Geotech Geol Eng DOI 10.1007/s10706-017-0312-y
ORIGINAL PAPER
Prediction of Large Deformation Behavior in Tunnels Based on AHP–FUZZY Method and Numerical Simulation Method Jian-bo Xu . Jian-ping Chen . Shuang-lan Wu . Yi-heng Pan . Wei Wang . Qi-qi Luo
Received: 22 February 2017 / Accepted: 19 July 2017 Springer International Publishing AG 2017
Abstract In this paper, two different research methods are applied to predict large deformation behavior in tunnels and take Tianjiashan tunnel as the case study which is located in Xindianping town, Zhejiang city, Hunan province. The paper introduces the basic principle of the analytic hierarchy process and the fuzzy mathematics method, and classifies the influence factors of the large deformation in tunnels into eight kinds (C1–C8). Basing on the AHP–FUZZY method, this paper applies the results into the large deformation prediction analysis of Tianjiashan tunnel. In order to verify the accuracy of the evaluation results of AHP–FUZZY method, a numerical simulation model of DK394 ? 625–DK394 ? 650 section of Tianjiashan tunnel is established. The results show that the tunnel deformation is very large, and the tunnel excavation is sure to cause large deformation. The numerical simulation result is in accordance with the AHP–FUZZY method. Finally, we track record of occurrence of large deformation during the actual construction in tunnel, and the actual results are coincide with AHP–FUZZY method and numerical simulation results, which reflects the effectiveness of J. Xu J. Chen (&) Y. Pan W. Wang Q. Luo Faculty of Engineering, China University of Geosciences, Wuhan 430074, China e-mail:
[email protected] S. Wu Faculty of Engineering, Kyoto University, Kyoto 606-8501, Japan
AHP–FUZZY method and numerical simulation method in predicting the large deformation behavior in tunnels. Keywords Large deformation Influence factors AHP–FUZZY method Numerical simulation method
1 Introduction Since the beginning of the twentieth century, many scholars had made extensive research on large deformation in formation mechanism theory, prediction methods, prevention and control measures and many other aspects (Morrison 1948; Brady 1977). In terms of the large deformation of surrounding rock in underground engineering, there is not a uniform and clear definition yet. Many researchers (Xu and Huang 2000) focus on a certain type of large deformation, such as soft rock, swelling rock, deep soft rock, squeezed soft rock deformation. As for the aspect of large deformation in highway tunnel, generally it could be described as a kind of coupling of water and force process, in which priority is given to extrusion, complementary to expansion (Bhasin 1995). The prediction of large deformation of surrounding rock is the most important content of the study of large deformation. Although the research has accumulated some research results (Aydan et al. 1993), however, this research is still the weakest link in the field of large deformation research.
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There are two main categorises of prediction methods of deformation: extrusion and expansion prediction. Muirwood used the robustness factor to predict the stability of surrounding rock (Muirwood 1972). Saari uses the tangential strain index to predict and judge the tunnel rock mass extrusion deformation. Animoto put forward the elastic–plastic solution to estimate the strain of surrounding rock. Nydan uses tangential relative strain values to predict a potential extrusion trend in the surrounding rock (Kimura et al. 1987). Anognostou combined with previous studies of several scholars summed up a more comprehensive model for the prediction of the trend of the expansion of rock and structural simulation. Although previous studies have accumulated some achievements, the prediction of large deformation is still the weakest link in the field of large deformation research, and its use in the design and construction has a great limitation (Yoshinaka et al. 1992, 1998; Lunardi 1990, 2008; Yano et al. 1978). The AHP–FUZZY method is a multi-criteria decision making technique, in combination with multiple factors and indexes (Yang and Wu 2005). AHP– FUZZY comprehensive evaluation prediction method for large deformation is organic combination of analytic hierarchy method and fuzzy mathematical evaluation method, which was employed to analyze and make a classification evaluation on its influence factors and its relationship between them. Even it constructed the hierarchical structure of the interaction between various influencing factors model. Thus, it was a multi-criteria decision making technique, in combination with multiple factors and indexes. AHP– FUZZY comprehensive evaluation has considered the various influence factors of large deformation, and it avoids the limitations brought by the criterion only consider a few factors. At the same time through hierarchy analysis method, more objectively influence degree of various factors affecting the value were given, to some extend it largely improved the reliability of large deformation comprehensive forecast evaluation. In 2007, Zhu Jin made use of fuzzy comprehensive evaluation method to study the rock breakage and water cut. Whereas the established model was relatively simple, fewer evaluation factors had been obtained. In 2009, as the fuzzy neural network technology was employed to establish a comprehensive geological forecast model, mainly aimed at the prediction on fault in the dissertation, karst caves, and rich hose area, etc. (Meng 2009).
