Effective stress σ′ is the stress acting on a soil’s skeleton due to the total stress σ, pore water pressure (Terzaghi 1943), interparticle capillary stress (Bishop 1959), and adsorptive stress (Lu and Likos 2006). A general effective stress is proposed (Lu and Likos 2006), using the suction stress σs as a function of water content w, including capillary stress σcaps(w) and adsorptive stress σadss(w)(1) σ′=σ−σs(w)=σ−σcaps(w)−σadss(w)An explicit form of suction stress and its dependence on soil water content was proposed and experimentally validated (Lu et al. 2010) for all types of soils under matric suction <1.5  MPa(2) σs(w)=−1αSWRw−wrws−wr[(w−wrws−wr)nSWR/(1−nSWR)−1]1/nSWRwhere wr = residual water content for adsorption; ws = saturated water content; αSWR is related to the inverse of the air-entry pressure; and nSWR is related to the pore size distribution for soil water retention (SWR). Recently, Lu and Zhang (2019) showed that defining matric suction ψm as the air pressure ua and pore water pressure uw difference (i.e., ua–uw) is incomplete, and a general definition including both adsorption and capillarity is(3) ψm(w)=ua−uw(w,x)−ψads(x)where x = statistical distance to a particle surface; and ψads(w) = soil sorptive potential (SSP). In light of the general matric suction and SSP concepts, suction stress equations more general than Eq. (2) have been proposed under a full range of water content [Fig. 1(a)] (Zhang and Lu 2020)(4a) σcaps(w)=−w2αSSws[1+erf(4w−wamaxSSwamaxSS)]⁢[(wws)nSS/(1−nSS)−1]1/nSS(4b) σadss(w)=12σdrys[1−erf(βw−wamaxSSwamaxSS)]where αSS is related to the inverse of the average capillary suction stress; nSS is related to the pore size distribution; wamaxSS is related to maximum adsorptive water content; σdrys = suction stress at the oven-dry state; and β = strength of the adsorptive suction stress. Capillary suction stress [Eq. (4a) and Fig. 1(a)] is due to capillary pressure (ua−uw) and varies nonmonotonically with water content, whereas adsorptive suction stress [Eq. (4b) and Fig. 1(a)] is due to SSP and varies monotonically at low water content.Experimental ValidationThe experimental data of suction stress from the drying cake technique (Dong and Lu 2017) for various types of soils [Fig. 1(b)] show that Eq. (4) can well represent suction stress variations with soil types and water content, confirming the validity and generality of the effective stress Eqs. (1) and (4) under all saturation conditions.SignificanceEq. (4) can be reduced to the Lu et al.’s (2010) Eq. (2) when capillarity dominates the SWR, and Eqs. (1) and (4) can be reduced to the Bishop’s effective stress when capillarity is the sole SWR mechanism and can further be reduced to the Terzaghi’s effective stress when soil is saturated (Zhang and Lu 2020).With the general effective stress described by Eqs. (1) and (4), all classical solutions of effective stress for various foundation problems such as limit-state equilibrium in slopes, and lateral earth pressure, retain the same mathematical forms, and thus may be readily implemented for design and analysis of foundation soil under both saturated and unsaturated conditions.References Bishop, A. W. 1959. “The principle of effective stress.” Tek. Ukebl. 106 (39): 849–863. Dong, Y., and N. Lu. 2017. “Measurement of suction-stress characteristic curve under drying and wetting conditions.” Geotech. Testing J. 40 (1): 107–121. Terzaghi, K. 1943. Theoretical soil mechanics. New York: Wiley.

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