Study On Punching Shear Failure Mode Of Cave Roof In Karst Area Under Different Eccentric Distance

Basing on the influencing factors of the roof stability of the buried karst,this paper discusses the quantitative analysis method of the commonly used karst roof failure mode,and analyzes the shortcomings of the existing shear model and the bending model to analyze the failure mode of karst roof.The parabolic more theory is based on the functional analysis of the limit analysis method to solve the failure mode of the concealed circular karst roof.Then the failure mode of concealed circular karst roof under a certain eccentric pile end load is analyzed,and the method of elliptical concealed karst to circular karst approximate transformation is proposed.Finally,the horizontal elliptical karst roof is analyzed when the eccentricity is not zero.Destruction mode.The feasibility of the model is verified by the finite element numerical analysis method and the actual engineering verification method.The main conclusions are:?1?When the influence of water body,gas,stratum structure and ground stress is not considered,the damage of karst roof is affected by the compressive tensile strength,roof thickness,eccentricity,karst length and thickness of the karst,and the thickness of the roof.The failure mode is determined by the diameter of the bottom end of the blanking body of the boundary condition and the vertical distance from the end of the pile at the farthest end of the punching body.?2?Calculating and deriving the punching failure body when the roof of the karst area is punched and destroyed is not a trapezoidal frustum,but the bus bar is a rotary punching body whose shape is an exponential function curve.The shape of the bus bar r?x?is controlled by d₁/d.When 0<d₁/d<1,the rupture body is an inverted cone,and it is impossible to cause damage due to the constraint of the surrounding rigid body.When1<d₁/d<a/d,there is a punching failure of the hidden karst roof,wherein when d₁/d tends to 1,it is a shear failure mode.When d₁/d tends to a/d,the broken cone busbar is an exponential function curve,and its damage influence range tends to the entire karst overlying roof.?3?The failure mode analysis function of the circular karst roof when the eccentricity is not zero and the approximate transformation method of the elliptical karst to circular karst transformation when the eccentricity is zero are given,and the radius of the circle is proposed for the convenience of engineering.And the concept of the angle of destruction of the circle,finally proposed the failure mode analysis function of the elliptical karst roof when the eccentricity is not zero.?4?Establish the functional relationship between the influencing factors.By solving the partial differential equation,the ultimate bearing capacity of the roof,the minimum safe thickness of the roof,the radius of the circle,the angle of destruction of the circle and the body of the punching body can be solved.The bus equation.