance between them is less than the height of the loosened zone caused by the new tunnel excavation, induced stress and settlement of the existing structures due to the new tunnel excavation may exceed the design allowable value and even cause the concrete to crack. Reinforcement measures to prevent the upward expansion of the loosened zone may be effective.
5. Conclusions In this paper, a three-dimensional numerical finite element model validated by a case history has been used to analyze the stress redistribution and the soil arching evolution induced by EPBS tunneling. Based on the calculated results, the following conclusions may be drawn: (1) The boundary between the soil arching zone and the loosened zone is determined by the inflection points of σzz-depth curves. The height changes of the inflection points during tunneling reflect the expansion of the loosened zone, which can be used as an important index to evaluate the influence of shield tunneling on the surrounding environment. (2) For case 1–1 with support pressure of 0.2P1 and grouting pressure of 1.0P2 (P1 = initial horizontal stress at the tunnel axis and P2 = 1.2P1), with EPBS tunneling, the loosened zone gradually
4.2. Influence of shield-driving parameters on evolution of soil arching The evolution of soil arching is closely related to the changes of stress field and displacement field of soil mass. The soil around the tunnel can be easily disturbed in shield tunneling (Meng et al., 2018). Therefore, the influence of shield-driving parameters (i.e. support pressure, grouting pressure) on the soil arching is investigated as follows. 11
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expands upward, meanwhile, the arch zone also expands upward and outward. Finally, the loosened zone extends to nearly 0.73D above the tunnel crown in vertical direction and 0.33D beyond the tunnel springline in horizontal direction. The height of the arch zone is about 1.27D above the loosened zone in vertical direction and the width is about D beyond the loosened zone in horizontal direction. (3) Three-dimensional stress-transfer mechanism in soil arching zone above tunnel during tunneling is demonstrated. The horizontal soil arching in front of EPBS occurs in the X-Y plane in the depth range of about 0.67D below the ground surface. Then, the horizontal soil arching gradually transforms into the vertical soil arching with EPBS driving, and the vertical soil arching effect in the X-Z plane is more obvious than that in the Y-Z plane. After EPBS passes, the earth pressure is finally mainly transferred via vertical soil arching in the X-Z plane, which is similar to the result of Terzaghi’s plane strain condition. (4) The coefficient of lateral earth pressure above the tunnel crown increases with EPBS tunneling, and the increment of Kx is larger than that of Ky. After EPBS passes, the coefficient of lateral earth pressure along the depth above the tunnel crown is C-shaped distribution, and the maximum coefficient of lateral earth pressure appears near the ground surface. (5) The limited increase of support pressure only affects the soil in the tunnel range in front of the face. The excessively high or low support pressure not only affects the soil in the range of tunnel, but affects the soil above the tunnel. There are significant changes in the height of loosened zone above the grouting zone for different grouting pressures. With the increase of grouting pressure, the height of loosened zone decreases. The proper combination of shield-driving parameters for controlling the expansion of the loosened zone is support pressure of 0.6P1 − 2.2P1 and grouting pressure of 1.0P2 − 1.8P2.
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Three-dimensional stress-transfer mechanism and soil arching evolution induced by shield tunneling in sandy ground
T
Xing-Tao Lin, Ren-Peng Chen , Huai-Na Wu, Hong-Zhan Cheng ⁎
Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education, Hunan University, Changsha 410082, China National Center for International Research Collaboration in Building Safety and Environment (NCIRCBSE), Hunan University, Changsha 410082, China College of Civil Engineering, Hunan University, Changsha 410082, China
ARTICLE INFO
ABSTRACT
Keywords: Earth pressure balance shield (EPBS) Numerical modeling Stress redistribution Soil arching effect
Tunnel excavation inevitably causes variations in stress and displacement fields in soil, which could affect the serviceability and safety of the adjacent underground structures. Change of the earth pressure acting on the existing structures is closely related to soil arching effect caused by a new tunnel excavation, but it is still lack of full understanding. In this study, a finite element method (FEM) model was first verified by field measurements based on a case history of Metro Line 2 construction in Changsha, China. Then, a series of simplified threedimensional (3D) FEM models were established to investigate the stress redistribution and the soil arching evolution induced by earth pressure balance shield (EPBS) tunneling. The changes of the earth pressure, the coefficient of lateral earth pressure, and the settlement of soil mass above the tunnel during tunneling were analyzed and the soil arching zone was determined. 3D stress-transfer mechanism in soil arching zone during tunneling was revealed. In addition, the influences of shield-driving parameters (i.e. support pressure, grouting pressure) on soil arching evolution were also investigated. The results show that the loosened zone extends to nearly 0.73D (D = tunnel diameter) above the tunnel crown in vertical direction. The height of the arch zone above the loosened zone is about 1.27D. The horizontal soil arching in front of EPBS occurs near the ground surface. With EPBS advancing, the horizontal soil arching gradually transforms into the vertical soil arching. After the installation of lining, the earth pressure is finally mainly transferred by vertical soil arching in the transverse section. The proper combination of shield-driving parameters for controlling the expansion of the loosened zone is support pressure of 0.6P1 − 2.2P1 and grouting pressure of 1.0P2 − 1.8P2, where P1 is initial horizontal stress at the tunnel axis and P2 = 1.2P1.
