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Optimizing Supporting Parameters of Metro Tunnel Based on Improved Particle Swarm Optimization Arithmetic
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 4857 – 4861 www.elsevier.com/locate/procedia
Optimizing Supporting Parameters of Metro Tunnel Based on Improved Particle Swarm Optimization Arithmetic Jiang Annan, Wen Zhiwu Highway and Bridge Engineering Institute,Dalian Maritime University, Dalian, China
Abstract The optimization of anchor and spay layer parameters of tunnel not only concerns the stability of surrounding rock, but also concerns the economic cost. Aiming to the implicit nonlinear relation between anchor parameters and surrounding rock stability, and the contradiction of stability object and economics object. The paper proposed a anchor parameters optimization method based on improved particle swarm optimization arithmetic and orthogonal designing scheme numerical test. The method firstly analyzed the sensibility of anchor parameters affecting surrounding rock stability and regressed function using numerical test data, then the limit displacement of surrounding rock is acted as the stability constraint condition and the cost function is as evaluation function, and the improved PSO is carried out. The method is used in metro tunnel of Dalian City of China, the result is good which states the method is feasible.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011] Key words: Metro tunnel; Anchor parameter optimization; orthogonal designing; particle swarm optimization;
1. Introduction Underground space development is closely relate to the nation economic development, the utilization of underground space extends to each field of society. However, geological body is a complex media and structure, having anisotropic, discrete, nonlinear and complex load-unload conditions, After excavation, the initial balance state is destroyed, the stress of surrounding rock changed complexly. While the surrounding rock deform and loosen zone developed too much, the collapse should be occurred[1]. Rock anchor is the main supporting mean of tunnel construction, it has vital function to change the surrounding rock from load to bearing ring, maximally take the self-supporting action, guarantee the stability of the surrounding rock.. Spray also is used cooperating anchor supporting, which keeps the
* Corresponding author. Tel.:13504110548; fax: +0-411-84724290. E-mail address:[email protected]
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.906
4858 2
Jiang Annan andetWen Zhiwu / Procedia Engineering (2011) 4857 – 4861 Jiang Annan al/ Procedia Engineering 00 (2011)15000–000
whole surrounding rock integrating. Anchor and spray associated supporting mean is the sign of modern tunnel construction theory, and is the main content of famous new Austrian tunnelling method[2]. The conventional supporting parameters selection generally relies on experience and norm, which is affected by human factor easily. The experience formula also is difficult to express the relation between parameters and rock stability. Because of the complexity of anchoring mechanism, the analytical formula adopts too many assumed conditions, it has large error. The paper proposed an optimization method of parameters of anchor and spray, synthetically considering the objects of surround rock stability and cost. The anchor spray parameters optimization method based on improved PSO. 1.1. The improved PSO PSO is a global optimization method proposed by Kennedy and Eberhart [3.4] in order to solve nonlinear global optimization objective. Each solution of the optimization problem is deemed as a particle, something like a bird. In addition, each particle has the fitness value decided by optimization function in PSO, and the velocity determines its direction and distance. The two extreme values are to be tracked by the particles in each iteration. The first point is the optimal solution in all the particles by all the searching history, i.e. the global optimal solution gbest, gbest=[g1,g2,……,gn]. The second point is the optimal solution of each particle in the experience of itself, i.e. individual optimal solution pbest, pbesti=[pi1,pi2,……,pin]. The Ith particle is expressed by xi=[xi1,xi2,……,xin], The kth correction(particle velocity) is vik=[vi1k,vi2k,……,vink]. The iteration formulas are as follows.
vidk = wi vidk −1 + c1 × rand1 × ( pidk −1 − xidk −1 ) + c 2 × rand 2 × ( g dk −1 − xidk −1 )
xidk = xidk −1 + vidk
(1) (2)
where i=1,2,……,m; d=1,2,……,n. m is the number of the particles in the swarm, n is the dimension number of the solution vectors, c1 and c2 are respectively two positive constants, rand1 and rand2 is random numbers between zero and 1 respectively. wi is the inertia weight. In order to improve the performance of particle swarm optimization, adjust inertia weight according to the equation as follows [11].
