Validating a Unified Effective Stress Equation for Soil
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 148, Issue 6
Effective stress is the stress acting on a soil’s skeleton due to the total stress , 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 as a function of water content , including capillary stress and adsorptive stress
(1)
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 where = residual water content for adsorption; = saturated water content; is related to the inverse of the air-entry pressure; and is related to the pore size distribution for soil water retention (SWR). Recently, Lu and Zhang (2019) showed that defining matric suction as the air pressure and pore water pressure difference (i.e., ) is incomplete, and a general definition including both adsorption and capillarity iswhere = statistical distance to a particle surface; and = 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)where is related to the inverse of the average capillary suction stress; is related to the pore size distribution; is related to maximum adsorptive water content; = suction stress at the oven-dry state; and = strength of the adsorptive suction stress. Capillary suction stress [Eq. (4a) and Fig. 1(a)] is due to capillary pressure 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.
(2)
(3)
(4a)
(4b)
Experimental Validation
The 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.
Significance
Eq. (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. https://doi.org/10.1520/GTJ20160058.
Lu, N., J. Godt, and D. Wu. 2010. “A closed-form equation for effective stress in variably saturated soil.” Water Resour. Res. 46 (5). https://doi.org/10.1029/2009WR008646.
Lu, N., and W. J. Likos. 2006. “Suction stress characteristic curve for unsaturated soil.” J. Geotech. Geoenviron. Eng. 132 (2): 131–142. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:2(131).
Lu, N., and C. Zhang. 2019. “Soil sorptive potential: Concept, theory, and verification.” J. Geotech. Geoenviron. Eng. 145 (4): 04019006. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002025.
Terzaghi, K. 1943. Theoretical soil mechanics. New York: Wiley.
Zhang, C., and N. Lu. 2020. “Unified effective stress equation for soil.” J. Eng. Mech. 146 (2): 04019135. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001718.
Information & Authors
Information
Published In
Copyright
This work is made available under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/.
History
Received: Dec 1, 2021
Accepted: Dec 15, 2021
Published online: Mar 24, 2022
Published in print: Jun 1, 2022
Discussion open until: Aug 24, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Chao Zhang, Shaojie Hu, Zemin Qiu, Ning Lu, A poroelasticity theory for soil incorporating adsorption and capillarity, Géotechnique, 10.1680/jgeot.22.00097, (1-18), (2022).