1. Introduction In the past few decades, EPBS tunneling technology has been widely used in the construction of the urban subway tunnel (Reilly, 1999; Chen et al., 2011c, 2019; Shen et al., 2014; Wu et al., 2015, 2018; Zhang et al., 2019). If the earth pressure in shield’s chamber is insufficient or the grouting pressure setting at tail is unreasonable, shield driving will easily cause disturbance in surrounding soils, which could induce safety problem of the adjacent underground structures. Changes in stress and displacement fields in soil are a reflection of the soil arching effect due to tunnel excavation. Thus, it is of great significance for ensuring existing underground structure safety to study the soil arching effect caused by tunnel excavation. The soil arching effect widely exists in the civil engineering (e.g., the tunnel, the piled embankment, the retaining wall and the
⁎
foundation pit etc.) (He and Zhang, 2015; Lai et al., 2018; Wang et al., 2018; Wang and Chen, 2019). For the soil arching around the tunnel, many researchers have performed much meaningful work in the theoretical analyses, model tests and numerical simulations. Based on the trapdoor tests, some theoretical researches have been conducted to study the variation of the earth pressure around tunnel (Terzaghi, 1943; Getzler et al., 1970; Li et al., 2013; Chen et al., 2015; Son, 2017). The laboratory tests were also frequently used to investigate the soil arching effect and stress redistribution caused by the tunnel excavation (Adachi et al., 2003; Berthoz et al., 2018; Chen et al., 2013, 2018b; Dewoolkar, 2007; Franza et al., 2018; Idinger et al., 2011; Kirsch, 2010; Lee et al., 2006a,b; Li et al., 2011; Liu et al., 2018; Murayama and Matsuoka, 1971; Nakai et al., 1997). Based on the trapdoor modeling tests, Terzaghi (1943) observed the changes of vertical stress distribution above the tunnel after excavation, as depicted in Fig. 1. The increasing
Corresponding author at: College of Civil Engineering, Hunan University, Changsha 410082, China. E-mail addresses: [email protected] (X.-T. Lin), [email protected] (R.-P. Chen), [email protected] (H.-N. Wu), [email protected] (H.-Z. Cheng).
https://doi.org/10.1016/j.tust.2019.103104 Received 29 March 2019; Received in revised form 12 July 2019; Accepted 27 August 2019 Available online 04 September 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
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economical method. Recently, the numerical simulation has played a significant role in studying shield tunneling. Numerous numerical models have been established to research the soil arching effect and stress redistribution ahead of the tunnel face or around tunnel (Vermeer et al., 2002; Ng and Lee, 2005; Gomes and Celestino, 2009; Chen et al., 2011a, 2011b; Jiang and Yin, 2012; Lin et al., 2018; Kong et al., 2018, 2019). Jiang and Yin (2012) analyzed the effect of the buried depth and tail gaps on the stress redistribution in soil and the earth pressure around the tunnel due to excavation by using two-dimensional (2D) discrete element method (DEM). It was found that the soil arching effects were slightly unaffected by the depth and tail gaps of the tunnel when those values were larger than certain values. Kong et al. (2018) built many 2D numerical models to investigate arching mechanism in rock mass, and defined the three characteristic lines of the pressure arch (i.e. the outer boundary line, the centroid line and the inner boundary line) based on the changes of horizontal and vertical stresses distributions of the rock around tunnel. However, the above analyses of arching effect were limited to 2D because these results were obtained under the condition of plane strain. Chen et al. (2011b) investigated the failure mechanism of a tunnel face in dry sandy ground by using 3D DEM. It was found that soil arching occurred in the upper part of the failure zone and the soil become loosened in the failure zone. Chen et al. (2011a) set up a series of 3D finite element models to research the vertical stress distribution variations above the tunnel roof during tunneling. Selecting the changes of inflection point at the σzz-depth curve act as the reliable indexes to reflect the development of the soil arching. However, the scope of arch zone is not given by Chen et al. (2011a). Yang et al. (2015) established a 3D numerical model to study arching mechanism in rock mass, and determined the inner and outer boundaries of the arch zone according to the variations of the maximum principle stress of the rock surrounding tunnel. It was found that as the span-to-height of tunnel increased, the shape of arch zone varied from a circular to a flat, meanwhile the arch zone opening also increased. Although the 3D numerical models were built in the above researches, there is the lack of full analyses in three directions stresses during tunnel excavation. So 3D soil arching effect is not clearly revealed. Moreover, the stress redistribution caused by EPBS tunneling is significantly affected by the shield-driving parameters. But the above researches mainly focus on the unlined tunnel, which was excavated using mining method in rock mass. To sum up, although many researches on the arching effect due to tunnel excavation have been made, there are still two problems: i) the 3D stress-transfer mechanism and evolution process of soil arching during the shield tunneling are not full revealed; ii) there is a lack of the understanding of the effects of the shield-driving parameters on soil arching effect around the tunnel. In this study, a 3D FEM model is first validated on a case history of Metro Line 2 construction in Changsha, China. Subsequently, a series of simplified 3D numerical analyses are conducted to investigate the soil arching evolution and stress redistribution caused by the shield tunneling. The changes of the three direction earth pressures, the coefficient of lateral earth pressure and the settlement of soil mass above the tunnel during EPBS tunneling are discussed. Additionally, the influence of shield-driving parameters on soil arching evolution is also investigated.
Fig. 1. Vertical stress profile at centerline after tunnel excavation: (a) shallow tunnel; (b) deep tunnel (Terzaghi, 1943).
trend of the vertical stress for the shallow tunnel gradually slows down with the increase of the depth, and then keeps constant when the depth reaches a certain value (see Fig. 1(a)). The vertical stress for the deep buried tunnel is equal to the self-weight stress as the depth increases, and then sharply decreases when the depth reaches a certain value (see Fig. 1(b)). Thus, Terzaghi (1943) thought that the soil arching effect occurs in the region below this depth. Adachi et al. (2003) carried out a series of 3D trapdoor experiments, which were simulated tunnel excavation. Based on the experimental results, it was found that the distribution of earth pressure was greatly affected by the process of the excavation. Lee et al. (2006a, b) investigated the tunnel stability and soil arching effects during tunneling in sandy soil and soft clayey soil by a series of centrifuge model tests. The boundaries of arch zone were determined according to the changes of earth pressure around the tunnel, and the positive and negative arch zones boundaries were also suggested. Chen et al. (2013) researched the evolution of soil arching during face failure by monitoring the redistribution of earth pressure in front of the face based on large-scale laboratory test. Then, a two-stage failure pattern was proposed based on the observation of earth pressure redistribution. These experimental studies improve the understanding of the interaction between the tunnel and the surrounding soils. However, the model tests are limited sometimes due to time consuming and cost expensive. The numerical analysis has been widely adopted in the investigation of tunnel excavation since it is an effective and
2. Case history and verification of the numerical model 2.1. Introduction of the case history To investigate soil arching effect around the tunnel during shield tunneling, a 3D FEM model was established. A case history of the construction of the left tunnel of Metro Line 2 in Changsha, China, near the Yingwanzhen station, is chosen as the research objective for validating the reliability of the numerical modeling method. The study area is located in the section between Yingwanzhen station and Juzizhou 2
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Table 1 Material properties of EPBS and tunnel lining.