⎛ ⎛ k − 1 ⎞n ⎞ ⎟ w = w0 ⎜1 − ⎜ ⎜ ⎝ k ⎟⎠ ⎟ ⎝ ⎠
(3)
where w0 is a given constant, k is the number of flights, n is a constant. 1.2. The anchor spray parameters optimization procedure. Anchor and spray parameters optimization is actually a multi-objective optimization problem, and these objectives are incompatible, ie if the decrease the parameters the cost will decrease, but the stability of surrounding rock stability will be affected. In order to solve the incompatible objectives, the stability objectives changed to constraint condition, which is expressed as limit displacement. The optimization problem is described as follows. min f ( X ) s.t g i ( X ) < g i 0
(4)
Jiang Annan WenetZhiwu / Procedia Engineering (2011) 4857 – 4861 Jiangand Annan al / Procedia Engineering 0015 (2011) 000–000
In formula, min means the optimization adopts objective function as minimal value. X is the parameters of anchor and spray, including anchor diameter, anchor length, distance of anchors and spay thickness etc. gi(x) is the constraint index corresponding the stability criterion, in this paper it means the deform of surrounding rock. gi0 means the limit deform of the surrounding rock. It is selected because the construction monitoring also generally obtain the convergence deform of rock, the limit deform can reflect the rock stability well. The datasets take the X (x1, x2, x3, x4 ) as input, take deform of surrounding rock as output parameter. There are many functions can be used for the relation, through test calculation, the vertical convergence displacement AD and horizontal convergence displacement BC are respectively listed as follows. The limit deform of surrounding rock is ascertained by experience and norm. Then the formula (4) is optimized by improved PSO, the anchor and spray parameters should be optimized. The optimization procedure is shown in Fig.1.
Fig.1 The parameters optimization procedure.
2. Engineering application 2.1. Engineering introduction The studied engineering of Dalian City metro tunnel is excavated by boring burst method and underhand bench construction method, the section has horseshoe shape, the excavation span is 6.3m and the height is 8m. The buried depth is 12m, the surrounding rock mainly is rotten slate. The initial stress is self weight stress. The mechanics parameters of anchor and spray are not to be optimized. In the numerical model, the parameters are adopted as follows: The elastic modulus of anchor is 45 GPa, the maximal tension strength is 250kN, the rigidity of sand grout of each unit length is 17.5MPa, the cohesion of cement grout of each unit length is 2×105N/m. For spray layer, the elastic modulus is 6GPa, the density is 2200kg/m3. The numerical model and the convergence monitoring lines are shown in Fig.2. FLAC3D 3.00 Step 2364 Model Perspective 10:30:09 Tue Apr 26 2011 Center: X: 7.000e+000 Y: 1.550e+001 Z: 1.900e+000 Dist: 1.421e+002
A
Rotation: X: 0.000 Y: 0.000 Z: 0.000 Mag.: 1.25 Ang.: 22.500
Sketch
Magfac = 0.000e+000 Linestyle
cable Axial Force
Magfac = 0.000e+000 tension compression
C
B
Maximum = 2.146e+003
cable Grout Stress
Magfac = 0.000e+000 in (+) avg. axial-dir in (-) avg. axial-dir Maximum = 9.173e+003
cable Grout Slip
slipping now Itasca Consulting Group, Inc. Minneapolis, MN USA
D
4859 3
4860 4
Jiang Annan andetWen Zhiwu / Procedia Engineering (2011) 4857 – 4861 Jiang Annan al/ Procedia Engineering 00 (2011)15000–000 Fig.2 The anchoring model and monitoring arranging
