Three-dimensional stability study of tunnel surrounding rocks induced by a concealed karst cave based on spatial discretization technique

When a proposed tunnel is located in close proximity to a concealed karst cave，the superimposed effects of construction disturbance and cave pressure may lead to the collapse of the rock mass situated between the tunnel and the karst cave. This study constructs a three-dimensional failure mechanism for the rock mass of the tunnel roof，taking into account the failure characteristic associated with the concealed karst cave existing above. The spatial discretization technique and upper bound theorem are employed to develop this failure mechanism. Utilizing the constructed failure mechanism，the stability number of the rock mass is proposed，with the objective function derived from calculating the internal and external energy consumption of the failure mechanism. The upper bound solution for the stability number and the corresponding three-dimensional collapse surface of the rock mass are obtained through optimization calculations. By comparing the stability numbers and collapse surfaces derived from theoretical analysis with results obtained from numerical simulations and model tests，the validity of the proposed theoretical approach is validated. Parameter analysis indicates that the stability number of the rock mass decreases with the increase of the geological strength index(<italic>GSI</italic>)，material constant of the rock mass(<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mtext>i</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)，the distance between karst cave and tunnel(<italic>H</italic>)，and unit weight of the rock mass(<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi></mml:math></inline-formula>)，while it increases with the increase of cavity pressure(<italic>T</italic>).