EPBS Tunnel lining
Table 3 Parameters for soils constitutive models (data from Lin et al. (2019)).
Young’s modulus E (GPa)
Poisson’s ratio v
Volumetric weight γ (kN/m3)
230 31
0 0.1
120 25
Table 2 Soil basic physical property index (data from Lin et al. (2019)).
Parameter type
Soil layers
Constitutive model
Backfill MC
Gravel MC
MCS HSS
φ′ Ψ c′ Eref
18.5 0 46 –
37.4 0 0 –
34 4 2 37,800
[°] [°] [kN/m2] [kN/m2]
–
–
37,800
[kN/m2]
–
–
113,500
[kN/m2]
4750 –
27,850 –
– 0.5
[kN/m2] [–]
–
–
189,200
[kN/m2]
–
–
10-4
[–]
– –
– –
100 0.2
[kN/m2] [–]
0.3 19 0.9
0.27 20 0.9
– 19.5 0.9
[–] [kN/m2] [–]
ref
50
Soil layer
Depth (m)
e0
γ (kN/m2)
w (%)
k (m/d)
E
oed
Fill Gravel Medium coarse sand
0–2.2 2.2–5.0 5.0–40
0.74 0.65 0.40
19.0 20.0 19.5
22.1 – 15.7
2.0 10.0 8.6
Eref
ur
E′ m
Note: e0 = void ratio; γ = soil unit weight; w = water content; k = hydraulic conductivity.
Gref γ0.7
station, and starts from the Yingwanzhen station until the end of 150 m from it. In the study area, the average burial depth of Metro Line 2 is about 9.0 m. The outer and inner diameters of tunnel are 6.0 m and 5.7 m, respectively. The length of each segmental ring is 1.5 m. Metro Line 2 was excavated using EPBS, with excavation diameter of 6250 mm, the length of 12.5 m, and the cutter opening ratio of 37%. The material parameters for the tunnel lining and EPBS are summarized in Table 1. The sub-soils in the construction site mainly consist of backfill, gravel and medium coarse sand. The distribution and physical properties of the soils are listed in Table 2. Metro Line 2 is located in the medium coarse sand layer. The groundwater level is about 2.0 m under the ground surface. The settlement of ground surface was measured during EPBS tunneling.
pref vur v γ Rf
0
Effective friction angle Dilatancy angle Effective cohesion Reference secant stiffness in triaxial test Reference tangent stiffness for oedometer loading Reference unloading/reloading stiffness Effective Young’s modulus Power that controls the stress dependency of stiffness Reference shear modulus at very small strains (ε < 1 0 −6) Shear strain at which Gs = 0.772G0 Reference stress Poisson ratio of unloading/ reloading Poisson ratio for MC model Soil unit weight Failure ratio
Unit
Note: MCS = medium coarse sand.
2.2.2. Material model and parameters The soil mass around the tunnel is subjected to complex forces (i.e support pressure, shield shell friction, grouting pressure, etc.) during EPBS tunneling. However, the simple elastic-perfectly plastic soil constitutive model is difficult to simulate the behavior of soil accurately. There are many advanced constitutive models in existing literature (Benz, 2007; Chang et al., 2010; Jin et al., 2016; Yin et al., 2010, 2016, 2018). To simulate the behavior of medium coarse sand around tunnel during excavation, an advanced elasto-plastic constitutive model, namely Hardening Soil model with Small Strain Stiffness (HSS) (Benz, 2007) used frequently in PLAXIS, was adopted in this study. Meanwhile, to save computational time and cost without affecting the numerical results, the Mohr-Coulomb model was employed to simulate the behavior of the fill and gravel. The parameters of soils models, which are from Lin et al. (2019), used in this study are shown in Table 3. The lining segments and EPBS were modeled as linear elastic, the parameters of which are listed in Table 1. Since the EPBS/lining and the surrounding soils have different roughness, the contact properties between EPBS and soils as well as lining and soils depend on the type of soil. In this paper, the interface elements have the same constitutive law
2.2. Three-dimensional numerical simulation 2.2.1. Numerical model The 3D FEM model was established to investigate EPBS tunneling using the geotechnical software PLAXIS 3D, as shown in Fig. 2. Considering the symmetry of the research object, the numerical model employed half of the domain. To eliminate the influence of boundary conditions on the results, the dimensions of the model are 150 m in length, 100 m in width, and 40 m in depth. The soil mass and lining were modeled as 10-node tetrahedral elements. The EPBS was modeled by 6-node plate elements. As for boundary conditions of model, the horizontal displacements of all vertical boundaries were fixed, but the vertical displacements were free. The displacements of the bottom plane were fully fixed in three directions. There was no displacement constraint on the top plane.
Fig. 2. Model geometry and schematic of EPBS tunneling details simulation. 3
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as the surrounding soil. Due to the tunnel locating in medium coarse sand in this paper, the soil-lining contact interface is roughness. Thus, the reduction factor, which reflects the reduction of the stiffness and shear strength of the interface elements, is set to be 1.0.