2.2. Orthogonal design and sensitivity analysis The orthogonal test include 4 factors, they are anchor length l, anchor diameter d, distance of anchors s and the thickness D of spray layer. The scope of above parameters are as follows: l form 2.0m to 4.0m, d from 10 mm to 50mm, s from 0.7m to 1.1m, D from 15cm to 35cm. Design the orthogonal test table and combining parameters groups, carried out the three dimensional numerical simulation, get the displacements of AD and BC. The order of the four factors impacting the displacements of AD and BC is D, l, d and s. That states that thickness of spray layer affects surrounding rock most obviously, and it affects the vertical convergence line AD more obviously than BC. Relatively, the length of anchor length has more obvious affect than other parameters. According to the dataset from above orthogonal design scheme and numerical calculation, using least square method to regress the functions.The coefficients of regression models corresponding to formulas are not listed in the paper limited by paper length.. 2.3. The parameters optimization based on improved PSO Programming the code of improved PSO, set particles population as 50, set the iteration number as 30, the coefficient of momenta term is changing accord to w =0.3*(1-(k-1/k)2), c1=c2=2, running the program and optimized the results as follows: length of anchor is 2.27m, distance of anchors is 0.715m, anchor diameter is 20.4mm, the optimized parameters are roundly adopted as integers listed in Table 1. 240
FLAC3D 3.00 Step 4314 Model Perspective 10:03:37 Thu May 26 2011
w=0.2
190
Center: X: 7.000e+000 Y: 1.550e+001 Z: 1.900e+000 Dist: 1.421e+002
w=0.3 140
Rotation: X: 0.000 Y: 0.000 Z: 0.000 Mag.: 1.95 Ang.: 22.500
Contour of Z-Displacement
w dynamic adjusting
Magfac = 0.000e+000 -2.1504e-002 to -2.0000e-002 -2.0000e-002 to -1.7500e-002 -1.7500e-002 to -1.5000e-002 -1.5000e-002 to -1.2500e-002 -1.2500e-002 to -1.0000e-002 -1.0000e-002 to -7.5000e-003 -7.5000e-003 to -5.0000e-003 -5.0000e-003 to -2.5000e-003 -2.5000e-003 to 0.0000e+000 0.0000e+000 to 2.5000e-003 2.5000e-003 to 3.3465e-003 Interval = 2.5e-003
w=0.4 90 40 -10 0
10
20
30
40
Fig3. The PSO convergence with different w
Itasca Consulting Group, Inc. Minneapolis, MN USA
Fig4. The vertical displacement based on optimum scheme
The fitness values corresponding to different w according to the iteration is shown in Fig3. It is shown that in the PSO optimization process, the different coefficient of momenta term w affects the fitness value convergence velocity and precision, this paper adopts dynamic w according to formula (3) has better convergence velocity and precision than the content w. According to experience and norm, in the optimization process, the AD convergence limit displacement adopts 25mm, the BC convergence limit displacement adopts 3mm. Using the optimized parameters, numerically simulated the tunnel construction process, the vertical displacement of surrounding rock is shown in Fig.4. It is shown that the sedimentation of arc is larger than raising of floor. The maximum convergence of top and floor is about 24.8mm, less than the limit displacement. The optimized scheme and original design scheme are shown in Table 1 It is shown that the optimized scheme decrease the construction cost from original 11865 Yuan to 10472 Yuan of each linear meter. If the tunnel has length 1000 meters and the supporting cost will save 139,3000Yuan.
