Erratum for “Correlation between Soil-Shrinkage Curve and Water-Retention Characteristics” by Ning Lu and Yi Dong

In this erratum, we correct three errors made in producing Figs. 4 and 6. Though these errors do not invalidate the major findings of the paper, they do affect the quantitative results in the suction stress and void ratio. Fig. 4 shows the computed suction stress curves from the measured soil shrinkage data, and Fig. 6 shows the results of the computed soil shrinkage curves in comparison with the measured soil shrinkage data in various soils. The three errors are missing the effect of vertical displacement in Eq. (4), missing the effect of the initial void ratio effect in Eqs. (6b) and (6c), and implementing a wrong sign in the void ratio change due to the increase in the elastic modulus during soil shrinkage.

The first error in Eq. (4) was made in the assumption of a plane-stress problem in developing a theory for interpreting the shrinkage tests in Lu and Kaya (2013). For a drying soil specimen with a cylindrical cake geometry, an assumption of a plane-stress problem was made as a first approximation, leading to the neglect of the vertical displacement due to the suction stress. However, even though the surface of the specimen is free of the total stress, suction stress or effective stress exists in every point of the specimen in all three directions. Considering the existence of suction stress in all three directions and following the same solution procedure in Lu and Kaya (2013), a more rigorous equation for the incremental suction stress change $\mathrm{\Delta }{\sigma }^{\mathrm{s}}$ can be arrived at as follows:where $E(\theta )$ = elastic modulus as a function of volumetric water content $\theta$; $u_r$ = radial displacement; $r$ = distance to the displacement field center; and $v$ = Poisson’s ratio.

In comparison with the original equation, a factor of 2 is added in front of Poisson’s ratio in Eq. (4). With this improvement, the suction stress characteristic curves (SSCCs) for the various soil shrinkage tests can be calculated and replotted with comparisons to the suction stress characteristic curves in the original Fig. 4. As shown, assuming 0.25 of the Poisson’s ratio, about 50% of relative error between the revised SSCC and the original one can be observed.

The second error involves missing one term of the initial void ratio effect in converting the void ratio from volumetric strain. Under the suction stress–based effective stress framework, soil shrinkage curve can be computed as follows:where $\mathrm{\Delta }{e}_t$ = total void ratio reduction; $\mathrm{\Delta }{e}^{\sigma }$ = void ratio reduction due to suction stress decrease; $\mathrm{\Delta }{e}^E$ = increase in void ratio due to elastic modulus hardening; and $e_0$ = initial void ratio. Eqs. (6b) and (6c) correct the missing factor of ($1+e_0$) in the calculation of the original paper.

The third error was made when computing the void ratio change due to the increase in the elastic modulus during drying. The term in Eq. (6c) should be negative in value, indicating an increase in void ratio due to soil hardening during drying. The original paper implemented this term as positive in value, leading to an incorrect plot in Fig. 6.

The revised Fig. 6 shows comparisons between the measured soil shrinkage data and the computed soil shrinkage curve after the correction of the two errors. It demonstrates that soil shrinkage during drying is due to two mechanisms with opposite effects: decreasing in suction stress further reduces the void ratio [Eq. (7a)], whereas modulus hardening further increases the void ratio [Eq. (7b)]. It also shows that suction stress–based effective stress can accurately predict soil shrinkage curve.