The Influence of Tunnel Construction with Dynamically Changing Soil Mechanics Parameters on Soil Disturbance

Zhe Liu, Ping He* , Anqi Zhang, Xiuying Wang, Jinhua Wang

Tunneling and Underground Engineering Research Center of Ministry of Education, Beijing Jiaotong University, Beijing, 100044, China *Corresponding author. e-mail: [email protected].

ABSTRACT In this paper, we deduced the relationship of the soil void ratio and the volumetric strain of soil, based on the three phases of soil system and the division of soil area disturbed by tunnel construction. We studied the change of disturbed soil mechanics parameters during tunnel excavation by calculating volumetric strain at different regions of soil using finite element analysis as well as using the relationship of soil mechanics parameters and void ratio as reference. The results indicated that: In the case of the large deformation at the top of the tunnel, the ground subsidence is larger considering the changing of soil mechanics parameters. The influence is greater in the area above the tunnel. The plastic range of disturbed soil increased significantly considering the dynamic changes of soil mechanics parameters, moreover.

KEYWORDS: tunnel excavation; soil mechanics parameters; ground deformation; strength

criteria; plastic region

INTRODUCTION

The settlement of formations will cause adverse effect on existing structures around the tunnel, while, tunnel excavation has great influence on the settlement of formations. Domestic and foreign scholars have done a lot of research on the deformation of formations by tunnel excavation. The calculation methods include empirical, analytical and finite element method. In empirical method study, Peck [1] proposed empirical formula to predict surface subsidence according to the observed data. Sagaseta [2] proposed the principles of mirror law which deduced elastic analytical solutions. The analytical solutions give the results of the displacement and stress distribution of shallow tunnel, however, the results are based on the single material. Verruijt and Booker [3] popularized the solution based on the principles of mirror law. Baochen [4], Yang Jun-sheng [5] made a lot of achievements

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Vol. 20 [2015], Bund. 14 6398 with the methods of stochastic medium theory in the field of ground displacement caused by tunnel excavation. However, these studies are based on the condition that the mechanics parameters of soil remain constant when tunnel is excavating. As a matter of fact, the change of the mechanics parameters of soil has a great deal of influence on the nearer structures which cannot be ignored. In particular, in the case of large ground displacement where the change of the mechanics parameters of soil is obvious, if the changes are ignored, the result will deviate sharply from the true. Some scholars have done much researches on soil mechanics induced by construction disturbance through field and laboratory tests. Yi Hongwei [6], Xu Yongfu [7] did research on the disturbance mechanism in the soft clay caused by shield construction, and used the index of penetration resistance and pore water pressure in field-teste to validate their research is feasible and effective. Zhang meng xi[8] take loess into account, focused the change of soil stress , strain state, water content and void ratio when tunnel is excavating. In the paper, the volumetric strain of disturbed soil is obtained by finite element method, and then through the three-phase relationship can the contact between the volumetric strain and void ration be established. With the assistance of relationship between void ration and the mechanics parameters, the relationship between the volumetric strain and the mechanics parameters can be obtained. Thus, the volumetric strain as a bridge makes using finite element method to consider how the mechanics parameters change caused by tunnel excavation influence the scope of plastic zone, strength of disturbed soil and ground displacement possible.

THEORETICAL ANALYSIS

The relationship between the soil void ration and volumetric

strain

[9] According to Loganathan ’s study, the influence zone of tunnel excavation is mainly from hance oblique upward 45 degree. The area above the tunnel center line is divide into A,B,C three zones based on different influence degree(as shown in Fig 1).Assume that tunnel is buried in the k layers(as shown in Fig 2). According to the three-phase system of soil, total volume of soil v , pore volumev and soil particle volumev relationship: v

s = + （1）

Pore volume of soil includes the volume of𝑣𝑣 pore𝑣𝑣𝑣𝑣 water𝑣𝑣𝑠𝑠 and pore gas. Compared with gas, water can be considered to be incompressible. So the change of pore water volume is namely the pore volume 𝑣𝑣𝑣𝑣 changes. Vol. 20 [2015], Bund. 14 6399