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In the past century, the numerical calculation methods of rock mechanics have been developed rapidly, such as finite difference method, finite element method, boundary element method and discrete element method. The finite difference method is first finite differencing the partial differential equations of describing objective function, and then solved by the finite difference equations instead of partial differential equations (Xu 1982). This method is simple and intuitive, and it is often used in the fields of hydrodynamics, heat exchange and solid mechanics. The difference grid of the traditional difference method is regular, and it is not suitable for simulating the actual rock mechanics problem because of its defect in the treatment of the joints, complex boundary and heterogeneous material in rock mass. In order to overcome the limitation of the traditional finite difference method (Perrone and Kao 1975). Brighi et al. (1998) proposed a generalized finite difference method based on the triangular grid technique. Lizzka and Orkisz (1980) further used the finite difference method of any irregular grid to calculate and analyze. Although a lot of research have been done in large deformation prediction, rarely there are studies on prediction of large deformation behavior in tunnels based on AHP–FUZZY method and 3-D numerical simulation method. In this paper, AHP–FUZZY method is used to predict large deformation behavior in tunnels and 3-D numerical simulation method is used to verify the accuracy of the results of AHP– FUZZY method.
2 Engineering Profile Tianjiashan tunnel, located in Xindianping town, Zhejiang city, in Hunan province, is one of the important engineering in the study section. Its beginning-ending mileage was DK394 ? 235– DK394 ? 778, with 543 m long. It character with shallow buried and bias, and the maximum buried depth was about 50.4 m, with the design speed of 350 km/h. The covering soil layer was quaternary Holocene residual layer (Qelþdl ), underlying bedrock was the 4 lower cretaceous (K1), sandy mudstone, argillaceous sandstone, which were easily softening and disintegration under the influence of water, thus its project performance was poor. The rock formations were monoclinal structure, the attitude of the rock was
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136–160\17–21. Also the rock mass was high weathering and fissure developing.
3 AHP–FUZZY Method and Analysis 3.1 AHP–FUZZY Method 3.1.1 AHP Analysis Method Analytic hierarchy process (AHP) is recommended by T. L. Satty. Based on the theory of network system, it is a hierarchy weighting multi-objective comprehensive evaluation decision analysis method. It is combined quantitative analysis with qualitative analysis, and it is used for multi-objective decision-making and evaluation on the complex problems. Based on fuzzy comprehensive evaluation, a four step procedure is applied: Step 1
Establish AHP structure model.
Step 2
Establish the comparative judgment matrix.
Step 3 Calculate the element relative weights following the single criterion and its consistency check. Step 4 Calculate the element relative weights following the total criterion and its consistency check. 3.1.2 FUZZY Method As for the FUZZY method, the influencing factors assemble U, and the corresponding level assemble V were required firstly. Where the U, its every single factor is corresponded to the V, of its corresponding single criterion fuzzy matrix R, and then according to its degree of each factor to its total assembles, the weight matrix A is obtained. At last, it conducts the fuzzy exchanging from R to A, and then the goal judgment matrix of B can be obtained from Eq. (2) (Zhang et al. 1988; Chen and Lu 2008). The fuzzy decision-making process is basically following steps: Step 1 Establish the factors assemble U, namely, U = {u1, u2, u3, …, un}. Step 2 Establish evaluation matrix V, namely V = {v1, v2, v3, …, vn}. Step 3 The single evaluation f: U ? g(V), namely, ui| ? f(ui|)(vi) = rij.
