Inversion Analysis of Initial Geo-Stress in Tunnel of Daping Mountain

Inversion Analysis of Initial Geo-stress in Tunnel of DaPing Mountain

Zhemin You PhD candidate, Faculty of Engineering, China university of Geosciences; No.388, Lumo Road, Wuhan, 430074, [email protected]

Jianping Chen Professor, Faculty of Engineering, China university of Geosciences; No.388, Lumo Road, Wuhan 430074, China. [email protected]

Yongsong Li PhD candidate, Rock Foundation Division, Yangtze River Scientific Research Institute, Hubei Wuhan 430010, China, song90397@sohu. com

Ying Xu PhD candidate, Faculty of Engineering, China university of Geosciences; No.388, Lumo Road, Wuhan 430074; [email protected]

ABSTRACT

Based on the geological conditions and measured data of in-situ stress in DaPing mountain tunnel, the initial geo-stress field of tunnel area is analyzed by 3D multivariate FE regression. A 3D FE computational model is established to compute geo-stress in four cases, including gravity, tectonic stress field for horizontal extrusion and shear. And the regression coefficients are solved using the least square method , and then the calculation value of the measured points , eventually the regression stress field of the whole area especially important engineering parts .Through comparison between the calculated and measured geo-stresses of measuring points, it is found that these two are similar, which suggests that the geo-stress field obtained by regression is reasonable and conforms to the historical background of geological structure. The results of the geo-stress field have important reference value of the dynamic design and construction of projects.

KEYWORDS: DaPing Mountain; deep buried tunnel; initial geo-stress field; FEM;

regression analysis

INTRODUCTION

Guzhu (Gucheng-Zhuxi) expressway in Hubei province of China is an important section of the skeleton road network planned which includes six longitudinal and five horizontal and one

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Vol. 17 [2012], Bund. P 2256 toroidal part, connected Fuzhou-Yinchuan highway with Pingli-Ankang highway in Shanxi province. Once completed, it is of great strategic significance on the implementing of the rise of the central and western regions, accelerating social and economic development along the regions.

DaPing mountain tunnel is one of the separate tunnels with great depth and super-length in Guzhu highway(the length 8252m*2, maximum depth 900m), which lies in the Zijin and Siping town of Xiangyang city, with the hole axis 218°. The tunneling lie in area with low mountains and terrain large ups and downs, effected by structure eroding. Along the route the strata exposed are as follows: shale(S1x), biological clastic limestone mixed up with a few carbon shale and powder sand shale(O1n-O3s1l), muddy limestone, carbonaceous limestone with shale partly(Є1s-sl), dolostone and limestone(Z2-Є1dn). Qingfeng fault, stretching EW nearly, passed through the tunnel axis with small angle, formed more than 10 secondary faults, caused surrounding rock broken, local groundwater rich, overall stability poor. Because of the geological activity and great depth, the tunnels may pass through high geo-stress area, and come across a series of deep engineering geology and “weak rock” mechanical problems inevitably. The distribution of regional initial stress field has great importance on the stability of surrounding rock. Therefore, it is necessary to calculate the initial stress field by limited measured data, provide the good premise for the safety of the tunnel construction.

The initial stress field of rock mass is the primary factors which need to be considered in geotechnical engineering design and construction, and the important research subject in rock mechanics and engineering. However, it is always a problem of reflecting the initial stress field accurately in underground engineering1~2, whether the initial stress field reliable, parameter of rock mass selected reasonable, they will influence the reliability and safety of the design and construction directly. Complex stress cause and influence factors, less measured data due to measurement condition and the limited funds, measurement error, all these make the results a certain degree of discrete. Therefore, it is necessary to analysis the initial stress field through the proper calculation method, in order to obtain stress field more accurately, widely applicable scope3. At present there are two kinds of inversion and regression analyzing methods of stress field widely-used: the one is displacement back analysis. That is, inverse the regional stress field according to the tectonic deformation observation or the displacement monitoring during engineering construction and excavation. It is an indirect method, which is suitable for the situation as lacking measured data or even exists but is disturbed stress, and often used in local scope of stress field of rock mass inversion. For some large projects, generally the second method are used, the stress regression analysis method, that is, geo-stress field is obtained through fitting the 3D numerical simulation and measured stress data4.

