Strains Due to Coupled Phenomena – Particle-level Analyses Dante Fratta University of Wisconsin-Madison. Madison, WI 53706. USA J. Carlos Santamarina Georgia Institute of Technology. Atlanta, GA 30332. USA ABSTRACT: The interaction between the solid particles and the pore fluid in granular materials affects vari- ous interparticle forces. The change in any one of these forces triggers the response of the granular skeleton, causes strain and even important fabric changes. Coupling phenomena that result in skeletal strains are related to fluid properties, electrical-chemical interactions, and thermal effects. The relevance of such couplings in- creases as the particle size d and the effective skeletal confinement σ' decrease, and well-defined coupling re- gions can be defined in the d-σ' space. Experimental results support order-of-magnitude estimates based on particle-level analyses. 1 INRODUCTION Hooke's law predicts the strain induced by a change in the state of the stress (Sokolnikoff 1956; Heyman 1972). In the case of poroelastic media, such as granular materials, strains result from changes in the pore fluid pressure as well as changes in the stress carried by the skeleton (Biot 1941; Scott 1963; Terzaghi and Peck 1967). Furthermore, in some granular materials, strains also result from changes in electrical, chemical and thermal condi- tions (Casagrande 1948; Ikeda 1990; Mitchell 1991). These forms of energy coupling are macroscale- compatible with fundamental physical principles, in particular energy conservation and Le Châtelier's Principle (a system in equilibrium will oppose any disturbance). When energy coupling phenomena are analyzed at the particle-level, the essential nature of material behavior becomes apparent, and the magni- tude of energy coupling parameters characterizes the medium and the physical processes that govern it. Energy coupling effects are repeatable when low- energy input excitations are applied; for example, a small-strain mechanical excitation is accompanied by elasto→electrical coupling (e.g., seismoelectric- ity – Thompson 1936; Pride 1994; Santamarina and Fratta 2003), elasto→thermal coupling (e.g., ther- moelasticity – Luong 1996) and elasto→chemical coupling (local ion displacement – Thompson and Gist 1993). Severe non-linear energy coupling effects may also develop in particulate materials; coupling- induced strain often falls in this category. In order to understand the development of non-linear coupling, the fundamental nature of particulate materials must be uncovered first. This study starts with a review of particle-level forces; then, the microscale impact of changes in electrical and chemical conditions and the ensuing strains are analyzed. 2 PARTICLE-LEVEL FORCES Soils involve mineral grains forming a porous skele- ton. The interconnected pores are filled with fluid, e.g., air, water, organics, or a mixture. All these phases (i.e., solid, liquid, and gas), not only interact through skeletal forces but also through hydrody- namic forces, capillarity forces, and electrical forces (details in Santamarina 2002). Skeletal Forces. A boundary effective stress σ’ [Pa] acting on a random packing of spheres with void ratio e [ ] will cause an average normal contact force F ske [N], ( ) [ ] 12 e 1 2 ske d ' F + π σ = for 0.4<e<1.0 (1) where d [m] is the particle diameter. However the distribution of normal contact forces is not uniform: some particles align into load-carrying columns to support the applied boundary stresses while other particles provide confinement to prevent buckling in the columnar formation.