Uniqueness of Suction Stress Value at Liquid Limit of Soil

The liquid limit (LL) is a soil property index in the Unified Soil Classification System, originally devised by Swedish scientist Albert Atterberg in 1911 and later refined by Casagrande’s percussion cup test. The LL marks water content at certain strength of a soil and can be related to undrained shear strength of $\sim 1.7\mathrm{kPa}$ in the fall-cone test (Hansbo 1957; Claveau-Mallet et al. 2012). Because the conventional test for determining the LL involves manual operation, repeated trials, and visual judgment, it suffers from poor repeatability, and it is labor intensive.

Effective stress ${\sigma }^{\prime }$ is the stress acting on soil’s skeleton due to the total stress, pore water pressure (Terzaghi 1943), and interparticle suction stress (Lu and Likos 2006). The unified effective stress equation for soil under both saturated and unsaturated conditions is (Lu and Likos 2006)where ${\sigma }^{\mathrm{s}}(w)=\mathrm{a}$ soil’s suction stress characteristic curve (SSCC) being a function of water content $w$.

Under the unified effective stress Eq. (1), the LL is the undrained shear strength equal to the prevailing suction stress of $-1.7\mathrm{kPa}$ when a soil is fully saturated. Herein, the effective stress reaches its critical state (i.e., zero) or the total stress equals to the prevailing suction stress. Thus, a soil’s SSCC can be directly linked to the liquid limit.

Soil shrinkage curve test [Fig. 1(a), Dong and Lu 2017] is used to measure a soil’s SSCC from its slurry state. From the measured SSCC, water content at the suction stresses corresponding to $-1.7\mathrm{kPa}$ (LL) can be uniquely quantified [Fig. 1(b)].