4861 5
Jiang Annan WenetZhiwu / Procedia Engineering (2011) 4857 – 4861 Jiangand Annan al / Procedia Engineering 0015 (2011) 000–000 Table.1 The results of Optimization compared with the results of original design
3. Conclusion The optimization of metro tunnel anchor and spray concerns not only surrounding rock stability but also economic cost. The paper has conclusions as follows. 1) The relation between anchor spray parameters and surrounding rock stability(limit displacement) has been gotten by three numerical simulation of orthogonal design schemes, orthogonal design method can get representative data set and as possible as decreasing numerical test numbers. Based on orthogonal numerical test results, the range analysis has been carried out to get the sensibility of anchor parameters affecting the surrounding rock stability. 2) In order to solve the problem of implicit nonlinear relation between anchor spray parameters and surrounding rock stability can not derivate and the conflict between stability and economic objectives, the paper proposed an optimization model with cost objective function and limit displacement constraint. And introduced the improved PSO to optimize the anchor parameters of metro tunnel. The regress function using ANN model replacing 3Dnumerical simulation, obviously improving calculation speed. 3）The proposed method has been applied in metro tunnel of Dalian City of China, and gets satisfied results, which states that the method is feasible. The optimized parameters of anchor and spray have important guiding meaning for the engineering. Acknowledgement The authors deeply appreciate support from Fundamental Research Funds for the Central Universities(2011JC012), Liaoning Province Education Department Fund(L2010063) and the National Natural Science Foundation (51079010). References: [1] ZHOU Weiyuan, YANG Qiang. Rock mechanics numerical calculation method. Beijing: China Electric Power Publishing Press, 2005. [2] C.Sagasseta. A general analytical solution for the required anchor force slopes with toppling failure .Int J.Rock Mech.Min.Science.2001(3):421-435. [3]Shi Y H,Eberhart R C.A modified particle swarm optimizer. IEEE World Congress on Computational Intelligence. Anchorage,1998.69-73. [4]Eberhart R C,Shi Y H. Comparing inertia weights and constriction factors in particle swarm optimization. Proc 2000 Congress Evolutionary Computation. Piscataway:IEEE Press,2000.84-88. [5]Yuan Z F, Zhou J.Y, Multivariate statistical analysis，Science Press，2002，10.
optimized scheme original design
Length of Anchor(m)
Distance of anchors (m)
Diameter of anchor(mm)
Spray layer thickness(cm)
Supporting Cost(Yuan)
2.3 3.0
0.7 1.0
20 25
30 30
10472 11865
Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 4857 – 4861 www.elsevier.com/locate/procedia
Optimizing Supporting Parameters of Metro Tunnel Based on Improved Particle Swarm Optimization Arithmetic Jiang Annan, Wen Zhiwu Highway and Bridge Engineering Institute,Dalian Maritime University, Dalian, China
Abstract The optimization of anchor and spay layer parameters of tunnel not only concerns the stability of surrounding rock, but also concerns the economic cost. Aiming to the implicit nonlinear relation between anchor parameters and surrounding rock stability, and the contradiction of stability object and economics object. The paper proposed a anchor parameters optimization method based on improved particle swarm optimization arithmetic and orthogonal designing scheme numerical test. The method firstly analyzed the sensibility of anchor parameters affecting surrounding rock stability and regressed function using numerical test data, then the limit displacement of surrounding rock is acted as the stability constraint condition and the cost function is as evaluation function, and the improved PSO is carried out. The method is used in metro tunnel of Dalian City of China, the result is good which states the method is feasible.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011] Key words: Metro tunnel; Anchor parameter optimization; orthogonal designing; particle swarm optimization;
1. Introduction Underground space development is closely relate to the nation economic development, the utilization of underground space extends to each field of society. However, geological body is a complex media and structure, having anisotropic, discrete, nonlinear and complex load-unload conditions, After excavation, the initial balance state is destroyed, the stress of surrounding rock changed complexly. While the surrounding rock deform and loosen zone developed too much, the collapse should be occurred[1]. Rock anchor is the main supporting mean of tunnel construction, it has vital function to change the surrounding rock from load to bearing ring, maximally take the self-supporting action, guarantee the stability of the surrounding rock.. Spray also is used cooperating anchor supporting, which keeps the