Taking the j layer soil as the research object, before the excavation of tunnel, soil particle volume of is , pore volume is , void ratio is , and after excavation, soil particle volume of is , pore ′ volume𝑠𝑠𝑠𝑠 is , void ratio𝑣𝑣 𝑣𝑣is . 𝑗𝑗 s𝑗𝑗 𝑣𝑣 ′ 𝑣𝑣 ′ 𝑒𝑒 𝑣𝑣 𝑣𝑣𝑣𝑣𝑗𝑗 𝑒𝑒𝑗𝑗

Figure 1: Partition schematic diagram of disturbed soil

Figure 2: Tunnel in the No. k soil layer

The relationship between these variables is:

= / （2）

𝑗𝑗 𝑣𝑣𝑣𝑣 𝑠𝑠𝑠𝑠 𝑒𝑒 =𝑣𝑣 /𝑣𝑣 （3） ′ ′ ′ 𝑗𝑗 𝑣𝑣𝑗𝑗 s𝑗𝑗 Then the volumetric strain is: 𝑒𝑒 𝑣𝑣 𝑣𝑣

= ′ = ′ ′ （4） 𝑣𝑣𝑗𝑗−𝑣𝑣𝑗𝑗 �𝑣𝑣𝑣𝑣𝑣𝑣+𝑣𝑣s𝑗𝑗�−�𝑣𝑣𝑣𝑣𝑣𝑣+𝑣𝑣𝑠𝑠𝑠𝑠� 𝜀𝜀𝑗𝑗 𝑣𝑣𝑗𝑗 �𝑣𝑣𝑣𝑣𝑣𝑣+𝑣𝑣𝑠𝑠𝑗𝑗� At the same time, the change of soil particle volume is ignored, then

= （5） ′ 𝑣𝑣𝑠𝑠𝑠𝑠 𝑣𝑣s𝑗𝑗

= ′ （6） 𝑣𝑣𝑣𝑣𝑣𝑣−𝑣𝑣𝑣𝑣𝑣𝑣 𝜀𝜀𝑗𝑗 𝑣𝑣𝑣𝑣𝑣𝑣+𝑣𝑣𝑠𝑠𝑠𝑠 the contact between the volumetric strain and void ration is:

= 1 + + （7） ′ 𝑒𝑒𝑗𝑗 � 𝜀𝜀𝑗𝑗�𝑒𝑒𝑗𝑗 𝜀𝜀𝑗𝑗 Vol. 20 [2015], Bund. 14 6400

Strength criterion

Grainy character, three-phase system and natural variability are the three features of soil as a special material. It also determines the completely different properties between soil material and other materials including metal, concrete. Strength theory of soil represented by stress state combination can reveal the failure mechanism of soil theory. Strength theory in general can be expressed as:

f , k = 0 （8）

ij i In which represent stress tensor, represent�σ strength� parameter.

Mohr𝜎𝜎-𝑖𝑖 𝑖𝑖Coulomb and Drucker-𝑘𝑘Prager𝑖𝑖 strength criterion which have simple and clear model parameters are chosen as basis to analyze the plastic zone by tunnel excavating. The Mathematical expressions of Mohr- Coulomb and Drucker-Prager criterion can be written as formula(9)and(10):

( , , ) = sin + sin + + cos + sin cos = 0 (0° 60°) （9） 1 𝜋𝜋 �𝐽𝐽2 𝜋𝜋 1 1 2 1 2 𝑓𝑓 𝐼𝐼 𝐽𝐽 𝜃𝜃 3 𝐼𝐼 𝜑𝜑 �𝐽𝐽 �𝜃𝜃 3(� , √)3 = �𝜃𝜃+ 3� 𝜑𝜑=−0𝑐𝑐 𝜑𝜑 ≤ 𝜃𝜃 ≤ （10）