Take DaPing mountain tunnel of Guzhu highway as an example, the stress regression analysis is used, and a 3D geological model is set along the area, calculate based on the measured data, and gain the initial stress field about the whole area. Vol. 17 [2012], Bund. P 2257

MATERIAL AND METHODS

Theory of regression analysis

Generally, the shallow rock stress field is mainly composed of horizontal tectonic stress field and gravity field related to terrain5.This paper will set up according to the view of the stress field mathematical model, using multiple regression method fitting to the analysis. Based on the above statement, mathematics calculation model is established.

According to the theory of the multiple regression method6, geo-stress calculation value is the dependent variable, and its Components the independent variable, such as gravity stress and tectonic stress field, calculate based on the limited measured data. And in accordance with the least square method the equation is solved with the sum of squared residuals minimum value, and the regression coefficients corresponding, making the calculation stress and the measured stress to achieve optimal fitting, then the initial stress field of engineering area7.

σ σ σ σ σ ++++Δ= aaaa σ 44332211 (1)

σ Δσ σ σ σ where is The calculation value of the initial stress field, is random error, 1 、 2 、σ 3 、 4 is the initial stress components respectively such as gravity, the extrusion structure along X, Y,

XY plane, a1、a2、a3、a4is the Corresponding regression coefficient.

Geo-stress regression analysis in DaPing mountain tunnel

The geological model is the basis of the calculation model, in-depth understanding of the engineering geological conditions and the reasonable generalization is an important prerequisite for the establishment of geological generalization model8. Comprehensive considering the factors of the landform features and rock mechanics properties, take the tunnel axis calculation model Gucheng-Zhuxi as the x direction (218°), the GuCheng import as a starting point. Coordinate z- axis vertical up, the y-axis accord with the right hand screw rule. The total range of the Calculation model is 8375m×3000m, with the bottom elevation -1000m (Fig 1). It includes the tunnel site primarily, with drilling point near the middle of the field (Fig 2). The computational domain is divided into 340 277units, 63 079nodes. On the basis of the flexibility assumption of the geo-stress field, linear elastic secant modulus is used to compute. Vol. 17 [2012], Bund. P 2258

Figure 1: Computation model

Figure 2: Calculation zone and drill hole position

The axis geological profile of DaPing mountain tunnel is shown in Figure 3, and the physical and mechanical parameters of rock mass in Table 1.

218° Zhuxi Gucheng

F9 F10 F8 F7 F26 F4+F5

F11 O1n-O 3S1l s-sl F3 1 Z2 1 dn F6 Z 2 dn Z dn bioclastic 2 1 limestone dolostone O1n-O 3S1l limestone dolostone bioclastic dolostone 1s-sl S1x shale limestone limestone s-sl 1 limestone limestone limestone limestone tunnel axis Figure 3: Geological section of tunnel axis of DaPing Mountain Vol. 17 [2012], Bund. P 2259

Table 1: Mechanical parameters of rock masses Number Lithology Level E/GPa μ ρ/g·cm-3 ① Dolostone limestone Ⅴ 2.0 0.35 2.0 ② Dolostone limestone Ⅳ 5.0 0.31 2.3 ③ Dolostone limestone Ⅲ 18.0 0.26 2.4 ④ shale Ⅳ 3.0 0.32 2.2 ⑤ shale Ⅴ 1.2 0.35 2.0 ⑥ F7、F 8、F 9 Ⅳ 1.5 0.32 2.2 ⑦ F3-6、10-11、26 Ⅴ 0.8 0.36 2.0

Stress regression model imposes the boundary conditions of displacement in the gravity field and the three boundary horizontal tectonic stress field respectively. The density measured of rock mass is used to calculate the gravity stress field under its weight, displacement constraints on the side and bottom of the model; all is limited only to the normal direction of displacement. Apply uniformly normal displacement with different direction in the two sides of the model, to simulate the horizontal direction of tectonic stress field, the same constraints of lateral and bottom boundary constraint conditions as gravity stress field simulation. Shear stress in the horizontal plane, is simulated via imposing boundary displacements9. The hydraulic fracturing method is used to test in situ stress in two drillings, which located nearby the middle of the tunnel site. Results are shown beelow in table Ⅱ. To identify the stress distribution of the area, geo-stress value of 15 points from two sets drilling are obtained using hydraulic fracturing10 (Fig 4).