* Corresponding author. Tel.:13504110548; fax: +0-411-84724290. E-mail address:[email protected]
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.906
4858 2
Jiang Annan andetWen Zhiwu / Procedia Engineering (2011) 4857 – 4861 Jiang Annan al/ Procedia Engineering 00 (2011)15000–000
whole surrounding rock integrating. Anchor and spray associated supporting mean is the sign of modern tunnel construction theory, and is the main content of famous new Austrian tunnelling method[2]. The conventional supporting parameters selection generally relies on experience and norm, which is affected by human factor easily. The experience formula also is difficult to express the relation between parameters and rock stability. Because of the complexity of anchoring mechanism, the analytical formula adopts too many assumed conditions, it has large error. The paper proposed an optimization method of parameters of anchor and spray, synthetically considering the objects of surround rock stability and cost. The anchor spray parameters optimization method based on improved PSO. 1.1. The improved PSO PSO is a global optimization method proposed by Kennedy and Eberhart [3.4] in order to solve nonlinear global optimization objective. Each solution of the optimization problem is deemed as a particle, something like a bird. In addition, each particle has the fitness value decided by optimization function in PSO, and the velocity determines its direction and distance. The two extreme values are to be tracked by the particles in each iteration. The first point is the optimal solution in all the particles by all the searching history, i.e. the global optimal solution gbest, gbest=[g1,g2,……,gn]. The second point is the optimal solution of each particle in the experience of itself, i.e. individual optimal solution pbest, pbesti=[pi1,pi2,……,pin]. The Ith particle is expressed by xi=[xi1,xi2,……,xin], The kth correction(particle velocity) is vik=[vi1k,vi2k,……,vink]. The iteration formulas are as follows.
vidk = wi vidk −1 + c1 × rand1 × ( pidk −1 − xidk −1 ) + c 2 × rand 2 × ( g dk −1 − xidk −1 )
xidk = xidk −1 + vidk
(1) (2)
where i=1,2,……,m; d=1,2,……,n. m is the number of the particles in the swarm, n is the dimension number of the solution vectors, c1 and c2 are respectively two positive constants, rand1 and rand2 is random numbers between zero and 1 respectively. wi is the inertia weight. In order to improve the performance of particle swarm optimization, adjust inertia weight according to the equation as follows [11].
⎛ ⎛ k − 1 ⎞n ⎞ ⎟ w = w0 ⎜1 − ⎜ ⎜ ⎝ k ⎟⎠ ⎟ ⎝ ⎠
(3)
where w0 is a given constant, k is the number of flights, n is a constant. 1.2. The anchor spray parameters optimization procedure. Anchor and spray parameters optimization is actually a multi-objective optimization problem, and these objectives are incompatible, ie if the decrease the parameters the cost will decrease, but the stability of surrounding rock stability will be affected. In order to solve the incompatible objectives, the stability objectives changed to constraint condition, which is expressed as limit displacement. The optimization problem is described as follows. min f ( X ) s.t g i ( X ) < g i 0
(4)
Jiang Annan WenetZhiwu / Procedia Engineering (2011) 4857 – 4861 Jiangand Annan al / Procedia Engineering 0015 (2011) 000–000
In formula, min means the optimization adopts objective function as minimal value. X is the parameters of anchor and spray, including anchor diameter, anchor length, distance of anchors and spay thickness etc. gi(x) is the constraint index corresponding the stability criterion, in this paper it means the deform of surrounding rock. gi0 means the limit deform of the surrounding rock. It is selected because the construction monitoring also generally obtain the convergence deform of rock, the limit deform can reflect the rock stability well. The datasets take the X (x1, x2, x3, x4 ) as input, take deform of surrounding rock as output parameter. There are many functions can be used for the relation, through test calculation, the vertical convergence displacement AD and horizontal convergence displacement BC are respectively listed as follows. The limit deform of surrounding rock is ascertained by experience and norm. Then the formula (4) is optimized by improved PSO, the anchor and spray parameters should be optimized. The optimization procedure is shown in Fig.1.
Fig.1 The parameters optimization procedure.