The fuzzy matrix Eq. (1): 2 r11 r12 6 r21 r22 R¼6 4 rn1 rn2
R is obtained following the 3 r1m r2m 7 7 5 rnm
ð1Þ
R is also called the single factor evaluation matrix. The goal evaluation assemble B is calculated by the Eq. (2): B¼AR
ð2Þ
where the B = [B1, B2, …, Bn], among which, the Bn denotes the sorting weight vector with regard to constraints of nth, and the max value of Bi, corresponding to its level, is conceded to the final evaluation level. 3.1.3 AHP–FUZZY Comprehensive Method To conduct the AHP–FUZZY comprehensive analysis, first of all, it is very important to determine the weight of each two factors of all levels. According to the subordinate relations approved by evaluation index system, degree of important factor was presented using fuzzy pairwise comparisons, based on the expert responses to questionnaires. Coupled with 1–9 scale referred by Saaty (1980), as illustrated in Table 1, an evaluation matrix of each level factor is established. Note that the judgment matrix of 1–2 order are complete consistent; when the order is more than 2, if CR B 0.10, the consistency of judgment matrix is acceptable, otherwise it demands to modify the judgment matrix to meet the requirement. The elaborated comprehensive evaluation process of AHP–FUZZY is given in Fig. 1. 3.2 The Large Deformation Influencing Data Layers The influencing factors can be summarized into three aspects: lithology condition, in situ stress condition and surrounding rock condition. 3.2.1 Lithologic Condition As lithology condition is one of the basic condition leading to large deformation, it can be determined by its rock strength, Young’s modulus of rock and rock
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Geotech Geol Eng Table 1 Meaning of 1–9 scales
Scale
Meaning
1
i is exactly the same important, or i or j compare to itself
3
i slightly more important than j
5
i obviously more important than j
7
i much more important than j
9
i extraordinary more important than j
2, 4, 6, 8
Scales between two above
Reciprocal
Contrary to above condition, namely j more important than i
Evaluation index and factors FUZZY
AHP
Quantitative evaluation index
Establish structure model
Determine of evaluation level
Establish the judgment matrix
Determine the membership function
Single sort and consistency check
Calculate each factor membership
Total sorts and consistency check
Establish the fuzzy matrix
Determine the weights of each factors
AHP-FUZZY comprehensive evaluation
Fig. 1 Comprehensive evaluation process of AHP–FUZZY
swelling. And as following the rules, the lower the rock compressive strength and elastic modulus were, the more possibility of plastic flow increases, and the more likely they were lead to large deformation.
higher the initial geostress value was, the greater the strength of large deformation may occur.
3.2.2 The in situ stress condition
Rock mass structure was the most influential factor to the formation of large deformation. It was far much easier to see large deformation under the conditions of broken rock mass and high geostress.
High in situ stress is one of the basic condition for large deformation, it can be clearly seen that, the
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3.2.3 The surrounding rock condition
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Groundwater was also one of the necessary factors causing large deformation. As the underwater could soften the rock and rock mass, and reducing in rock mass strength largely, and accelerating the deformation of rock mass. Also, the rock mass class was a comprehensive indicator reflects the geological condition of surrounding rock, and the large deformation can easily be seen in poor and adversity geological conditions, mostly in IV, V and VI level. Through the application of analytic hierarchy process (AHP) to the analysis on various factors influencing the large deformation, it set up the hierarchical structure model, which was shown in Fig. 2, as it can be seen clearly, it total treated the large deformation prediction as the total goal, and the conditions which ranking the first level was lithologic condition for B1, the geostress for B2 and rock mass surrounding conditions for B3. And the secondary indicators were contained with the following eight aspects: the rock compressive strength, elastic modulus and rock swelling ration, the initial major principal stress, the ration of strength to stress, the rock mass structure, the groundwater and rock mass class. According to the above eight indexes for different performance characteristics of large deformation level, and in combination with the large deformation of surrounding rock tunnel classification standard which was put forwarded by Liu et al. (2008), a large deformation comprehensive classification standard is established, as it can be seen in Table 2. It can be seen clearly that, level of large deformation is divided into four types, namely no big deformation, slight