（a）ZK10 （b）ZK11 Figure 4: Curve of geo-stress measurement with depth

Figure 4 shows that, the value of σH/σh, σv is increasing linearly with the depth in test range. Lateral pressure coefficient of drillings is greater than 1, indicating that the tectonic stress is integral part of the stress field in the project area. Vol. 17 [2012], Bund. P 2260

Table 2: The measured values of hydro fracturing of drillings

Drill Hole Depth /m σH/MPa σh/MPa σv/MPa Direction of σH

228 8.18 6.27 5.93

237 9.45 6.93 6.16

ZK10 310 11.74 8.18 8.06 319 9.72 8.55 8.29 325 11.65 8.62 8.45 NE14o

390 13.17 9.56 10.14 409 14.14 10.29 10.63 NE16o 418 14.74 11.17 10.87

83.2 2.43 2.11 2.16

131.5 5.93 4.01 3.42

ZK11 173.8 6.56 4.49 4.52 228.2 7.72 5.80 5.93 NE17o 258.4 8.89 6.60 6.72 294.6 9.76 7.07 7.66 318.8 10.21 7.46 8.29 NE19o

3 Note: Gravity stress is calculated by overlying weight of rock, σv=γH, γ=26 kN/m .

RESULTS AND DISCUSSION

Analysis of the geo-stress inversion results

In line with drilling measured data and simulation results of geo-stress field, the regression coefficients of the four independent variables are obtained by using least square method as follows:

L1=1.03，L2=-4.1，L3=-1.4，L4=-0.05. Substitute them into Formula (1) to obtain calculated values of the measuring point drilling. To test the reliability of the simulation results, and considering the measured geo-stress representative and rationality, eliminate the unreasonable value11. Table 3 shows that Comparison the simulation results with the measured value including coefficient of lateral pressure of σH. Vol. 17 [2012], Bund. P 2261

Table 3: Comparison of the geo-stress measurement and regression value

σH σh σv Drilling Measure Depth point (m) M C R.E/% M C R.E/% M C R.E/% M C /MPa /MPa /MPa /MPa /MPa /MPa /MPa /MPa

1* 228 8.18 9.81 17.69 6.27 -1.92 -112.26 2.83 2.16 14.50 1.38 4.54 2 237 9.45 9.79 3.61 6.93 -0.58 -108.31 6.16 6.96 13.04 1.53 1.41 3 310 11.74 11.10 -5.42 8.18 1.17 -85.66 8.06 8.88 10.12 1.46 1.25 ZK10 4* 319 9.72 11.19 15.92 8.55 0.26 -83.77 5.69 5.93 10.38 1.17 1.89 5 325 11.65 11.38 -2.35 8.62 1.53 -82.28 8.45 9.33 10.38 1.38 1.22 6 390 13.17 12.47 -5.35 9.56 3.02 -68.43 10.14 10.98 8.27 1.30 1.14 7 409 14.14 12.78 -9.62 10.29 3.50 -66.01 10.63 11.62 9.29 1.33 1.10 8 418 14.74 12.93 -12.29 11.17 3.73 -66.65 10.87 11.93 9.71 1.46 1.08

1* 83.2 2.43 6.86 182.24 2.11 4.77 126.27 2.16 2.83 31.07 1.13 2.42 2 131.5 5.93 7.92 33.57 4.01 5.38 34.24 3.42 3.80 11.10 1.73 2.08 3 173.8 6.56 8.21 25.21 4.49 5.62 25.17 4.52 4.63 2.49 1.45 1.77 ZK11 4 228.2 7.72 8.51 10.30 5.80 5.85 0.87 5.93 5.69 -3.98 1.30 1.50 5 258.4 8.89 8.73 -1.82 6.60 5.97 -9.59 6.72 6.25 -6.99 1.32 1.40 6 294.6 9.76 8.66 -11.24 7.07 6.08 -14.03 7.66 6.96 -9.19 1.27 1.24 7 318.8 10.21 8.61 -15.66 7.46 6.15 -17.61 8.29 7.21 -13.08 1.23 1.19

