SMT-GP method of prediction for ground subsidence due to tunneling in mountainous areas

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Abstract

This paper introduces a new analysis method – stochastic medium technique (SMT) combined with genetic programming (GP) in the prediction of ground subsidence due to tunneling in mountainous areas. The methodology involves the use of stochastic medium theory to generate theory models and to predict ground subsidence due to tunneling in mountainous areas. The parameters in the theory models which are optimized by genetic programming. The use of the integrated methodology is demonstrated via a case study in the prediction of ground subsidence due to tunneling in mountainous areas in Hebei, North China. The results show that the integrated stochastic medium technique – genetic programming (SMT-GP) gives the smallest error on the ground subsidence data when compared to traditional finite element method. The SMT-GP method is expected to provide a significant improvement when the ground subsidence data come from mountainous areas. The agreement of the theoretical results with the field measurements shows that the SMT-GP is satisfactory and the models and SMT-GP method proposed are valid and thus can be effectively used for predicting the ground surface subsidence due to tunneling engineering in mountainous areas and urban areas.

Highlights

► Stochastic medium combined with genetic programming in the subsidence prediction. ► The parameters in the theory models which are optimized by genetic programming. ► GP uses continuous functions when applied to the prediction of theory parameters. ► SMT-GP technique can improve upon more traditional analysis techniques. ► SMT-GP calculations are much closer to measured points than FEM predictions.

Introduction

Tunneling causes the formation of a surface subsidence trough. The prediction of the consequences of tunneling is an important task for the engineering surveying service (Liu, 1993, Li, 1998, Yang et al., 2004). The knowledge about the surface activity caused by tunneling, and the prediction of subsidence enable efficient repairs of the tunneling damage, and has a positive impact on the economic results of tunneling. Accurate and reliable prediction can, beside other factors, influence significantly the strategy of the operation of the tunnel.

The stochastic medium theory method was proposed by Litwiniszyn in 1957. The stochastic medium theory method was extended to predict the surface subsidence caused by tunneling and underground mining in flat ground (Li, 1983, Liu, 1993, Li et al., 2010). According to the stochastic medium theory method, the ground surface subsidence of tunneling on stratum equals the sum of subsidence of numerous infinitesimal elements due to tunnel excavation. With the stochastic medium theory method as a basis, the ground surface subsidence caused by tunneling, can now be described. In this research, the applications of stochastic medium theory to estimate and predict ground subsidence due to tunneling in mountainous areas are presented.

However, it is difficult to determine all the engineering parameters (ground subsidence parameters) in stochastic medium theory formulae, and it is even more difficult to determine their relative impact. Due to a large number of parameters influencing the behavior of the rock above the excavated space, the prediction of ground subsidence and engineering parameters is a demanding task. The determination of ground subsidence parameters is a complex problem, which is related with several factors. Genetic programming (GP) has a good ability to deal with complex and nonlinear problems, and therefore the genetic programming (GP) approach is proposed to predict engineering parameters in this article.

This paper introduces a new stochastic medium technique combined with genetic programming in the prediction of ground subsidence due to tunneling in mountainous areas. The methodology involves the use of stochastic medium theory to generate theory models and to predict ground subsidence due to tunneling in mountainous areas. The parameters in the theory models are optimized by genetic programming. The use of the integrated methodology is demonstrated via a case study in the prediction of ground subsidence due to tunneling in mountainous areas in Hebei, North China.

In this paper, the applications of stochastic medium theory (SMT) and genetic programming (GP) to estimate and predict ground subsidence due to tunneling in mountainous areas are presented. Based on results of the statistical analysis of a large amount of measured data in tunneling engineering, the genetic programming method of determining engineering parameters is given by using the theory of genetic programming and GP approach is proposed to determine the engineering parameters and ground surface subsidence due to tunneling in mountainous areas. Genetic programming is trained by using tunneling engineering data.