deformation (ranking I), medium large deformation (ranking II) and fierce large deformation (ranking III) strongly. 3.3 Consistency Check Based on the AHP structure model of rockburst intensity, and in combination with the 1–9 scale referred, the degree of important factor was presented using fuzzy pairwise comparisons, namely, the weighing value of B1–B3, C1–C8 were obtained. At last, four judgment matrixes, A–B, B1–C, B2–C and B3–C were calculated. Among which, the concordance index of matrix A–B was CR = 0.0176, and anther three concordance index of matrixes of B1–C, B2–C and B3–C were 0.0516, 0.000 and 0.0516, respectively. As all R B 0.10, the consistency of judgment matrix was acceptable accordingly. And the layout result related to software Yaahp was given by Fig. 3. 3.4 The Element Relative Weights Rely on the results of consistency check, it further calculated the ranking weighing of A–B, B–C following the single criterion, and its total order weight, as illustrated in Table 3. 3.5 The Determination on Membership Function In the large deformation of fuzzy comprehensive evaluation, according to the basic principles of establishing membership degree, the evaluation indexes were divided into two ways for calculation. The first category of evaluation index was the
Large deformation prediction A
Lithoogy B1
rock uniaxial compressive strength C1
Rock elastic modulus C2
Geo-stress condition B2
rock swelling ration C3
Initial geo-stress C4
ration of strength to geostress C5
Surrounding rock condition B3
Rock macc structure C6
Groundwater C7
Rock mass class C8
Fig. 2 AHP structure model of large deformation intensity
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Geotech Geol Eng Table 2 Large deformation comprehensive classification standard Classification indexes
No
Slight (I)
Medium (II)
Fierce (III)
Lithologic condition The uniaxial compressive stress (MPa)
[30
15–30
5–15
\5
Young’s modulus of rock (MPa) Rock swelling ration (%)
[2000 \40
2000–1500 40–65
1500–1000 65–90
\1000 [90
In situ stress conditions The major principal stress (MPa)
\20
20–30
30–45
[45
The ration of strength to geostress
[0.5
0.5–0.25
0.25–0.15
\0.15
Surrounding rock conditions Rock mass structure
–
Mosaic cataclastic structure
Cataclastic structure
Loose structure
Groundwater
–
Dry–moist
Moist–seepage
Seepage–drip
Rock mass class
–
IV–V
V–VI
VI
Table 3 Weights of large deformation factors in total sorts B–C ranking
Total order weight x
A–B ranking B1 0.387
B2 0.443
B3 0.170
C1
0.528
0.000
0.000
0.2045
C2
0.139
0.000
0.000
0.0541
C3
0.333
0.333
0.000
0.1288
C4
0.000
0.667
0.000
0.1478
C5
0.000
0.000
0.000
0.2956
C6
0.000
0.000
0.168
0.0331
C7 C8
0.000 0.000
0.000 0.000
0.483 0.349
0.0835 0.0525
From the results above, the weigh matrix was A [0.204, 0.0541, 0.1288, 0.1478, 0.2956, 0.0331, 0.0835, 0.0525] Fig. 3 Output results of judgment matrix
qualitative factors, which meant that the qualitative indexes were described in words (e.g., rock mass structure, rock mass). As for its discrimination of index, the membership function was using the characteristic function. That is: 1 u ¼ ui ði ¼ 1; 2; . . .; 8Þ uðxÞ ¼ ð3Þ 0 u 6¼ ui ði ¼ 1; 2; . . .; 8Þ The second one was quantitative indexes. According to the definition of each level range, a fuzzy set was applied, and a major contribution of fuzzy set theory was its capability of representing vague data. The theory also allowed mathematical operators and
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programming to apply to the fuzzy domain. A fuzzy set was a class if the objects with a continuum of grades of membership. Such a set was characterized by a membership (characteristic) function, which assigned to each object a grade if membership ranging between zero and one, and its membership degree distribution graphics as can be seen in Fig. 4. Also, each index can be calculated by the formulas from 4 to 7. As for the small evaluation index (near the threshold value), it took the down half trapezoid distribution. And as for the great evaluation index (near maximum limit value), it took up half a trapezoidal distribution, while, in terms of the evaluation index for intermediate values, it took the trapezoidal distribution. And