Notes：The serial number with belt * in the table is being removed points, M:Measurement, C:Caculation, R.E: Relative Error

It can be seen from Table 3 that there are some characteristics as follows：

(1) Simulation of the level of large principal stress (σH instead behind) of ZK10 is ideal. The relative error range of each point is -12.29%～17.69%, of which measured minimum relative error of point 5 is -2.35%. The relative error of the rest points is between -10% and 10%, overall consistent with the measured values.

Relative to the level of σH, simulation of the effect of the minor principal stress level (σh instead behind) is poorer. The maximum relative error of 8 points is up to -112.26%, with the minimum -66.01%.The author believes that there are two main reasons of higher error obviously. First, the drilling is located in the mountain slope, The size of the main stress deflects and appears a stress concentration. The second, part of the measured data is unreasonable, which also leads to increase on the error of simulation results.

(2) To ZK11, the regression results of σH/σh is in good agreement with the measured results, while difference on stress value of the individual point is large. For point 2, the measured value of σH is 5.93 MPa, and the calculated value 7.92 MPa, with the relative error 33.57%. The main reason is due to the relatively poor parts of the rock mass quality of the measuring point, which leads the measured value small. While the formula of regression analysis does not Vol. 17 [2012], Bund. P 2262 truly reflect the reduced values, iit makes the larger error of these measurements12. (3) The calculation results and measured of gravity stress of two drillings are basically the same that conforms to the assumptions to stress inversion analysis, which is mainly the gravity stress vertically. (4) In addition to the individual points, the coefficient of horizontal pressure of the measured λ = μ and calculated values is greater than that without the tectonic disturbance (namely 1− μ ) within the depth. It is shown that tectonic stress field gives priority to the area, overlying the gravity stress field. This is also consistent with the regularity of distribution of the actual stress field13.

The initial stress field of tunnel site

The calculation results of geo-stress field no longer apply only to the rock mass nearby drillings, but apply to a wide range of that. As for the main project site without measured vallues, the whole stress field is obtained according to four subsystems stacked byy the regression coefficients. It can be easily informed the stress state of any point, and thus provides conditions for the stability analysis of the specific parts of the underground engineering. Figure 5 shows the principal stress distribution trend of the DaPing tunnel axis of the longitudinal profile. From figure 5,we know the value of σH /σh is growing approximate lineally with depth. The distribution of stress is closely related in topography, which has great influence on stress in the shallow. Along with the buried depth increases, its influence is relatively minor. When terrain changes greatly, the contour of the stress is relatively close, the change gradient is great. It is consistent with the law of the actual stress field, which explains the stress field along longitudinal section of DaPing mountain tunnel is reasonable14. H/m

Tunnel axis

station/m

（a）σH H/m

Tunnel axis

station/m

（b）σh Figure 5: Contour diagram at the axial lengthways section Vol. 17 [2012], Bund. P 2263

In addition, the influence of stress contours of the geological structure is also great 15, in the fault and its influence in the belt, stress isoline appears abrupt. The main reason is that the physical and mechanical indexes of the fault with weak geological structure are smaller than that of the adjacent position, leading to severe change of stress in these parts, contour density greater.

According to the regression calculation, the value range of σH is 2.15~21.6MPa, with σh -

13.0~12.0MPa, σV 0.20~32.87MPa, σH/σC(Uniaxial Compressive Strength) is relatively modest. All these show that the tunnel axis of the vertical section is at a moderate stress level, and should be paid attention to the possibility of moderate rock burst.