Settlement (mm)
0
2.2.3. Numerical simulation process The width of single precast concrete lining segments in this project is equal to 1.5 m. Hence, EPBS advances 1.5 m in each step of the staged excavation. The length of EPBS is set to be 12 m, which is exactly equal to the sum of the width of 8 segments, as shown in Fig. 2. The front 10.5 m length region is employed to simulate the cone-shaped EPBS and the volume loss caused by tunneling, which has a linear contraction with a reference value of 0.4% (Cref) at tail with increment of −0.0381%/m (Cinc). The rest 1.5 m length region is adopted to simulate the tail of EPBS, which has a uniform contraction of 0.4%. The support pressure acting on the tunnel face is used to keep the stability of the soil ahead of the tunnel. Based on the measured data, the support pressure is 72.4 kPa at the crown of tunnel face, and with the depth increasing, the pressure increases linearly with a gradient of 9.2 kPa/m. The grouting pressure in the shield tail, which acts on the crown of tunnel, is 147.3 kN/m2 with pressure gradient of 9.2 kPa/m. The average jacking thrust is 1775 kN/m2. The transverse measurement section is 20 m from the Yingwanzhen station (see Fig. 2). To eliminate the influence of initial position of EPBS on the monitoring point and to reduce the number of advancing rings, the initial position of the tunnel face of EPBS is 18.5 m (almost 3 D) from point 1. The detailed tunnel excavation for a total number of 36 steps is simulated. The shield tunneling procedure is modeled in a step-wise manner (Meng et al., 2018; Lin et al., 2019). More detailed descriptions can refer to the above corresponding literature.
-2
Z
Y
Ground surface L<0
-4
EPBS
L
-6 -8
-10 -5
L>0
Measured L=-0.33D L=1.17D L=4.17D
Monitoring section
L=0.42D L=1.92D
Calculated L=-0.33D L=0.42D L=1.17D L=1.92D L=4.17D
Tunnel
-4 -3 -2 -1 0 Normalized distance from tunnel centerline (X/D)
(a)
Settlement (mm)
0 Measured Calculated
-2 -4 -6
2.3. Verification of the numerical model
-8
Fig. 3 presents comparison of measured and calculated settlements on ground surface during shield tunneling, where L stands for normalized distance between the tunnel face and the monitoring section. L < 0 indicates that the tunnel face doesn’t pass through the monitoring section. L > 0 shows that the tunnel face has passed through it (see Fig. 3). It can be seen that the calculated results of transverse settlement troughs for various tunnel face position are in good agreement with the measured data. Especially, the computed results of the settlement development at monitoring point 1 well match the measured data (see Fig. 3(b)). Therefore, the numerical modeling method adopted in this study is confirmed to be reliable.
-3
-2
-1 0 1 2 3 4 5 Normalized distance between tunnel face and monitoring point (Y/D)
6
(b) Fig. 3. Comparison of measured and calculated settlements on ground surface: development of (a) transverse settlement trough and (b) settlement at monitoring point 1 during EPBS tunneling.
3. Simplified numerical simulation 3.1. Numerical model To study the 3D stress-transfer mechanism and soil arching effect around the tunnel during shield tunneling, based on the example of Changsha Metro Line 2 project, a hypothetical EPBS tunneling in homogeneous dry medium coarse sand was modeled in this study. The diameter of the tunnel is taken as 6 m, and the burial depth is 12 m, as shown in Fig. 4. According to the previous investigation of Line 2 numerical model, the dimensions of the model are 90 m (length) × 30 m (width) × 40 m (depth). Numerical simulation process in this section is the same as Section 2.2.3, unless stated otherwise. The support pressure is assumed to be equal to the initial horizontal stress at the tunnel axis (i.e P1 = 128.7 kN/m2). The grouting pressure is generally recommended to be larger than the support pressure at the same depth. Thus, the value of grouting pressure in this study is assumed to be equal to 1.2 times of the support pressure (i.e P2 = 1.2 P1 = 154.4 kN/m2). The average jacking thrust (P3) is 2000 kN/m2. The monitoring section, located at Y = 37.5 m (see Fig. 4), is investigated during EPBS tunneling. Points A, B, C and D at the tunnel centerline of the monitoring
Fig. 4. Simplified numerical model and position of monitoring section.
4
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away from the monitoring point. Then the settlement becomes stable when the face passes 5D away. So the initial position of the excavation face of EPBS is 16.5 m (almost 2.8D) from the monitoring section. Then EPBS advances 1.5 m in each step of the staged excavation until the excavation face is 39 m (almost 6.5D) away from the monitoring section. The soil in this study is the medium coarse sand and parameters are presented in Table 3. The lining segments and EPBS were also modeled as linear elastic, the parameters of which are shown in Table 1.
Table 4 Analysis cases. Support pressure (P1)
Grouting pressure (P2)
Analysis case
0.2 0.6 1.0 1.4 1.8 2.2 2.6 3.6 1.0
1.0
1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 2-1 2-2 2-3 2-4 2-5
0.2 0.6 1.8 2.7 3.6
3.2. Analysis cases To investigate the influence of shield-driving parameters (i.e. support pressure, grouting pressure) on evolution of soil arching and stress redistribution, thirteen numerical models were established, as shown in Table 4. The support pressure is usually less than the initial horizontal stress at the depth of tunnel axis during EPBS tunneling. Therefore, the next section focuses on the analysis and discussion of case 1–1.