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3.6 The Large Deformation Prediction Results
Fig. 4 The distribution of membership function
there was a principle that each level threshold middle 1/3 value range of the grade of membership for ‘‘one’’. When the evaluation index grade was reversed with size relations, it can just put the rating according to the analysis in the opposite direction. 8 1 > > > 2a þ a 3x > < 1 2 u1 ðxÞ ¼ a2 a1 > > > > :0
x a1 1 a1 x a1 þ ða2 a1 Þ 3 1 x a1 þ ða2 a1 Þ 3
4 Numerical Simulation Analysis ð4Þ
8 0 > > > > 2a2 þa3 3x > > > > 1 a3 a1 > > > > < u2 ðxÞ ¼ 1 > > 2a2 þa3 3x > > > > > a3 a1 > > > > > : 0
xa1 1 a1 \x\a1 þ ða2 a1 Þ 3 1 2 a1 þ ða2 a1 Þ\x\a2 þ ða2 a1 Þ 3 3 2 1 a2 þ ða2 a1 Þ\x\a2 þ ða3 a2 Þ 3 3 1 xa2 þ ða3 a2 Þ 3
ð5Þ 8 > 0 > > > > > > > 2a2 þa3 3x > > < 1 a a 3 1 u3 ðxÞ ¼ > > > 1 > > > > > > > : 3ða3 xÞ a3 a2
u4 ðxÞ ¼
8 > > >0 <
1 xa2 ða2 a1 Þ 3 1 1 ða2 a1 Þ\x\a2 þ ða3 a2 Þ 3 3 1 a2 þ ða3 a2 Þxa3 3
ð6Þ
x[a3
3ða3 xÞ 1 > > > a 3 a2 : 1
Based on this method, the large deformation of Tianjiashan tunnel is predicted. The factors of large deformation proneness were given in Table 4, and the results were shown in Table 5 accordingly. Also, the statistics analysis on large deformation of Tianjiashan tunnel can be clearly seen in Table 6. Form the Table 5, as for the large deformation level, the I level was accounted for 42.36%, which was at a length of 230 m, and the II level was accounted for 21.18%, which was at a length of 115 m, and the III level reached to 36.46%, at a length of 198 m. Additionally, the fierce large deformation occurred in the shallow depth section, thus, it demonstrated that, large attention should be paid to its reinforce and control measurements on the construction of shallow sections.
1 x a3 ða3 a2 Þ 3 1 a3 ða3 a2 Þ\x\a3 3 x [ a3 ð7Þ
where, ui(x) denotes the degree for the ith element as every evaluated index for the judgment goal set. x is the fact value of the evaluated index, and ai denotes the standard limited value.
In order to verify the accuracy of the evaluation results of AHP–FUZZY method, we establish a 3D numerical simulation model of DK394 ? 625–DK394 ? 650 section of Tianjiashan tunnel by using ANSYS software, and load calculation by FLAC3D software. The finite difference numerical simulation was employed on the numerical analysis on the mechanism of large deformation of the tunnel, to obtain the basic deformation law. On the analysis of evaluation, the numerical ion is employed on simulating excavation process of underground engineering, and the analysis on surrounding rock deformation and plastic zone, and supporting structure stress distribution, etc., to evaluate surrounding rock stability, which plays a significant and important role on its application (Wang et al. 2006). 4.1 The Whole Simulation Model and Parameters As ‘‘Tianjiashan tunnel’’ project profiles and engineering geological conditions were previously expressed above, it was omission here. Figure 5 shows the elaborate numerical model. This mesh consists of 162,374 elements, which give rise to 57,858 nodes. The model was created by program ANSYS and was calculated by program FLAC3D. In order to well capture the soil deformation especially the sediments area, and the development of plasticity around the
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Geotech Geol Eng Table 4 The factors of large deformation proneness Mileage
Rock uniaxial compressive strength (MPa)
Elasticity modulus of rock (MPa)
Rock swelling ration (%)
The major principal stress (MPa)
The ration of strength to geostress
Rock mass structure
Groundwater
Rock mass class
DK394 ? 235– DK394 ? 280
0.5
1100
–
28
0.02
Loose structure
Drip
V
DK394 ? 280– DK394 ? 310
5
1700
–
25
0.20
Cataclastic structure
Drip
V
DK394 ? 310– DK394 ? 350
5
1700
–
17
0.29
Cataclastic structure
Seepage
IV
DK394 ? 350– DK394 ? 510
5
1700
–
26
0.19
Cataclastic structure
Moist
V
DK394 ? 510– DK394 ? 625
5
1700
–
21
0.24
Cataclastic structure
Moist
V
DK394 ? 625– DK394 ? 658
1
1300
–
21
0.05
Loose structure
Moist
