A Three-Dimensional (3D) Semi-analytical Solution for the Ultimate End-Bearing Capacity of Rock-Socketed Shafts

Semi‐analytical solution for ultimate bearing capacity of smooth and rough circular foundations on rock considering three‐dimensional strength

“…Considering the failure criterion in Equation ( 1) and the relation between different stress components in Equation (5) under the axisymmetric condition, the newly modified GZZ criterion under the axisymmetric condition is further simplified and expressed by two Lambe parameters 𝑝 L and 𝑞 L as 22 𝑓 NMGZZ = 𝐹 (𝑝 L , 𝑞 L )…”

“…The differential equations of the two groups of characteristic lines in the failure mesh are: $$$$\begin{equation} { \frac{{{\mathrm{d}}r}}{{{\mathrm{d}}z}} = \tan \left( {\psi \pm \omega } \right) } \end{equation}$$$$ $$$$\begin{equation} {\omega = \frac{\pi }{4} - \frac{\rho }{2}} \end{equation}$$$$where Equation (10a) with “+” and “−” sign governs the $${{\alpha}}$$ and β characteristic lines, respectively; $$\rho $$ = instant friction angle of rock mass; and $$\omega $$ is self‐evident. Following Chen et al 22 $$$$\begin{equation} {\displaystyle \sin \rho = \frac{{{\mathrm{d}}{q}_{\mathrm{L}}}}{{{\mathrm{d}}{p}_{\mathrm{L}}}} = \frac{{{\mathrm{d}}{\sigma }_1 - {\mathrm{d}}{\sigma }_3}}{{{\mathrm{d}}{\sigma }_1 + {\mathrm{d}}{\sigma }_3}} = \frac{{1 - {{\mathrm{C}}}_{13}}}{{{{\mathrm{C}}}_{13} + 1}}} \end{equation}$$$$ …”

“…Considering the failure criterion in Equation (1) and the relation between different stress components in Equation (5) under the axisymmetric condition, the newly modified GZZ criterion under the axisymmetric condition is further simplified and expressed by two Lambe parameters $${p}_{\mathrm{L}}$$ and $${q}_{\mathrm{L}}$$ as 22 $$$$\begin{equation} { {f}_{{\mathrm{NMGZZ}}} = F\left( {{p}_{\mathrm{L}},{q}_{\mathrm{L}}} \right)} \end{equation}$$$$where $$$$\begin{equation} { {p}_{\mathrm{L}} = \left( {{\sigma }_1 + {\sigma }_3} \right)/2 } \end{equation}$$$$ $$$$\begin{equation} { {q}_{\mathrm{L}} = \left( {{\sigma }_1 - {\sigma }_3 } \right)/2 } \end{equation}$$$$…”

Modification of bearing capacity of rock-socketed pile: considering concrete-rock interface roughness and gravity stress of concrete

“…A machine learning method is also used to predict the bearing capacity of rock-socketed piles [3]. The three-dimensional semi-analytical solution of the ultimate bearing capacity of the rocksocked shaft was given by Chen et al [5], and the correctness of the analytical solution was verified by 8 test piles. Although the roughness has a great influence on the bearing capacity of rock-socketed piles, the calculation of the ultimate bearing capacity of rock-socketed piles in the current pile design code and still only considers the compressive strength of rocks, and the influence of roughness and concrete gravity stress is also ignored.…”

Influence of Humic Acid on the Strength of Cement‐Soil and Analysis of Its Microscopic Mechanism

“…e cement-soil mixing method is a mature technology for the treatment of soft soil foundation, which has the advantages of less impact on the surrounding environment, exible reinforcement form, and low cost [1][2][3][4][5][6]. Cement-soil had better strength properties than the original soil [3].…”