Study On Vertical Bearing Capacity At The Tip Of Shallow Rock-Socketed Pile In Inclined Rocks Based On Limit Analysis

With the rapid development of transportation infrastructure in China,the construction of roads,bridges and other infrastructures in mountainous areas are steadily boosted.A great number of bridge piles are built in inclined rock slopes.The bearing mechanism of rock-socketed pile on inclined rock surface is complicated,and the related theoretical research lags behind the engineering practice.At present,there is no appropriate method to calculate the bearing capacity at the tip of rock-socketed pile in inclined rocks,and the influence of the inclined rock surface is not considered in most pile foundation design codes.In view of the above background,this thesis utilizes the limit analysis method to derive the upper bound solution for vertical bearing capacity of shallow rock-socketed pile tip in inclined rocks.The proposed method’s accuracy is validated through comparative analysis with the characteristic line method and numerical techniques,and the application range of the upper bound solution for bearing capacity of pile tip is defined.Consequently,this thesis presents a calculation method for the determination of the bearing capacity of pile tip in inclined rocks.The main research work is outlined as follows:(1)Based on the limit analysis method,a multi-wedge translation failure mechanism at the tip of piles embedded in flat rocks is firstly established.Instead of the modified Hoek-Brown failure criterion,a tangential line is employed to calculate the external work rate and the internal energy dissipation rate.This transforms the solution for bearing capacity of pile tip into a nonlinear programming problem of minimizing the objective function,and the optimal upper bound solution for the ultimate bearing capacity of shallow rock-socketed pile tip is obtained.The influence law of the Geological Strength Index(GSI)and rock mass disturbance coefficient on bearing capacity of pile tip is analyzed.Besides,the upper bound values of bearing capacity of shallow rock-socketed pile tip for different types of rocks are given.The results indicate that the bearing capacity at the tip of a shallow rock-socketed pile increases with the increase of the embedment ratio.When the embedment ratio reaches the limit embedment ratio,the pile tip reaches its ultimate bearing capacity.Further increases in the embedment ratio do not affect the bearing capacity of pile tip.The bearing capacity of pile tip increases as a power function with the increase of the GSI and decreases linearly with the increase of rock mass disturbance coefficient.(2)Based on the upper bound theorem of limit analysis,a nonsymmetrical failure mechanism composed of a single radial shear zone is established,according to the section shape of inclined rock surface.The optimization process is employed to calculate the upper bound solution for bearing capacity of shallow rock-socketed pile tip in inclined rocks.To verify the correctness of the theoretical model,a calculation model is established using Plaxis3 D finite element software,and the numerical results are compared with the theoretical calculation values.The influences of the embedment ratio,the GSI and the disturbance coefficient on bearing capacity are investigated under different inclined slope angles.The results reveal that for slope angle less than 40°,the upper bound solution appears more accurate,with an error less than 15% when compared to the numerical solution.When the slope angle exceeds 40°,the error grows rapidly.(3)Applying the characteristic line method,the ultimate bearing capacity formula for shallow rock-socketed pile tip in inclined rocks is derived based on the modified Mohr-Coulomb criterion.This approach considers the ease of obtaining Mohr-Coulomb strength parameters.Influences of factors such as the slope angle,the GSI and the friction angle on the bearing capacity of pile tip are analyzed.The results show that when the embedment ratio exceeds the limit embedment ratio,the load factor for the bearing capacity of pile tip remains unaffected by the slope angle,which can be calculated and analyzed according to a pile in flat rocks.The limit embedment ratio increases as a power function with the increase of the slope angle.In cases where the rock integrity is poor,the limit embedment ratio experiences a significant increase with an increase in the friction angle.When the limit embedment ratio is not reached,the load factor of pile tip decreases significantly with the increase of the slope angle.Under such circumstances,it is essential to consider the influence of the inclined rock surface and calculate the bearing capacity of pile tip using the formula designed for inclined rocks.The research can provide theoretical guidance for the calculation of bearing capacity of rock-socketed piles in inclined rocks.