V
DK394 ? 658– DK394 ? 778
1
1100
–
17
0.06
Loose structure
Moist
V
Table 5 The evaluation results of large deformation Mileage
No
Weak (I level)
Media (II level)
Fierce (III level)
Evaluation results
DK394 ? 235–DK394 ? 280
0.129
0.183
0.056
0.632
III
DK394 ? 280–DK394 ? 310
0.129
0.343
0.324
0.204
I
DK394 ? 310–DK394 ? 350
0.277
0.299
0.220
0.204
I
DK394 ? 350–DK394 ? 510
0.257
0.319
0.218
0.206
I
DK394 ? 510–DK394 ? 625
0.230
0.258
0.308
0.204
II
DK394 ? 625–DK394 ? 658
0.233
0.214
0.054
0.499
III
DK394 ? 658–DK394 ? 778
0.277
0.141
0.032
0.550
III
Table 6 The statistics analysis on large deformation of Tianjiashan tunnel Large deformation level
No
I
II
III
Prediction length (m)
0
230
115
198
The ration of total length (%)
0
42.36
21.18
36.46
tunnel, an extension of the model should be considered. The longitudinal boundaries of the model are located a distance of 120 m, while the lateral length of the mesh is fixed to 65 m of both sides from the tunnel axis, with a restriction to the normal horizontal displacement. And the height is up to 77 m, with a
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free surface boundary while all constraints at the bottom. 4.1.1 The Simulation Model and Mechanical Parameters In the simulation, the computation was carried out by different elements: the solid elements for the whole sedimentary and geology layers, as well as the antipiles, the 3-nodes linear elastic shell elements for net shotcrete layers, with the thick of 150 mm and the strength level of 25 MPa, and grids applying the 8 mm diameter steel bars, and an interval of 250 mm, and cable elements for the anchors, utilizing 22 mm diameter steel bars, which length 5 m and at horizontal spacing 1.5 m and dip angle 15 degree.
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Excavation area
The small
Anti-piles
z
The large
Y
X
Fig. 5 Three-dimensional numerical model
The soil behavior is assumed to be governed by an elastic perfectly plastic constitutive relation based on the Mohr–Coulomb criterion, while the linear elastic for others. On the basis of the laboratory and field tests, the specific parameters are listed in Table 7. Note that the parameters of the forepole and the grouted on the surface are simulated through a generalized way, by improving the strength of rock mass (Ding et al. 2011). 4.1.2 The Simulation of Process For the sake of simplicity, this analysis is conducted by two phases. The first level is to the height of 315.00 m by slope and 311.20 m by linear slopes for the second level. Apart from this, the computation was carried out in six stages listed in Table 8 (He et al. 2011). 4.2 The Instability Mechanism Analysis We can better understand the instability mechanism of the slope from the computation results, such as the process of the stress, deformation and plastic zone distribution. Figures 6 and 7 give a graphical summary of the displacement of X direction of the heading slope. We can see that the displacement after the excavation of first level slope, were 0.989 mm in the large mileage and -0.863 mm in the small mileage in respect, while the final displacement is 1.396 mm and
-1.343 mm relatively insofar the complete of second level of linear slopes. Thus, the ratios of the first displacement to the final displacement were 70.85 and 64.26%, respectively. Therefore, it was well manifested that the lateral deformation has reached its elastic limit already insofar the excavation of slope, whereas, the linear slopes were just convenient to increase working face by partial excavation, thus its affection scope is smaller. We can conclude that the most adverse phase among the excavation stages was the excavation of slope. In order to further analyzing the deformation characteristics of Ming dig after the excavation, it selected qualitative mapping x and y direction of the surface monitoring deformation displacement curves of 16 typical and representative points. In Fig. 8, it can be seen that, in the x direction, all the measuring points produced displacement towards excavation area. As the first level (Stage 4) slope excavation is completed, all the deformation monitoring points had reached more than 75% of its total deformation, which illustrated for the entire tunnel section, the first level of slope excavation is the worst stage during Ming dig tunnel construction. And this also verifies the deposit in the site construction