Note: P1 = initial horizontal stress at the tunnel axis; P2 = 1.2P1.
section are selected for detailed study. Point A is located on the ground, and the distance among points A, B and C is 4 m. The interval between points C and D is 3.5 m. Based on the results of Line 2 numerical model, the ground settlement begins to develop when the tunnel face is 2.5D
Fig. 5. Variation of σ-depth curves at tunnel centerline during tunneling: (a) σzz; (b) σxx; (c) σyy. 5
Tunnelling and Underground Space Technology 93 (2019) 103104
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200
35
Face passing
30
Ground surface A
25
Tail arriving Tail passing
160
2D
20
xx
15
yy
Tunnel
10
zz
Initial value of horizontal stress
-5 -4
-3
-2 -1 0 1 2 3 4 5 6 Normalized distance between tunnel face and monitoring section (Y/D)
100
40 -4
zz
Initial value of horizontal stress
-3
-2 -1 0 1 2 3 4 5 6 Normalized distance between tunnel face and monitoring section (Y/D)
100
225
1.33D
yy zz
Tunnel
80 60
Initial value of horizontal stress
20 -4
-3
-2 -1 0 1 2 3 4 5 6 Normalized distance between tunnel face and monitoring section (Y/D)
xx
175
yy
150 125 75 50
Tail passing
Face passing
200
D 0.08D Tunnel
zz
Initial value of horizontal stress
Tail arriving
Face passing
Tail passing
100
Tail arriving
40
Ground surface
250
B
Stress (kPa)
Stress (kPa)
275
Ground surface xx
7
(c)
160
120
Tail arriving Tail passing
Face passing
(a) 140
0.64D
Tunnel
yy
120
60
7
C xx
140
80
5 0
Ground surface
180
Stress (kPa)
Stress (kPa)
40
25 -4
7
(b)
-3
-2 -1 0 1 2 3 4 5 6 Normalized distance between tunnel face and monitoring section (Y/D)
7
(d)
Fig. 6. Variation of stresses (σxx, σyy, σzz) at the four monitoring points during tunneling: (a) point A; (b) point B; (c) point C; (d) point D.
4. Results and discussion
In order to reduce the development of deformation of soil, the soil arching is formed at the upper part of the loosened zone (Chen et al., 2011b). The arch foot acts on the soil mass ahead of the loosened zone, which is defined as the stability zone. Due to the stress transfer function of arch foot, the stresses of the stability zone increase. Therefore, the monitoring section may be located in the stability zone at this time. Phase III (L = −0.25D) The σzz-depth curve becomes obvious nonlinear and sharply decreases. Both σxx and σyy above the tunnel crown begin to increase, and the increment of σxx is larger than that of σyy. σxx in the range of the tunnel slightly increases, whereas σyy sharply decreases. This shows that the area in front of the tunnel face forms loosened zone because of the lack of the support pressure. The inflection points with marker in the σzz-depth curve are chosen as the characterize points of soil arching development (Terzaghi, 1943; Chen et al., 2011a; Lin et al., 2018). There are two inflection points on σzz-depth curve, which are represented by points a and b, respectively. With the increase of depth above point a, the vertical stress gradually reduces relative to the initial stress. This indicates that the vertical stress is transferred to surrounding soil mass through the soil arching. The vertical stress sharply decreases in the depth range of points a and b, which shows that the soil mass in this zone may be in the loosened state. The vertical stress begins to increase with the increase of depth below point b, and the increment is larger than that of the initial vertical stress (γΔH).
4.1. Soil arching effect A typical case 1–1 was analyzed. The variations of stresses and settlements in the monitoring section during tunneling were measured to investigate the evolution of soil arching and stress-transfer mechanism. 4.1.1. Variations of stresses (σxx, σyy, σzz) at the monitoring section The stresses of soil around the tunnel constantly change during EPBS tunneling. Fig. 5 presents variation of σ-depth curves at tunnel centerline during tunneling. Based on variation of σ-depth curves, the following five phases can be determined. Phase Ⅰ (L < −2.25D) The σ-depth curves are linear and equal to the initial earth stress (see Fig. 5(a)). The monitoring section is not affected by tunnel excavation. Phase Ⅱ (L = −0.75D) The σzz-depth curve becomes nonlinear in the range of tunnel (−3 < Z/D < −2) and σzz is larger than the initial earth stress (σzz = γH). σxx slightly increases in the whole region above the bottom of the tunnel, whereas σyy hardly change. This indicates that, due to over-excavation, the loosened zone emerges in front of the tunnel face. 6
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Ka= 0.28 K0= 0.44
Normalized depth (Z/D)
0.0 -0.5
L=-2.25D L=-0.25D L=0.5D L=2D
-1.0 -1.5 -2.0
L=-0.75D L= 0 L=1.25D L=3.25D
Crown of the tunnel
-2.5 -3.0
Bottom of the tunnel
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 x
(a) Ka= 0.28
K0= 0.44
Fig. 8. Variation of settlement-depth curve at tunnel centerline during tunneling.
0.0
2 L=-2.25D L=-0.25D L=0.5D L=2D
-1.0 -1.5
L=-0.75D L= 0 L=1.25D L=3.25D
-2.5 -3.0
Ground surface A 0.67D B 0.67D C 0.58D D
-2
Crown of the tunnel
-2.0
-0.75D
0 Settlement (mm)
Normalized depth (Z/D)
-0.5
-4 -6
Point A Point B Point C Point D
-8
-10
Bottom of the tunnel
-12
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Face passing
-14
y
(b)
-3
Fig. 7. Variation of coefficients of lateral earth pressure at tunnel centerline during tunneling: (a) Kx; (b) Ky.
Tunnel
-2
Tail arriving Tail passing
-1 0 1 2 3 4 5 6 Normalized distance between tunnel face and monitoring section (Y/D)
7
Fig. 9. Development of settlement at the four monitoring points during tunneling.
