Error in Ito and Matsui’s Limit-Equilibrium Solution of Lateral Force on a Row of Stabilizing Piles

Stabilizing piles are commonly employed as an effective approach for slope or landslide stabilization. The limit equilibrium solution of a pile force acting on a row of stabilizing piles proposed by Ito and Matusui (1975) has been widely adopted by researchers to develop a general method of stability analysis for a slope reinforced by piles, such as the friction circle method (Hassiotis et al. 1997), the upper bound limit analysis (Li et al. 2012), and others. Thus far, the accuracy of Ito and Matsui’s solution has not been investigated despite its numerous applications in research and practice.

This abstract evaluates the accuracy and validity of Ito and Matusui’s solution by employing the powerful finite element limit analysis (FELA) in OptumG2 software, as shown in Fig. 1. The problem of a soil gap ($S$) squeezed between a row of stabilizing rigid piles with a diameter ($D$) by a pressure ($p$) at the top boundary, similar to that of Ito and Matusui, is considered, wherein the plane strain condition is assumed in the direction of the pile depth. A cohesive-frictional weightless soil with cohesion ($c$) and friction angle ($\varphi$), obeying Mohr–Coulomb yield criterion with an associated flow rule, was considered. The interface roughness between the soil and pile was taken to be 0.67. The limiting pressure ($p$) on top of the boundary was optimized in FELA, and parametric studies were performed for $\varphi =0–40°$ and a soil gap ratio ($S/D$) of 0.1–3.0. The vertical force equilibrium was employed to directly calculate the lateral force acting on a pile per unit length ($F$) by considering a free-body diagram of one pile with half of the soil gaps in each side of the pile as $F=p(S+D)$. Fig. 1 compares the normalized pile force ($F/cD$) between FELA and Ito and Matusi. Clearly, the solution provided by Ito and Matusi generally failed to give a reasonable prediction of the pile force for all ranges of soil friction angles and soil gap ratios. In particular, it significantly underestimated $F/cD$ for a large $S/D$ and largely overestimated $F/cD$ for a small $S/D$. The degree of underestimation of the pile force increased with the friction angle of soil.

A new approximate solution of $F/cD$, shown in Eq. (1), is proposed by curve-fitting all computed lower bound solutions, with a coefficient of determination ($R^2$) of 99.95%, to supersede Ito and Matusi’s solution in research and practicewhere $a_1=5.8820$; $a_2=3.0265$; $a_3=0.05439$; $a_4=11.2633$; $a_5=1.5275$; and $a_6=0.8573$.