In this research, the applications of stochastic medium theory (SMT) to predict ground subsidence due to tunneling in mountainous areas and urban areas are presented. And the engineering parameters in SMT formulae are obtained by using the GP. And so, the “SMT-GP” method of prediction for ground subsidence due to tunneling in mountainous areas and urban areas is proposed in this paper (see Fig. 1).

Genetic programming (GP) has been applied to many fields in which engineering parameters prediction are present as, for example, in rock and soil engineering. GP is a novel global, random searched, and optimized technique (Li and Kou, 2001, Yun, 2000, Yun and Wang, 1997, Kim et al., 2001) which is based on the principle of biology and evolution. It is imitative of chromosomes to express problems, and it is based on the Darwinian principle of “survival of the fit test” through the operation of selection, crossover and mutation, therefore the random generated initial population can approach the optimized solution step by step.

Based on results of the statistical analysis of a large amount of measured data in tunneling engineering, the genetic programming (GP) method of prediction of ground subsidence parameters is given by using the theory of GP. In this paper, GP is given to determine the engineering parameters in SMT formulae, and the SMT-GP method is proposed to predict ground subsidence due to tunneling in mountainous areas and urban areas.

Section snippets

The stochastic medium theory model of ground subsidence due to tunneling in mountainous areas

It is difficult to calculate the accurate subsidence of every point in a body of rock because of the complexity of the problem. Instead, various approximate methods have been used for this calculation. In recent years, in tunneling engineering, theories of fuzzy mathematics and artificial neural networks (ANN) have been applied to analyze the problems of ground surface subsidence due to tunneling (Li, 1998, Kim et al., 2001, Li et al., 2007). Ground subsidence is a major problem associated with

Prediction for tangent of primary influence angle β

The independent variables, hardness factors of rock (X1), wall rock classification (X2), the ratio of excavation width and depth (X3), excavation methods (X4), the dip angle of rock strata (X5), the height of tunnel (X6), the ratio of excavation depth and height of tunnel (X7) are chosen in the genetic programming model.

Training samples are shown in Table 1 and the parameters of GP are provided in Table 2, after training of genetic programming, the best trees obtained are shown in Fig. 8.

The

Engineering example 1: Hanjiazhuang section of Bao-Fu highway tunnel, Hebei, China

The Hanjiazhuang tunnel was excavated in Bao-Fu highway of North in China. The tunnel crosses the Taihang Mountain Range rock mass; it is located at an average depth 42 m (the maximum expected depth is 120 m approximately) and comprises two parallel tunnels (called “left line” and “right line”), with 16 m diameter, excavated with a distance center to center of 90 m (from “left line” to “right line”). Main conditions of Hanjiazhuang tunnels are given in Table 3.

The topography in the district is

Discussion

The results obtained using the SMT-GP method, are compared to the subsidence profiles that were generated by the FEM (ANSYS software) calculations (Fig. 17, Fig. 21, Fig. 25). Results for subsidences indicate that SMT-GP calculations are much closer to measured subsidence points than FEM predictions.

This paper presents the SMT-GP method for the prediction of the tunneling-induced ground deformation in homogeneous and jointed rock mass. The SMT-GP model is combined with the method to consider

Conclusions

In this paper, SMT-GP method was used to predict ground surface subsidence due to tunneling. Our conclusions can be summarized as follows:

  • (1)

    SMT-GP method is highly accurate when compared to the results obtained with other more traditional methods – finite element method (FEM) (see ground subsidence curves in Fig. 17, Fig. 21, Fig. 25). Results for the subsidences indicate that SMT-GP calculations are much closer to data points than FEM predictions.

  • (2)

    Although supplied with 11 input parameters, GP

Acknowledgements

The Project Supported by Natural Science Foundation-Steel and Iron Foundation of Hebei Province is gratefully acknowledged (No. E2011201114). The efforts of all members of the Hebei Jianshe Construction Group Co. Ltd. involved in this project, and their respective support staff in collecting and processing the extensive quantity of data from the monitoring program, is acknowledged. The authors wishes to thank Dr. Raymond Leslie Sterling for reading the manuscript.

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