Phase Ⅳ (0 < L < 2D) The vertical stress (σzz) gradually decreases in this stage. The horizontal stresses (σxx, σyy) continue to increase. At this time, EPBS is passing through the monitoring section. These inflection points in the σzz-depth curve gradually moves up since the volume loss increases, which implies the expansion of the loosened zone. Phase Ⅴ (L > 2D) The grouting zone passes through the monitoring section first, and then the lining segments are installed, and the σzz-depth curve only slightly changes. This shows that the loosened zone is not upward development. Final vertical stress distribution above the tunnel is similar to the result of Terzaghi’s plane strain condition. Meanwhile, the horizontal stresses (σxx, σyy) near the crown of tunnel undergo complicated variations before and after the shield tail passing due to the shield friction, grouting pressure and segments installation. The area above the inflection point is defined the zone Ⅰ (i.e. Arch zone), and the area between the inflection point and the tunnel crown is defined the zone Ⅱ (i.e. Loosened zone). The height of zones Ⅰ and Ⅱ is 1.27D and 0.73D, respectively. Fig. 6 presents variation of stresses (i.e σxx, σyy, σzz) at the four monitoring points (i.e. A, B, C and D) during tunneling. The locations of
the four points can be referred to Fig. 4. At the points A and B (see Fig. 6(a) and (b)), when the tunnel face approaches the monitoring section, σxx gradually increases, σyy decreases, and σzz remains constant. It shows that the horizontal soil arching occurs in the X-Y plane in the depth range of 0.67D below the ground surface. σyy is transferred to the soil mass on both sides of settlement trough via the horizontal soil arching (as shown in Fig. 13(a)), the stress-transfer mechanism of which is similar to that of arch dam in water conservancy projects. As the tunnel face continues to approach the monitoring section until the shield tail reaches it, σyy begins to increase and σxx continues to increase. Moreover, σxx is always greater than σyy. σzz slightly decreases at point B. This indicates that the vertical soil arching occurs in the Y-Z and X-Z planes (i.e. the horizontal soil arching gradually transforms into the vertical soil arching, as shown in Fig. 13(b)), and the soil arching effect in the X-Z plane is more obvious than that in the Y-Z plane. As the shield tail passes through the monitoring section, σxx and σzz almost keep constant, but σyy begins to decrease and finally stay constant. This shows that the earth pressure above the tunnel is finally mainly transferred by means of vertical soil arching in the X-Z plane, as 7
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0
0
-2
1
γs (10-3)
6.00
Ground surface
Ground surface
-4
0.67D
-6
0.67D L=-0.75D 0.58D
1-1 2-2 3-3 4-4
Tunnel
Monitoring section
-10 -12
2-2 3-3 4-4
EPBS
-8
1-1
Normalized depth (Z/D)
Settlement (mm)
5.47
Possible shear surface
3.89
3.36
3
2.30 1.78 1.25
5
0.72
-5 -4 -3 -2 -1 Normalized distance from tunnel centerline (X/D)
0.19
6
0
-0.34
-5
-4
Ground surface
Ground surface 0.67D
1-1 2-2 3-3 4-4
0.67D 0.58D
L=0
-25
1-1 2-2 3-3 4-4
Tunnel
EPBS
Monitoring section
-10
-5 -4 -3 -2 -1 Normalized distance from tunnel centerline (X/D)
0
-1
0
25
50
75
(kPa)
Initial self-weight stress X0=0 X1=-0.13D X2=-0.27D X3=-0.4D X4=-0.53D
-0.5
-1.0
zz
100 125 150 175 200 225 250
Ground X4
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0
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Fig. 11. (a) Shear strain contour at transversal section; (b) σzz-depth curves of the different distances from tunnel centerline.
1-1
0.67D
2-2
0.67D 0.58D
3-3 4-4 Tunnel
of horizontal stresses (σxx, σyy) at point C is the same as that of points A and B. Whereas the variations of the horizontal stresses (σxx, σyy) at point D are complex and are different from other points. σzz at point C and D sharply decreases when the tunnel face is −0.5D from the monitoring section. As a result of grouting pressure at the shield tail, σzz at point D steeply increases during the shield tail passing through the monitoring section. The stresses at points C and D keep constant after EPBS completely passing.
Ground surface Monitoring section L=3.25D
EPBS
-5 -4 -3 -2 -1 Normalized distance from tunnel centerline (X/D)
0
4.1.2. Variations of coefficients of lateral earth pressure (Kx, Ky) The coefficient of lateral earth pressure, K, is equal to the horizontal stress divided by corresponding the vertical stress (i. e. Kx = σxx/σzz; Ky = σyy/σzz). Therefore, the coefficient of lateral earth pressure at various excavation stages is calculated by adopting the data of Fig. 5, as shown in Fig. 6, where the coefficient of lateral earth pressure at rest is taken as K0 = 1 − sinφ = 1 − sin34° ≈ 0.44, and the active coefficient of lateral earth pressure is calculated using the formula as follows: Ka = tan2(45° − φ/2) = tan2(45° − 34°/2) ≈ 0.28. When L = −2.25D, the theoretical value of K0 is close to the value obtained from the numerical simulation (see Fig. 7). Similar to the horizontal stress, the coefficients of lateral earth pressure of soil above the tunnel
Fig. 10. Comparison between transverse settlement troughs of different depths at the monitoring section: (a) L = −0.75D; (b) L = 0; (c) L = 3.25D.
shown in Fig. 13(b). With the tunnel face approaching the monitoring section, σzz at points C and D increases and reaches the maximum when the tunnel face is about −1.25D and -D from the monitoring section, respectively. But σxx and σyy change little. As the tunnel face continues to approach the monitoring section until the shield tail reaches it, the change trend 8
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(a)
Z
Y
yy
xx
X
BS
EP
Arch zone Loosened zone
Tunnel
Fig. 12. Porosity ratio contour after tunnel excavation: (a) transversal section; (b) longitudinal section.
crown increase with EPBS tunneling, and the increment of Kx is larger than that of Ky. When L = −0.25D, Kx and Ky in the range of tunnel are increased and decreased, respectively. This is because σxx changes little (see Fig. 5(b)), but both σzz and σyy significantly decrease (see Fig. 5(a) and (c)), and the decrement of σyy is larger than that of σzz. After EPBS passing, the coefficients of lateral earth pressure along the depth above the tunnel crown are C-shaped distribution, and the maximum coefficient of lateral earth pressure appears near the ground surface. This is because, near the ground surface, the increased horizontal stresses coupled with the relatively unaffected vertical stress result in the maximum coefficients of lateral earth pressure.
