The Residual Strength of Liquefied Soil

Abstract

Flow (or static) liquefaction is one of the most detrimental forms of ground failure. To determine flow slide potential, the residual strength of liquefied soil is needed. However, this is an extremely difficult parameter to estimate for soil deposits due to spatial variability of soil properties, potential for the formation of water films, the intermixing of soils, and the potential for partial drainage during flow liquefaction. Thus, the current state of practice for estimating the residual strength of liquefied soil (Sr) is via back calculations using case histories. However, the complexity of flow slides makes case histories difficult to interpret, and combined with the limited number of case histories, it inherently implies large uncertainties in the derived empirical relationships. Although such empirical relationships define the current state-of-practice for estimating Sr, laboratory studies and fundamental soil mechanics can provide insights and/or can be used to guide the form of the empirical relationships. For example, one issue that is an active area of debate is whether Sr normalizes by initial vertical effective stress (σ’vo). Olson and Stark (2002) present an empirical relationship estimating residual undrained strength ratio (i.e., Sr/σ’vo) as a function of normalized cone penetration test tip resistance whereas Kramer and Wang (2015) showed that Sr does not scale linearly with σ’vo. Hence, the objective of this study is to develop a more mechanistic understanding of the residual shear strength of liquefied soils based on fundamental soil mechanics and laboratory studies. Specifically, an expression for Sr/σ’vo is derived in terms of the effective angle of internal friction for residual strength, ϕ’r, and Skempton’s pore water pressure coefficient for residual conditions, Ar). Data from published laboratory studies are used to develop correlations for estimating both ϕ’r and Ar). The results show that ϕ’r is relatively constant for a range of sands, and the variability in its value does not significantly affect the computed value of Sr/σ’vo. Additionally, the results show that Ar correlates with the state parameter (ψ) for initial conditions and depends on whether the soil grains crush. Additionally, the value of Ar significantly affects the computed value of Sr/σ’vo. The derived laboratory-data-based ψ - Ar relationship is used in conjunction with an empirical relationship relating ψ and normalized cone penetration test (CPT) tip resistance (Qtn) to develop a relationship relating Sr/σ’vo to Qtn, which is then compared to similar relationships derived from back-analysis of case histories. The comparison shows that the proposed correlation most closely resembles Robertson’s (2010) correlation once adjustments are made to the relationship between Qtn and ψ.