Nonlinear Response of Lateral Piles with Compatible Cap Stiffness and p-Multiplier

Abstract

Response of lateral pile groups is modeled using the more accurate (than any other numerical modeling) p − y curves-based load transfer model. It is essentially underpinned by limiting force per unit length pmpu, modulus of subgrade reaction pmk, and p-multiplier pm (to cater for pile-pile interaction, pm ¼ 1 for single piles). With the model, new closed-form solutions are developed incorporating the cap-rotational stiffness kr. The solutions are presented in nondimensional charts for free-head (kr ¼ 0) through fixed-head (kr > 10 times the pile bending stiffness). The study reveals that the existing pm (bearing no link to the stiffness kr) is inconsistent with pm ¼ 0.25 for capped piles (at limiting state of elastic solutions). This casts doubt about the accuracy of available solutions, and a compatible stiffness kr and pm is required. The compatible normalized stiffness knr is equal to 0.275-0.333 (n ¼ 0.7) and 0.333-0.564 (n ¼ 1.7) for the associated pm at the design level of (ground-level) bending moment specified in the JGJ code. Use of the solutions is elaborated for a typical offshore pile group against measured response, which largely substantiates the deduced stiffness knr. The coupled kr and pm revealed are fundamental to design of the capped piles using any methods. The new solutions using the knr and pm values should be employed to conduct pertinent design. (n = 1.7) for the associated p m at the design level of (ground-level) bending moment 34 specified in the JGJ code. 35Use of the solutions is elaborated for a typical offshore pile group against measured response, 36 which largely substantiates the deduced stiffness k nr . The coupled k r and p m revealed are 37 fundamental to design of the capped piles using any methods. The new solutions using the k nr and 38 p m values should be employed to conduct pertinent design. 39 40

Response of rigid piles during passive dragging

“…The model is underpinned by the following stipulations: The spring has a subgrade modulus k s and mk s for the moving and the stable layer, respectively. The spring has a LIFPULD p s (= p ub z / l , p ub = limiting force per unit length at a free‐head, pile base, via the slider) increasing with depth z . As with the limiting force per unit length p u along active piles , the p s reduces with rotational stiffness k θ . The impact of soil movement is mimicked by the LIFPULD p s [= α p ub l m / l ] using increasing sliding depth l m . It is adjusted by the factor α, which depends on soil movement profile (other than uniform), loading distance [from pile(s)] and rotational restraint on pile(s). …”

“…increasing to the power of depth). Guo demonstrates that it is adequate to use uniform and LIFPULD p u profiles (with depth) to model active piles in clay and sand (stiff clay), respectively. As the problems addressing here are generally pertinent to sand or clay with sufficient strength, the p s due to moving soil is stipulated as linearly increase with depth.…”

“…The external p s is thus described by where p ub is the force per unit length at base level of a passive pile and l m is the sliding depth at loading position (except where specified). The parameters p ub and α are ascertained in the next section, for rotating (of free‐head, k θ = 0) and translating (of fixed‐head, k θ > 10 E p I p , E p I p = flexural stiffness of a pile) piles, respectively, although fixed‐head piles may rotate as well at l m > 0.5 l . The accuracy of the three‐layer model together with Equation is illustrated later through comparison with FEM analysis of slope stabilising piles, and embankment piles, respectively.…”

“…Response of lateral piles is dominated by net limiting force per unit length, which is denoted herein as p s for a passive pile because of soil movement, and as p u along a laterally loaded (active), single pile . The soil movement w s exceeding w s * (= p s / k s , k s = modulus of subgrade reaction of sliding layer) induces the p s over a depth l m .…”

“…This resembles conditions on laterally loaded, rotationally restrained piles. The latter is associated with a reduced limiting force per unit length of α p u (with α = 0.25–1.0) because of pile–pile interaction , or the pile cap‐rotational constraint . The ratio of 0.25, interestingly, is identical to the ratio of load on a fully fixed‐head pile over that on a free‐head pile at a given (elastic) head‐displacement .…”