(b) Fig. 13. Schematic diagram of three-dimensional soil arching zone: (a) horizontal soil arching near the ground surface; (b) vertical soil arching above EPBS and tunnel.
zone, and an important index to evaluate the influence of shield tunneling on surrounding environment. Fig. 9 shows development of settlement at the four monitoring points (i.e. A, B, C and D) during tunneling. The locations of the four points are depicted in Fig. 4. When the tunnel face is about −2.5D from the monitoring section, the four points begin to settle continuously. However, before the tunnel face reaches the position of about −0.75D from the monitoring section, the settlement rate of the point A is larger than that of other points, and the settlement rate decreases with the depth. The transverse settlement troughs corresponding to the depth locations of points A, B, C, and D are shown in Fig. 10. When the tunnel face is −2.5D from the monitoring section, the settlement of point A is largest, and that of point D is smallest (see Fig. 10(a)). As the tunnel face continues to approach the monitoring section, the settlement rates at the four points gradually increase, and point D increases the fastest, whereas points A, B and C are relatively close. At this time, the point D may be located in the loosened zone, whereas the points A, B and C may be located in the soil arching zone. When the tunnel face arrives at the monitoring section, the settlements of points A and D are larger than or
4.1.3. Variations of settlements at the monitoring section The inflection points in the σzz-depth curves are depicted in the corresponding settlement-depth curves, as shown in Fig. 8. It can be seen that the settlement of soil in zone Ⅰ is almost constant along the depth after the tunnel excavation. This indicates that the whole settlement occurs in soil mass of zone Ⅰ. However, the settlement of soil in zone Ⅱ sharply increases with the depth. This shows that soil mass in zone Ⅱ is in the loosened state due to the separation between soils. So it is reasonable that zone Ⅱ is called the loosened zone. It can be found from the above analysis that the soil in the zone Ⅱ may be in the limit state, while the shear strength of the soil in the zone Ⅰ may not be fully played. So the height of inflection point in the σzz-depth curves can be used as the boundary between the loosened zone and the soil arching 9
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Fig. 14. Development of arch zone and loosened zone during shield tunneling.
Ground surface
Normalized depth (Z/D)
0.0 -0.5
case1-1 case1-3 case1-5 case1-8
Arch zone
-1.0 -1.5 Loosened zone
-2.0 -2.5
Lining
-3.0 Fig. 15. Comparison of arch zone and loosened zone at different cross-sections during shield tunneling.
EPBS
Tunnel face
Grouting zone
-4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 Normalized distance from tunnel face (Y/D)
(a)
equal to those of points B and C (see Fig. 10(b)). During shield passing through the monitoring section, the settlements at four points continue to increase. When the grouting zone passes through the monitoring section, the increment of settlement at point D begins to decrease. However, the settlements of other points are less affected. When the tunnel face is 3.25D from the monitoring section, as shown in Figs. 9 and 10 (c), the settlement of point D is maximum. The settlements of points A, B and C are close.
Normalized height of loosened zone above tunnel crown (Z/D)
1.0
4.1.4. Soil arching zone The relative displacement between soil masses produces the shear stress. The load of the yielded soil is transferred to the adjacent parts by the shear stress. This load transfer mechanism is so-called the soil arching effect. The shear surface generally occurs where shear strains are large. One side of the shear surface is elastic soil which is defined as the stability zone. The other side is the yielded part which is defined as the arch zone. The contour of shear strain at transversal section after tunnel excavation is shown in Fig. 11(a). The maximum shear strain extends from the springline of the tunnel along inclined line to the ground surface, indicating that this area may form a shear surface, which is defined as the outer boundary of the soil arching. The lower boundary of the soil arching zone is determined by the inflection points of vertical stress at different positions of the cross-section, as shown in Fig. 11(b). The boundary where the horizontal stress increases by more than 5% is defined as the upper boundary of the arch zone. Fig. 12 shows the porosity ratio contours at the cross-section and longitudinal section after tunnel excavation. The upper, lower and outer boundaries of the soil arching are depicted in the porosity ratio contours. It can be seen that the porosity ratio of the soil arching zone and the stability zone are smaller than that of the other zone, indicating that these zones are compacted. The porosity ratio of the loosened zone increases. This shows that the soil swelling occurs in this zone. According to the above method of determining the soil arching
0.8 0.6 0.4 0.2 0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Surpport pressure (P1)
(b) Fig. 16. Distribution of soil arching zone and loosened zone above tunnel crown in longitudinal section with different support pressures; (b) variation of height of loosened zone with different support pressures.
zone, the schematic diagram of 3D soil arching zone is shown in Fig. 13. Meanwhile, the stress-transfer mechanism in soil arching zone previously revealed is also depicted in Fig. 13. To better present the evolution of soil arching zone during EPBS tunneling, three typical sections were selected before and after tunneling from Fig. 13, as shown in Fig. 14. It demonstrates that with EPBS tunneling, the loosened zone gradually expands upward, meanwhile, the arch zone also expands upward and outward (see Fig. 15). Finally, the loosened zone extends to nearly 0.73D above the tunnel crown in vertical direction and 0.33D 10
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Normalized depth (Z/D)
4.2.1. Effect of support pressure To study the effect of support pressure on the soil arching, seven numerical models were built with support pressures of 0.6P1, 1.0P1, 1.4P1, 1.8P1, 2.2P1, 2.6P1 and 3.6P1, respectively (see Table 4). The modeling procedure is the same as that presented in Section 2.2. Based on the height of inflection point in σzz-depth curve, the boundary between soil arching and loosened zones above the tunnel for cases 1–1, 1–3, 1–5 and 1–8 was determined, as shown in Fig. 16(a). It can be found that both the boundaries for cases 1–3 and 1–5 are almost identical during tunneling. This is because the limited increase of support pressure only affects the soil in the range of tunnel in front of the face, and the soil in this area is excavated in the next step. When the support pressure largely decreases or increases (e.g. cases 1–1 and 1–8), the support pressure not only affects the soil in the tunnel range, but affects the soil above the tunnel. Therefore, the boundaries for cases 1–1 and 1–8 are higher than those for cases 1–3 and 1–5. As presented in Fig. 16(b), when the support pressure increases from 0.6P1 to 2.2P1, the variation of loosened zone height is small (from 0.33D to 0.38D). However, when the support pressure is 0.2P1 or more than equal to 2.6P1, the loosened zone height sharply increases from about 0.3D to 0.7D.