2 1 2 1 2 In which and k are material constants.𝑓𝑓 𝐼𝐼 𝐽𝐽 𝛼𝛼𝐼𝐼 �𝐽𝐽 − 𝑘𝑘

The mainα mechanical parameters of Mohr-Coulomb criterion are soil cohesion c and internal friction angle φ. Select Drucker-Prager round and Mohr-Coulomb hexagonal contacted by the external position in principal stress space. Then the relationship between , and c、 can be express by:

𝛼𝛼 𝑘𝑘 𝜑𝜑 = ， = （） ( ) ( ) 11 2 sin 𝜑𝜑 6𝑐𝑐 cos 𝜑𝜑 𝛼𝛼 √3 3−sin 𝜑𝜑 𝑘𝑘 √3 3−sin 𝜑𝜑 The relationship between soil void ration and the strength index

of soil cohesion and friction angle

The shear strength of soil is influenced by a lot of factors, such as the property of soil, the existence state of soil, the stress condition of soil and theory of strength .Some scholars have studied the relationship between the dry density of the soil and the strength index of soil -cohesion and friction angle by adopting the method of experiment, for example ChengRen Xiong, Jindang and Zhen Li have researched this relationship existing in Silt soil, silty clay and sand and gravel,respectively. According to the conversion formula between dry density and void ratio:

= 1 （12） 𝜌𝜌𝑠𝑠 𝑒𝑒 𝜌𝜌𝑑𝑑 − The relationship between soil void ratio and the strength index of soil can be obtained. As shown in Figure 3-5. Vol. 20 [2015], Bund. 14 6401

Figure 3: The relationship about void ratio,cohesion and friction angle in filling silt

Figure 4: The relationship about void ratio,cohesion and friction angle in clay

Figure 5: The relationship about void ratio,cohesion and friction angle in sand and gravel

Soil void ratio and volumetric strain can also establish relationalship, so as long as the relationship between void ratio and the strength index of soil-cohesion and friction angle be established, the soil cohesion and friction angle changes by computing the volumetric strain of soil which was induced by the excavation of tunnel can be obtained. Vol. 20 [2015], Bund. 14 6402

FEM CALCULATION

Engineering background

A certain shield tunnel was selected as the study object. From the surface of the earth top of the tunnel, the geological structure includes a 2.8m silt soil layer, a 9.6m clay layer and a 10.45m sand pebble layer. The base of the tunnel is sand pebble.

Table 1: The basic physical and mechanical index of foundation soil Soil Initial Soil Density Initial thick Initial

layer /kg·m-3 (°) (M𝐸𝐸pa) -ness e (kPa𝑐𝑐 ) 𝜑𝜑 (m) Silt 1650 38 6.1 6.1 2.8 0.88 Clay 1950 97 26.2 10 9.6 0.66 Sand 2050 10.1 45.3 46 10.4 0.47 Pebble 2100 0 47 78 17.2 0.43 Concrete 2.76 2000 — — — — Lining 10 4 ∗ Each layer of soil lithology characteristics are detailed in Table 1.Tunnel exists in the third layer- 10.45m sand pebble layer. The buried depth of the tunnel is16m,diameter is 6m. The maximum depth of drilling exploration is 50.0m, and there is underground water in the earth. The distribution of groundwater in the gravel layer, the still water depth is about 24.70m ~ 26.60m. Tunnel is above the phreatic water.

Model establishment and result analysis

Infinite element model is established on the above engineering background. The tunnel lining is 30cm.To eliminate the influence of boundary effect, the height of the model is 40m,the width is 50m, and the length of the direction along the tunnel is 36m. The calculation starts from simulating the condition of sinking at the top of the tunnel, from which we decide the sinking range of the earth’s surface and the plastic zone’s range around the tunnel, in which the geo-mechanics parameter is considered constant. After simulation calculation of tunnel digging, we extract the volumetric strain of finite elements, and apply them into the formula (7). Then we get the pore ratio of the soil in different areas, then through the comparing diagrams 3~5, we get the cohesive strength and friction of the soil in different areas, then do simulation calculation with the changed geo-mechanics parameter. This process is kept cycling till the differences of the volumetric strain of finite elements dependent viable and geo-mechanics parameters between the Nth recycle and Vol. 20 [2015], Bund. 14 6403 the (N+1)th recycle are all less than 5%.Finally, we concluded the calculation result of volumetric strain in Table 2,and the geo-mechanics parameter in different layers and different areas in Table 3.