2. Engineering application 2.1. Engineering introduction The studied engineering of Dalian City metro tunnel is excavated by boring burst method and underhand bench construction method, the section has horseshoe shape, the excavation span is 6.3m and the height is 8m. The buried depth is 12m, the surrounding rock mainly is rotten slate. The initial stress is self weight stress. The mechanics parameters of anchor and spray are not to be optimized. In the numerical model, the parameters are adopted as follows: The elastic modulus of anchor is 45 GPa, the maximal tension strength is 250kN, the rigidity of sand grout of each unit length is 17.5MPa, the cohesion of cement grout of each unit length is 2×105N/m. For spray layer, the elastic modulus is 6GPa, the density is 2200kg/m3. The numerical model and the convergence monitoring lines are shown in Fig.2. FLAC3D 3.00 Step 2364 Model Perspective 10:30:09 Tue Apr 26 2011 Center: X: 7.000e+000 Y: 1.550e+001 Z: 1.900e+000 Dist: 1.421e+002
A
Rotation: X: 0.000 Y: 0.000 Z: 0.000 Mag.: 1.25 Ang.: 22.500
Sketch
Magfac = 0.000e+000 Linestyle
cable Axial Force
Magfac = 0.000e+000 tension compression
C
B
Maximum = 2.146e+003
cable Grout Stress
Magfac = 0.000e+000 in (+) avg. axial-dir in (-) avg. axial-dir Maximum = 9.173e+003
cable Grout Slip
slipping now Itasca Consulting Group, Inc. Minneapolis, MN USA
D
4859 3
4860 4
Jiang Annan andetWen Zhiwu / Procedia Engineering (2011) 4857 – 4861 Jiang Annan al/ Procedia Engineering 00 (2011)15000–000 Fig.2 The anchoring model and monitoring arranging
2.2. Orthogonal design and sensitivity analysis The orthogonal test include 4 factors, they are anchor length l, anchor diameter d, distance of anchors s and the thickness D of spray layer. The scope of above parameters are as follows: l form 2.0m to 4.0m, d from 10 mm to 50mm, s from 0.7m to 1.1m, D from 15cm to 35cm. Design the orthogonal test table and combining parameters groups, carried out the three dimensional numerical simulation, get the displacements of AD and BC. The order of the four factors impacting the displacements of AD and BC is D, l, d and s. That states that thickness of spray layer affects surrounding rock most obviously, and it affects the vertical convergence line AD more obviously than BC. Relatively, the length of anchor length has more obvious affect than other parameters. According to the dataset from above orthogonal design scheme and numerical calculation, using least square method to regress the functions.The coefficients of regression models corresponding to formulas are not listed in the paper limited by paper length.. 2.3. The parameters optimization based on improved PSO Programming the code of improved PSO, set particles population as 50, set the iteration number as 30, the coefficient of momenta term is changing accord to w =0.3*(1-(k-1/k)2), c1=c2=2, running the program and optimized the results as follows: length of anchor is 2.27m, distance of anchors is 0.715m, anchor diameter is 20.4mm, the optimized parameters are roundly adopted as integers listed in Table 1. 240
FLAC3D 3.00 Step 4314 Model Perspective 10:03:37 Thu May 26 2011
w=0.2
190
Center: X: 7.000e+000 Y: 1.550e+001 Z: 1.900e+000 Dist: 1.421e+002
w=0.3 140
Rotation: X: 0.000 Y: 0.000 Z: 0.000 Mag.: 1.95 Ang.: 22.500
Contour of Z-Displacement
w dynamic adjusting
Magfac = 0.000e+000 -2.1504e-002 to -2.0000e-002 -2.0000e-002 to -1.7500e-002 -1.7500e-002 to -1.5000e-002 -1.5000e-002 to -1.2500e-002 -1.2500e-002 to -1.0000e-002 -1.0000e-002 to -7.5000e-003 -7.5000e-003 to -5.0000e-003 -5.0000e-003 to -2.5000e-003 -2.5000e-003 to 0.0000e+000 0.0000e+000 to 2.5000e-003 2.5000e-003 to 3.3465e-003 Interval = 2.5e-003
w=0.4 90 40 -10 0
10
20
30
40
Fig3. The PSO convergence with different w
Itasca Consulting Group, Inc. Minneapolis, MN USA
Fig4. The vertical displacement based on optimum scheme
