Implications of the principle of effective stress
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SHORT COMMUNICATION
Implications of the principle of effective stress Gerd Gudehus1 Received: 14 April 2020 / Accepted: 6 September 2020 Ó The Author(s) 2020
Abstract While Terzaghi justified his principle of effective stress for water-saturated soil empirically, it can be derived by means of the neutrality of the mineral with respect to changes of the pore water pressure pw . This principle works also with dilating shear bands arising beyond critical points of saturated grain fabrics, and with patterns of shear bands as relics of critical phenomena. The shear strength of over-consolidated clay is explained without effective cohesion, which results also from swelling up to decay, while rapid shearing of water-saturated clay can lead to a cavitation of pore water. The pw -neutrality is also confirmed by triaxial tests with sandstone samples, while Biot’s relation with a reduction factor for pw is contestable. An effective stress tensor is heuristically legitimate also for soil and rock with relics of critical phenomena, particularly for critical points with a Mohr–Coulomb condition. Therein, the pw -neutrality of the solid mineral determines the interaction of solid fabric and pore water, but numerical models are questionable due to fractal features. Keywords Effective stress Interaction of solid fabric and pore water Pore pressure neutrality of mineral Shear bands and cracks
1 Introduction Terzaghi [24] proposed the principle of effective stress in a paper for the first international conference on soil mechanics and foundation engineering. This short report, which constitutes Terzaghi’s most important contribution to soil mechanics, is inspiring although some of his arguments are contestable. He states that the principal stress components of a ‘mass of earth’ are sums of ‘solid phase’ components and the ‘neutral stress’ of the pore water for full saturation, writing n0I ¼ nI nw ; n0II ¼ nII nw and n0III ¼ nIII nw , so that shear stresses are transmitted only by the solid. Referring to experiments with water-saturated sand, clay and concrete, he writes that the stress of the solid is effective for ‘compression, distortion and failure’ of such ‘porous materials’ independently of the ‘neutral stress’ nw , and that the solid is not compressed by nw . Writing the principle in modern terms
& Gerd Gudehus [email protected] 1
Emeritus, Institute of Soil and Rock Mechanics, Karlsruhe Institute of Technology, Karlsruhe, Germany
rij ¼ r0ij þ pw dij
ð1Þ
with tensors rij and r0ij of total and solid fabric or effective stress, respectively, pore water pressure pw and unit tensor dij , I derive it in Sect. 2 from the neutrality of the mineral with respect to changes of pw . This argument is at variance with the theory of mixtures with partial pressures and (1) cannot be justified by means of minute contact flats in a grain fabric. I show also in Sect. 2 that the argument of Shao et al. [21] for (1) is tautological, while the thermodynamic derivation by Jiang et
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