Ground surface
0.0 -0.5
case 2-1 case 1-3 case 2-3
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-2.0 -2.5
Lining
-3.0
EPBS
Tunnel face
Grouting zone
-4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 Normalized distance from tunnel face (Y/D)
(a)
Normalized height of loosened zone above tunnel crown (Z/D)
1.0 0.8
4.2.2. Effect of grouting pressure To investigate the impact of grouting pressure on the soil arching, five numerical models were established with grouting pressures of 0.2P2, 0.6P2, 1.8P2, 2.7P2 and 3.6P2, respectively (see Table 4). According to the height of inflection point in σzz-depth curve, the boundary between soil arching and loosened zones above the tunnel for cases 2–1, 1–3 and 2–3 were determined, as presented in Fig. 17(a). It can be seen that the heights of loosened zone above EPBS for these three cases are the same. However, there are significant changes in these boundaries above the grouting zone. For the case 2–1, the height of loosened zone obviously increases after the grouting zone passing, but the height for the cases 1–3 and 2–3 slightly decreases. After the segment installed, the final height of loosened zone for the case 2–1 is about 0.52D higher than these of the cases 1–2 and 2–3. From the above analysis, we can see that small grouting pressure causes further upward expansion of the loosened zone, and then threatens the safety of surrounding underground existing structures. As shown in Fig. 17(b), the height of loosened zone decreases with the increase of the grouting pressure, and when the grouting pressure is more than 1.8P2, the height of loosened zone is little change. The height of loosened zone above the tunnel crown can be use as an important index to evaluate the influence of shield tunneling on the surrounding environment. From above analysis of shield-driving parameters, we can find that the proper combination of the parameters for controlling the expansion of the loosened zone is support pressure of 0.6P1 − 2.2P1 and grouting pressure of 1.0P2 − 1.8P2.
0.6 0.4 0.2 0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Grouting pressure (P2)
(b) Fig. 17. (a) Distribution of soil arching zone and loosened zone above tunnel crown in longitudinal section with different grouting pressures; (b) variation of height of loosened zone with different grouting pressures.
beyond the tunnel springline in horizontal direction. The height of the arch zone is about 1.27D above the loosened zone in vertical direction and the width is about D beyond the loosened zone in horizontal direction. The determinations of the soil arching zone and the loosened zone are helpful to understand the influences of tunnel excavation on surrounding existing structures. For example, for the project of the new tunnel construction beneath the existing structures (e.g., pipeline and tunnel) (Wang et al., 2011; Ng et al., 2013; Li et al., 2016; Chen et al., 2018a; Lin et al., 2019), if the vertical distance between them is less than the height of the loosened zone caused by the new tunnel excavation, induced stress and settlement of the existing structures due to the new tunnel excavation may exceed the design allowable value and even cause the concrete to crack. Reinforcement measures to prevent the upward expansion of the loosened zone may be effective.
5. Conclusions In this paper, a three-dimensional numerical finite element model validated by a case history has been used to analyze the stress redistribution and the soil arching evolution induced by EPBS tunneling. Based on the calculated results, the following conclusions may be drawn: (1) The boundary between the soil arching zone and the loosened zone is determined by the inflection points of σzz-depth curves. The height changes of the inflection points during tunneling reflect the expansion of the loosened zone, which can be used as an important index to evaluate the influence of shield tunneling on the surrounding environment. (2) For case 1–1 with support pressure of 0.2P1 and grouting pressure of 1.0P2 (P1 = initial horizontal stress at the tunnel axis and P2 = 1.2P1), with EPBS tunneling, the loosened zone gradually
4.2. Influence of shield-driving parameters on evolution of soil arching The evolution of soil arching is closely related to the changes of stress field and displacement field of soil mass. The soil around the tunnel can be easily disturbed in shield tunneling (Meng et al., 2018). Therefore, the influence of shield-driving parameters (i.e. support pressure, grouting pressure) on the soil arching is investigated as follows. 11
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expands upward, meanwhile, the arch zone also expands upward and outward. Finally, the loosened zone extends to nearly 0.73D above the tunnel crown in vertical direction and 0.33D beyond the tunnel springline in horizontal direction. The height of the arch zone is about 1.27D above the loosened zone in vertical direction and the width is about D beyond the loosened zone in horizontal direction. (3) Three-dimensional stress-transfer mechanism in soil arching zone above tunnel during tunneling is demonstrated. The horizontal soil arching in front of EPBS occurs in the X-Y plane in the depth range of about 0.67D below the ground surface. Then, the horizontal soil arching gradually transforms into the vertical soil arching with EPBS driving, and the vertical soil arching effect in the X-Z plane is more obvious than that in the Y-Z plane. After EPBS passes, the earth pressure is finally mainly transferred via vertical soil arching in the X-Z plane, which is similar to the result of Terzaghi’s plane strain condition. (4) The coefficient of lateral earth pressure above the tunnel crown increases with EPBS tunneling, and the increment of Kx is larger than that of Ky. After EPBS passes, the coefficient of lateral earth pressure along the depth above the tunnel crown is C-shaped distribution, and the maximum coefficient of lateral earth pressure appears near the ground surface. (5) The limited increase of support pressure only affects the soil in the tunnel range in front of the face. The excessively high or low support pressure not only affects the soil in the range of tunnel, but affects the soil above the tunnel. There are significant changes in the height of loosened zone above the grouting zone for different grouting pressures. With the increase of grouting pressure, the height of loosened zone decreases. The proper combination of shield-driving parameters for controlling the expansion of the loosened zone is support pressure of 0.6P1 − 2.2P1 and grouting pressure of 1.0P2 − 1.8P2.
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