The fitness values corresponding to different w according to the iteration is shown in Fig3. It is shown that in the PSO optimization process, the different coefficient of momenta term w affects the fitness value convergence velocity and precision, this paper adopts dynamic w according to formula (3) has better convergence velocity and precision than the content w. According to experience and norm, in the optimization process, the AD convergence limit displacement adopts 25mm, the BC convergence limit displacement adopts 3mm. Using the optimized parameters, numerically simulated the tunnel construction process, the vertical displacement of surrounding rock is shown in Fig.4. It is shown that the sedimentation of arc is larger than raising of floor. The maximum convergence of top and floor is about 24.8mm, less than the limit displacement. The optimized scheme and original design scheme are shown in Table 1 It is shown that the optimized scheme decrease the construction cost from original 11865 Yuan to 10472 Yuan of each linear meter. If the tunnel has length 1000 meters and the supporting cost will save 139,3000Yuan.
4861 5
Jiang Annan WenetZhiwu / Procedia Engineering (2011) 4857 – 4861 Jiangand Annan al / Procedia Engineering 0015 (2011) 000–000 Table.1 The results of Optimization compared with the results of original design
3. Conclusion The optimization of metro tunnel anchor and spray concerns not only surrounding rock stability but also economic cost. The paper has conclusions as follows. 1) The relation between anchor spray parameters and surrounding rock stability(limit displacement) has been gotten by three numerical simulation of orthogonal design schemes, orthogonal design method can get representative data set and as possible as decreasing numerical test numbers. Based on orthogonal numerical test results, the range analysis has been carried out to get the sensibility of anchor parameters affecting the surrounding rock stability. 2) In order to solve the problem of implicit nonlinear relation between anchor spray parameters and surrounding rock stability can not derivate and the conflict between stability and economic objectives, the paper proposed an optimization model with cost objective function and limit displacement constraint. And introduced the improved PSO to optimize the anchor parameters of metro tunnel. The regress function using ANN model replacing 3Dnumerical simulation, obviously improving calculation speed. 3）The proposed method has been applied in metro tunnel of Dalian City of China, and gets satisfied results, which states that the method is feasible. The optimized parameters of anchor and spray have important guiding meaning for the engineering. Acknowledgement The authors deeply appreciate support from Fundamental Research Funds for the Central Universities(2011JC012), Liaoning Province Education Department Fund(L2010063) and the National Natural Science Foundation (51079010). References: [1] ZHOU Weiyuan, YANG Qiang. Rock mechanics numerical calculation method. Beijing: China Electric Power Publishing Press, 2005. [2] C.Sagasseta. A general analytical solution for the required anchor force slopes with toppling failure .Int J.Rock Mech.Min.Science.2001(3):421-435. [3]Shi Y H,Eberhart R C.A modified particle swarm optimizer. IEEE World Congress on Computational Intelligence. Anchorage,1998.69-73. [4]Eberhart R C,Shi Y H. Comparing inertia weights and constriction factors in particle swarm optimization. Proc 2000 Congress Evolutionary Computation. Piscataway:IEEE Press,2000.84-88. [5]Yuan Z F, Zhou J.Y, Multivariate statistical analysis，Science Press，2002，10.
optimized scheme original design
Length of Anchor(m)
Distance of anchors (m)
Diameter of anchor(mm)
Spray layer thickness(cm)
Supporting Cost(Yuan)
2.3 3.0
0.7 1.0
20 25
30 30
10472 11865