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A Study on the time-dependent character of surrounding rock deformation of a test tunnel
Tunnelling and Underground Space Technology incorporating Trenchless Technology Research
Tunnelling and Underground Space Technology 19 (2004) 414
www.elsevier.com/locate/tust
WTC 2004
A study on the time-dependent character of surrounding rock deformation of a test tunnel Yang Linde a
a,*
, Yan Jianping a, Wang Yuezhao
b
Department of Geotechnical Engineering, Tongji University, Shanghai, 200092, P.R.China b Yixing Hydro-Power Corporation, Jiangsu, 214206, P.R.China
Since the underground hydro-power station usually has several parallel large caverns and the geological condition is often very complex, a test tunnel is often excavated to measure its deformation that developed with time, by which the initial rock stresses and the time-dependent properties of rock mass can be determined by back analysis, the displacement and stability of the surrounding rock can be estimated. Theoretically, based on the assumptions that the behavior of the surrounding rock of the tunnel conforms to the rule of Kelvin–Voigt model, that the stress boundary condition and drainage situation keep to be invariable and that the Poisson’s ratio is a constant, the calculation for 2-D plane strain visco-elastic problem in the homogeneous ground at any moment can be simplified as the analysis of 2-D elastic problem if the equivalent elastic modulus ðEt Þi at t ¼ ti is used to take the place of Young’s modulus in elastic formula, so that we have
ðEt Þi fugi ¼ ðEt Þiþ1 fugiþ1 ; E 1 1 1 2t ¼ þ 1 e g2 i ; ðEt Þi E1 E2
ð1Þ ð2Þ
where ðEt Þi and ðEt Þiþ1 are the equivalent elastic modulus at t ¼ ti and t ¼ tiþ1 , respectively, fugi and fugiþ1 are the relevant displacement matrix, E1 , E2 , g2 are parameters of Kelvin–Voigt model. Based on the measured data from the test tunnel and assuming E1 E0 , E2 and g2 can be determined by back analysis. Consequently, the deformation of surrounding rock caverns can be predicted. In order to consider the space effect of excavation face, the measured data of muti-extensometers installed after excavation should be revised. The coefficient of revision can be denoted as g and expressed as
g¼
1 ; 1n
ð3Þ
where n is the release coefficient of deformation, n ¼ d=D; d is the displacement value before excavation face arriving at the measuring section; D is its maximum in total. The total displacement values should be treated by regression to get the expressions of displacement–time curves. Finally, a case study is performed, which shows that the predicted displacements of surrounding rock are close to the measured and the parameters of Kelvin–Voigt model of surrounding rock by the method are approximate to that by using the method in [1]. The F test to check the error between measured and predicted values is also performed. The results show that they are close to each other remarkably when the significance level is chosen as 0.05. Therefore, the method can simulate the behavior of surrounding rock very well and can be adopted in practice. Keywords: Creep; Visco-elastic model; Surrounding rock deformation prediction; Back analysis
*
Corresponding author: Tel.: +86-21-6598-3982; fax: +86-21-6598-5210. E-mail address: [email protected] (Y. Linde).
doi:10.1016/j.tust.2004.02.033
Tunnelling and Underground Space Technology 19 (2004) 414
www.elsevier.com/locate/tust
WTC 2004
A study on the time-dependent character of surrounding rock deformation of a test tunnel Yang Linde a
a,*
, Yan Jianping a, Wang Yuezhao
b
Department of Geotechnical Engineering, Tongji University, Shanghai, 200092, P.R.China b Yixing Hydro-Power Corporation, Jiangsu, 214206, P.R.China
Since the underground hydro-power station usually has several parallel large caverns and the geological condition is often very complex, a test tunnel is often excavated to measure its deformation that developed with time, by which the initial rock stresses and the time-dependent properties of rock mass can be determined by back analysis, the displacement and stability of the surrounding rock can be estimated. Theoretically, based on the assumptions that the behavior of the surrounding rock of the tunnel conforms to the rule of Kelvin–Voigt model, that the stress boundary condition and drainage situation keep to be invariable and that the Poisson’s ratio is a constant, the calculation for 2-D plane strain visco-elastic problem in the homogeneous ground at any moment can be simplified as the analysis of 2-D elastic problem if the equivalent elastic modulus ðEt Þi at t ¼ ti is used to take the place of Young’s modulus in elastic formula, so that we have
ðEt Þi fugi ¼ ðEt Þiþ1 fugiþ1 ; E 1 1 1 2t ¼ þ 1 e g2 i ; ðEt Þi E1 E2
ð1Þ ð2Þ
where ðEt Þi and ðEt Þiþ1 are the equivalent elastic modulus at t ¼ ti and t ¼ tiþ1 , respectively, fugi and fugiþ1 are the relevant displacement matrix, E1 , E2 , g2 are parameters of Kelvin–Voigt model. Based on the measured data from the test tunnel and assuming E1 E0 , E2 and g2 can be determined by back analysis. Consequently, the deformation of surrounding rock caverns can be predicted. In order to consider the space effect of excavation face, the measured data of muti-extensometers installed after excavation should be revised. The coefficient of revision can be denoted as g and expressed as
g¼
1 ; 1n
ð3Þ
where n is the release coefficient of deformation, n ¼ d=D; d is the displacement value before excavation face arriving at the measuring section; D is its maximum in total. The total displacement values should be treated by regression to get the expressions of displacement–time curves. Finally, a case study is performed, which shows that the predicted displacements of surrounding rock are close to the measured and the parameters of Kelvin–Voigt model of surrounding rock by the method are approximate to that by using the method in [1]. The F test to check the error between measured and predicted values is also performed. The results show that they are close to each other remarkably when the significance level is chosen as 0.05. Therefore, the method can simulate the behavior of surrounding rock very well and can be adopted in practice. Keywords: Creep; Visco-elastic model; Surrounding rock deformation prediction; Back analysis
*
Corresponding author: Tel.: +86-21-6598-3982; fax: +86-21-6598-5210. E-mail address: [email protected] (Y. Linde).
doi:10.1016/j.tust.2004.02.033