Stability Analysis Of Surrounding Rock Of A Single Tunnel Using Discontinuity Layout Optimization

Stability problems are extremely important to geotechnical engineering because the information obtained from stability analysis demonstrates the degree of safety of geostructures.Recently,discontinuity layout optimization(DLO)becomes a potential numerical tool for performing stability problems.However,the application of the DLO in geotechnical stability problems is still limited.In this work,the stability analyses of surrounding rock of a single tunnel are analyzed using the DLO.The analyses are classified into three categories according to the differences in shape,angle of the ground surface,and joints.The entire problem is simulated by using the geotechnical analysis software LimitState:Geo under plane-strain conditions.Based on the parametric study and numerical investigations,the effects of the different parameters on the stability of the tunnel are discussed in detail,and the failure mechanisms of the tunnel obtained from the analyses are also presented.According to the results obtained from the analyses,some conclusions are drawn and highlighted as the following:(1)The stability and failure mechanism of surrounding homogeneous rock mass of a horseshoe-shaped,circular,or square tunnel is sensitive to the friction angle and dimensionless depth.The stability typically increases as the friction angle increases,but that decreases with the dimensionless depth of tunnel when φ’<35°.Therefore,the dimensionless depth does not have a significant influence on the stability whenφ’≥35°.In addition,the differences in the cross-sectional area due to the shapes also result in different stability.Indeed,the stability of the horseshoe-shaped tunnel is greater than the stability of the square tunnel,but it is smaller than that of the circular one.This is because of the differences in cross-sectional area.On the other hand,the failure mechanisms of this category are in symmetrical forms.With the same depth,the failure range gets larger in width as the friction angle decreases.With the same value of the friction angle,the failure range gets larger in both width and height as the dimensionless depth increases when φ’≤35°,but it almost remains the same in size with depth when φ’>35°.Furthermore,the development of collapse is affected by the shape of the tunnel as well.The failure mechanisms demonstrate that the collapse of the square shape always takes place at the corner for all cases of friction angle and depth.In contrast to the square shape,the collapse of the circular shape varies along the arch of the tunnel,related to the value of friction angle and dimensionless depth.(2)The behavior of the stability of surrounding homogeneous rock mass of a horseshoe-shaped tunnel in the case of the horizontal and the inclined ground surface is similar to each other only when β≤45°.In most cases,the influence of the dimensionless depth on the stability becomes less significant when β>45°.Generally,the stability of the tunnel decreases as the inclined angle of the ground surface increases.For cases with β≤45°,however,there are slight differences in the stability when the friction angle tends to be larger φ’>45°.In the case of the inclined ground surface,most of the failure mechanisms become asymmetry,and the failure range becomes larger as the inclined angle increases.(3)In the case of the horizontal ground surface,the behavior of the stability between surrounding jointed and homogeneous rock masses of the horseshoe-shaped tunnel is similar to each other for all cases of joint dip angle when joint spacing becomes wider s1≥ 9m.When joint spacing gets narrower s1≤6m,the dimensionless depth affects the stability of the tunnel when α1<45° with φ’≤25° but becomes less significant when α1>45°.In most cases,the stability of the tunnel typically decreases as the joint dip angle increases except in some cases especially when 60°≤α1≤90°.Furthermore,the increase or reduction in the value of joint spacing might not affect the stability when α1>45.On the other hand,the failure mechanisms of surrounding jointed rock mass of a horseshoe-shaped tunnel are in symmetrical forms when α1＝0 and 90°,and those are in asymmetry forms when 0<α1<90°.(4)The results of DLO is normally lower than the analytical upper bound limit analysis but higher than the finite element upper and lower bound limit analyses.The differences in result between the present study using DLO and the available literature using finite element upper bound limit analysis are relating to the quality of mesh generation and the mathematical optimization,linear or nonlinear programming,used in the methods.Although there are slight differences,the results of the present study are in good agreement with those from the available literature.