and lateral deformation mainly occurs in the first level of layered slope excavation, and the second straight slope excavation was only for the subsequent tunnel construction, in order to increase working face for partial excavation method, with small influence scope. From the Fig. 9, as one can see, during the excavation from the ground surface excavation (Stage 1) to 315 m elevation (Stage 4), for the deformation of measuring points towards y axis negative curve, its fitting curve tangent, exhibited that each former deposit excavation was larger than the next layer excavation, which illustrated for the deposit on the excavation, the total deformation towards y direction, was not only increasing, but also with incremental deformation for each layer excavation. It further demonstrated that after excavation scope of slope, the adoption of conventional spray anchor bracing effect was not obvious. While as for the straight slope excavation stage, all deformation towards y direction of all the monitoring points were leveling off, which demonstrated that after the completion of the first level, the deposit occurs large deformation and
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Geotech Geol Eng Table 7 Physicomechanical parameters of geology and support
Type of materials
E/GPa
c/(kN/m3)
C/kPa
u/(o)
v
Quaternary sediments
0.35
20.6
45
18
0.35
Weathered siltstone
0.8
19.3
200
32
0.32
Slightly weathered siltstone
4.1
26.6
800
44
0.20
Reinforced ring with forepoles
8.5
21.2
95
35
0.30
Reinforced soil layer with grouted
10.8
23
120
38
0.27
Secondary lining
31.5
25
–
–
0.167
Primary support
21
24
–
–
0.19
Net shotcrete layer Anchor (U22)
10 210
24 78
– –
– –
0.20 0.30
Anti-slide pile
31.5
25
–
–
0.20
Table 8 Calculation stages of the excavation The main phases
Calculation stages
The number of cycles per stage
Construction conditions
The original state
Stage 0
3000
Calculate the initial stress, and clear the displacement
The first level of slope
Stage 1
2000
Excavate to 320 m, install the 1 row of anchor on 321 m and net shotcrete
Stage 2
2000
Excavate to 318 m, install the 2 row of anchor on 319 m and net shotcrete
Stage 3
2000
Excavate to 320 m, install the 3 row of anchor on 317 m and net shotcrete
Stage 4
2000
Excavate to 320 m, install the net shotcrete
Stage 5
2000
Excavate to 313 m, install the 1 row of anchor on 313.5 m of straight slope and net shotcrete
Stage 6
4000
Excavate to 311.2 m, install the 1 row of anchor on 312 m of straight slope and net shotcrete
The second level straight slope
Fig. 6 Displacement of X direction on large mileage
reached a new equilibrium because of the stress redistribution. It should be noted that, as for the big range direction of deposit, mainly because it shifted towards the
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Fig. 7 Displacement of X direction on small mileage
excavated open face, rigid translation phenomenon happened in a certain range. So that the guide wall slipped thrust occurring topple damage. As for the small range direction, due to the terrain ups and downs
Geotech Geol Eng Fig. 8 x-Direction displacement. a Exit direction and b entrance direction
Fig. 9 y-Direction displacement. a Exit direction and b entrance direction
is bigger, it was character with severe shallow buried and bias, the excavation disturbance causes the unstability of the deposit, so that the surface produce large cracks. The results of numerical simulation show that this section is highly likely to occur fierce large deformation, which is in accordance with the AHP–FUZZY method (Table 5).
4.3 Large Deformation Performance Originally, the excavation ranging of DK394 ? 625– DK394 ? 650, which length 25 m, was ran by backfilling method. While in the operating of guide wall on DK394 ? 650, it resulted in cracking after the slope slipping, as illustrated in Fig. 10. At the same time, as the excavation by method of three-bench
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2.
Fig. 10 Slip-slumps of guide wall from the large mileage
3.
4.
5.
Fig. 11 Surface crack from the small mileage
seven-step excavation less than 10 m in the small mileage, crack on the surface occurred, along with localized cracking in the shotcrete and significant deformation in wide flange rib steel sets are observed, which can be seen in Fig. 11. The actual results are coincide with AHP–FUZZY method and numerical simulation results.