CONCLUSIONS

The FEM multiple regression method is used to calculate and analyse the distribution and characteristics of the regional stress field of DaPing tunnel with great depth and length, the conclusions are as follows: (1) The 3D FEM regression analysis method is used to calculate the initial regional stress field based on limited measurements, which can better reflect the topography, and geological conditions on the influence of the initial stress field on the initial stress field, proved that the method is effective and feasible. (2) By comparison, we can know that most of the calculated values are close to measured values. Within depth, ground stress field near the drilling tectonic stress field is mainly tectonic stress field. (3) The stress contours of the tunnel axis at the vertical section of the main figure shows: As the depth increases, the impact of the topography on the stress field gradually decreases, when terrain changes, change gradient of the stress is great. The value of σH /σh is growing approximate lineally with depth. It is consistent with the law of the actual stress field, which explains the stress field along longitudinal section of DaPing mountain tunnel is reasonable. (4) Regression results shows that, the tunnel axis of the vertical section is at a moderate stress level, and should be paid attention to the possibility of moderate rock burst.

REFERENCES

1. Liu Y.F., et al. (2000) “The Rock Body Grounds, Tress and Engineering Construction”. Wuhan: Hubei Scientific and Technological Press (in Chinese)

2. Wang L.J., Pan L.Z. (1991) “Stress Measuring and its Application in Engineering”. Beijing: Seismological press (in Chinese)

3. Liu Y.F. (1983) “Data Processing Method and Precision Analysis for Rock Stress Measurements”. Chinese Journal of Geotechnical Engineering, 5(2):110-125 (in Chinese)

4. Xiong P.H., Su K., Qian J. (2010) “Application of Multivariate Linear Regression to Initial Geo- Vol. 17 [2012], Bund. P 2264

stress Filed in Small Range”. Water Resources and Power, 28(6):39-42 (in Chinese) 5. Guo H.Z., Ma Q.C, Xue X.C. (1983) “The Analytical Method of the Initial Stress Held for Rock Mass”. Chinese Journal of Geotechnical Engineering, 5(3):64-75 (in Chinese) 6. Zhou J.X. (1990) “Practical Regressive Analysis Method”. Shanghai: Shanghai Scientific and Technical Publishers (in Chinese) 7. Zhao D.A., Li G.L., Chen Z.M. (2009) “Three-dimensional FE Regression Analysis of Multivariate Geo-stress Field of Wushaoling Tunnel”. Chinese Journal of Rock Mechanics and Engineering, 28(1): 2687-2694 (in Chinese) 8. Li Y.S., Yin J.M., Liu Y.K. (2007) “Regression Analysis of In-situ Stress Field for Yangjiang Pumped Storage Plant”. Engineering Journal of Wuhan University, 40(4):69- 73 (in Chinese)

9. Zhang Q.H.， Zhong Z.W., Gong B.X. (2000) “Method of Generating Pure Shear Stress by Adding Boundary Displacement and its Application to Back Analysis for Geo-stress Field”. Journal of Yangtze River Scientific Research Institute, 17(2):34-36 (in Chinese)

10. Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (2010) “Measurement Geo- stress Report of ZK10, ZK11 of DaPing mountain tunnel”, Hubei Province Guzhu highway. (in Chinese) 11. Zhang J.G., Zhang Q.Y., Yang W.D. (2009) “Regression Analysis of Initial Geo-stress Field in Dam Zone of Dagangshan hydropower station”. Rock and Soil Mechanics, 30(10):3071~3078 (in Chinese) 12. He J.D.， Xie H.Q.， Wang Q.Z. (2009) “Inversion Analysis of Initial Geo-stress in Dam Site of Guandi Hydropower Project”. Chinese Journal of Geotechnical Engineering, 31(2):166-171 (in Chinese)

13. Qiu X.B.， Li S.C.， Li S.C. (2003) “3D Geo-stress Regression Analysis Method and its Application”. Chinese Journal of Rock Mechanics and Engineering, 22(10):1613-1617 (in Chinese)

14. Yu C., Li H.B., Li G.W. (2010) “Inversion Analysis of Initial Stress Field of Dalian Underground Oil Storage Cavern”. Rock and Soil Mechanics, 31(12): 3984-3990 (in Chinese) 15. H. Konietzky, L. te Kamp, H. Hammer (2001) “Numerical Modeling of In-situ Stress Conditions as an Aid in Route Selection for Rail Tunnels in Complex Geological Formations in South Germany”. Computers and Geotechnics, 28:495-516.