Analysis and calculation of additional stress in foundation soil due to tip resistance of Y-shaped vibro-pile

The section of Y-shaped vibro-pile is complicated; its geometric characteristics has four independent variables and eight integral zones. It is difficult to achieve the expression of analytical solutions for additional stress coefficient at random point in the ground when the uniform tip load of the Y-shaped section acting in the ground; therefore, so far simple analytical solution hasn't been solved yet. Using the integral function NIntegrate of Mathematica software and referencing the idea from Geddes stress solution, the numerical computational method for vertical additional stress coefficient at random point in the ground under the uniform tip load of Y-shaped vibro-pile was achieved; and it is accurate according to the verification. The influences of four independent variables, R, θ, s, δ of Y-shaped section on vertical additional stress coefficient due to uniform tip load and errors produced by Geddes stress solution were analysed. The difference and regular in vertical additional stress coefficient at section center in the ground under the uniform tip load of Y-shaped, triangular, rectangular, quadrate, circular, annular, H, and T-shaped section were analyzed along with the change of acreage and calculation deepness. The additional stress calculation method in which the section shape of Y-shaped vibro-pile is considered was used in settlement calculation of single pile. The calculation result is consistent with the data of static loading test.