5 Conclusions 1.
Through the specific analysis into the influential factors of large deformation of tunnel, the corresponding grading criterion was given. The prediction of large deformation was established with the help of AHP–FUZZY method, and 8 influential indexes were determined from three aspects,
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lithology conditions, in situ stress condition and surrounding rock conditions. The importance of each index was reasonably considered via weight calculation, and the limitations of single factor classification were avoided. Based on the eight indexes for different performance characteristics of large deformation level, and in combination with the large deformation of surrounding rock tunnel classification standard, three deformation levels were established: slight deformation (ranking I), medium large deformation (ranking II) and fierce large deformation (ranking III). Based on AHP–FUZZY method, we predicted the large deformation of Tianjiashan tunnel. The forecasting shows that the I level large deformation accounted for 42.36%, at the length of 230 m. II level accounted for 21.18%. III level large deformation reached the rest. Established a 3D numerical simulation model of DK394 ? 625–DK394 ? 650 section of Tianjiashan tunnel. The result of the finite difference numerical simulation method showed that this section is very likely to occur large deformation, which verified the accuracy of the evaluation results of AHP–FUZZY method. The actual results are coincide with both AHP– FUZZY method and numerical simulation results, which reflects the effectiveness of AHP–FUZZY method and numerical simulation method in predicting the large deformation behavior in tunnels.
References Aydan O, Akagi T, Kawamoto T (1993) The squeezing potential of rocks around tunnels: theory and prediction. Rock Mech Rock Eng 26:137–163 Bhasin R, Barton N, Grimstad E, Chrvssanthakis P (1995) Strength anisotropic rocks in the Himalayan region. Geology 40:169–193 Brady BT (1977) Anomalous seismicity prior to rock bursts: implications for earthquake prediction. Pure Appl Geophys 115(1):357–374 Brighi B, Chipo TM, Gut E (1998) Finite differences on triangular grids. Numer Methods Partial Differ Equ 14:567–579 Chen X, Lu L (2008) Prediction of tunnel rock burst based on AHP–FUZZY method. J China Coal Soc 33(11):1230–1234
Geotech Geol Eng Ding Y, Zhou S, Wang J (2011) Three-dimensional numerical analysis of soil nailing for deep excavation. J Shanghai Jiaotong Univ 45(4):547–551 He Z, Cai Z, Cao P et al (2011) Numerical analysis for stratified rock slope stability reinforced by bolts. J Central South Univ (Sci Technol) 42(7):2115–2119 Kimura F, Okabayashi N, Kavamoto T (1987) Tunneling through squeezing rock in two large fault zone of Enasan Tunnel II. Rock Mech Rock Eng 20:151–166 Liszka T, Orkisz J (1980) The finite difference method at arbitrary irregular grids and its application in applied mechanics. Comput Struct 11:83–95 Liu Z, Zhu Y, LI W et al (2008) Mechanism and classification criterion for large deformation of squeezing ground tunnels. Chin J Geotech Eng 30(5):690–697 Lunardi P (1990) The cellular arch method: technical solution for the construction of the Milan railway’s venezia station. Tunnel Undergr Space Technol 5:351–356 Lunardi P (2008) Design and construction of tunnels. Springer, Berlin Meng L (2009) Study on the tunnel for geological forecast and its computer assistant system. Chengdu University of Technology, Chengdu Morrison RGK (1948) A series on rock bursts. Eng Miner J 148(9):62 Muirwood AM (1972) Tunnels for roads and motorways. Q J Eng Geol 5:119–120
Perrone N, Kao R (1975) Ageneral finite difference method for arbitrary meshes. Comput Struct 5:45–58 Saaty TL (1980) Fundamentals of the analytic hierarchy process. RWS Publications, Pittsburgh Wang J, Tang Y, Zhu H et al (2006) 3D monitoring and analysis of landslide deformation caused by Twin-Arch tunnel. Chin J Rock Mech Eng 25(11):2226–2232 Xu Z (1982) Elastic mechanics. Higher Education Press, Beijing, pp 191–244 Xu Z, Huang R (2000) Deep buried long tunnel and its construction geological disaster. Southwest Jiao Tong University Press, Chengdu Yang J, Wu X (2005) Comprehensive forecasting method for estimating rock burst. Rock Mech Eng 24(3):411–416 Yano T, Yamada N, Suzuki I (1978) Construction of the Enasan Tunnel and the design of the second stage. Pergamon Press, New York Yoshinaka R, Osada M, Tran TV (1992) Deformation behavior of soft rocks during consolidated-undrained cyclic triaxial testing. Int J Rock Mech Miner Sci Geomech Abstr 33(6):557–572 Yoshinaka R, Osada M, Tran TV (1998) Non-linear stress and strain-dependent behavior of soft rock under cyclic triaxial conditions. Int J Rock Mech Miner Sci 35(7):941–955 Zhang J, Deng B, Zhu Y et al (1988) Application FUZZY mathematics. Geological Publishing House, Beijing
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