Table 2: Changes in the value of soil volumetric strain due to tunnel excavation soil layer Area volumetric strain (10 ) −2 A 1.9 First B 0.33 C 0.07 A 6.44 Second B 1.1 C 0.22 A 2.8 Third B 0.48 C 0.1

Table 3: Changes in the value of soil mechanics parameters due to tunnel excavation Initial parameters Final parameters soil layer Area c(kPa) (°) c(kPa) (°) A 24.5 7.99 φ φ First B 38 6.1 35.6 6.43 C 37.4 6.17 A 75.6 24.54 Second B 97 26.2 93.3 25.92 C 96.2 26.14 A 9.28 42.6 Third B 10.1 45.3 9.96 44.92 C 10.06 45.22

Analysis of the ground surface settlement

Whether considering the change of the soil permanent can influence the ground surface settlement induced by the excavation of tunnel. The influence is shown in Figure 6. The max ground surface settlement is 8.1% bigger if the soil permanent is considered varying than constant,. So if we adopt constant parameter, we will underestimate the ground surface settlement induced by the excavation of tunnel.

The analysis of the plastic zone scope by excavation disturbance

The surrounding soil will have plastic failure when tunnel is excavated. Cohesion and friction angle of the soil directly determine the strength of the soil, and thus determine the plastic zone distribution induced by tunnel excavation. Because the tunnel exists in the third layer, plastic zone mainly exists in the third layer. So the third layer is the research object. Vol. 20 [2015], Bund. 14 6404

Figure 6: The earth's surface subsidence affected by constant and changing mechanical parameters

Figure 7: The plastic zone range under the conditions that disturbed soil mechanics parameters remain constantly

Figure 8: Comparison of the plastic zone range (The dotted line represents the case that disturbed soil mechanics parameters remain constantly, the solid line represents the case that disturbed soil mechanics parameters keeps changing during excavating.)

When f (I , J ) 0， the soil gets into plastic state. As a result, the soil inside the dotted-line zone starts to show yield failure because of the disturbance by tunnel digging. In order to compare the 2 1 2 ≥ distribution areas of plastic zones under these two conditions more clearly, plastic zones under two situations are plotted in Figure 8. Through “The number of lattice method”, we can see clearly that the area of plastic zone that geo-mechanics parameter considered varying is 55.6% larger than the area that the geo-mechanics parameter is considered constant during the digging of the tunnel. In the plastic zone located at the top of the tunnel, the length of the upper boundary increases apparently. So, if the cohesive strength and the friction of the soil during the digging of the tunnel are constant, we will under estimate the plastic degree and range of the soil resulted from the disturbing of digging. As a result, it Vol. 20 [2015], Bund. 14 6405 will pose unpredictable risks to the structure of the tunnel as well as the safety of the nearby architectures.

CONCLUSION

(1) By analyzing the parameter of the different influential zones after the excavation of the tunnel, we find that cohesion and friction angle both decreases to some extent. The bigger the crown settlement is, the more significant the soil parameter changes. Besides, the zone that soil parameter changes most significantly is directly above the tunnel. So we should pay close attention to the dynamic change of this zone’s parameter when the tunnel is excavating. (2) When the ground surface settlement is big,if we ignore the change of the parameter of the soil induced by tunnel excavation, the result will be obviously smaller than real situation. (3) The strength of the surrounding soil decrease when tunnel is excavating, thus the disturbed soil produce plastic fail more easily. Stress redistribution of surrounding soil caused by excavation, can reduce the carrying capacity of the soil. So it is essential to take the dynamic change of the surrounding soil when tunnel is excavating into consideration. Then we can adopt grouting method to reinforce the disturbed zone and thus guarantee the safety of the tunnel and adjacent buildings.

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