The lecture is part of the newly formed "Soil Behaviour" course.

Watch Soil Behaviour course on ISSMGE Virtual University

This course on **Stress-strain behaviour of geomaterials (mainly granular materials) from elastic behaviour to shear banding** is based on the lectures of the presenter for graduate students at University of Tokyo and Tokyo University of Science. The objective of the course is to introduce the major characteristic features of the stress-strain behaviour of geomaterials, mainly granular materials and also partially clays, cement-mixed soils and natural soft rocks. The contents of this course are explained only to a very limited extent in ordinary under-graduate courses, despite that it is required to properly understand them to deal with many geotechnical engineering problems/issues.

The course consists of the following six lectures covering the stress-strain behaviours in a very wide strain range.

**The first lecture** introduces the contents of the second to sixth lectures. It is explained that, in this course, it is attempted to bridge a gap in the stress-strain behaviour of geomaterials between the basic soil mechanics and the SOA geotechnical engineering practice.

**The second lecture** presents **the stress-strain behaviour at very small strains**, say lower than 0.001 %, which is essentially reversible and rate-independent (i.e., elastic). Several full-scale geotechnical case histories with data from laboratory and field measurements are presented. It is shown that the elastic properties measured by dynamic loading tests, wave propagation tests and static stress-strain tests (with local strain measurements) are essentially the same. A hypo-elasticity model in which the elastic properties are stress state-dependent and could be inherently anisotropic is explained. It is shown that the elastic properties from field shear wave velocities become the basis for non-linear FEM analysis in many geotechnical boundary value problems.

**The third lecture** presents **the dilatancy characteristics** in drained shear and their effects on undrained shear behaviour. The Rowes stress-dilatancy equation in monotonic loading and its extension to cyclic loading are explained. It is shown that, controlled by the dilatancy characteristics, the undrained stress-strain behaviour of saturated soil becomes highly dependent on the compacted dry density and this trend is stronger in cyclic loading than in monotonic loading. The importance of this feature in the seismic design of soil structures and natural slopes is explained.

**The fourth lecture** presents **the peak strength** of granular materials. **The effects of confining pressure** on the _{0} value from a very low value ( 2 kPa) to relatively high values were extremely carefully evaluated by triaxial and plane strain compression tests and torsional shear tests. It is also shown that **the inherent anisotropy **could be equally important as the effects of void ratio. The relationship between the strengths by ordinary triaxial compression test and the simple/direct shear test is explained taking into account the effects of the intermediate principal stress, the strength anisotropy and the fact that the shear plane in the simple/direct shear test deviates from the plane of maximum stress obliquity in a specific way.

**The fifth lecture **addresses **the shear banding**, which starts immediately before the peak stress state and develops in the post-peak strain-softening regime. Based on local strain fields carefully measured in a comprehensive series of plane strain compression tests, it is shown that the thickness of shear band is proportional to the mean particle size D_{50} (about 10D_{50}) and the local shear strain in a shear band has become about 80 % when arriving at the residual stress state, where the shear stress is kept essentially constant irrespective of shear strain. As a result, the local shear deformation of shear band required to arrive at the residual stress state increases with an increase in D_{50}. Then, based on the results of a comprehensive series of plane strain model tests in 1g with various footing sizes up to 0.5 m and centrifuge tests with small footing sizes, it is shown that the bearing capacity of strip footing on sand increases with an increase in the particle size relative to the footing size under the same pressure level. So, a centrifuge test on a small-scaled footing on a sand simulates the behaviour of a large prototype footing on a gravel. It is also shown that these test results can be correctly simulated by numerical analysis only when taking into account the particle size effects on post-peak strain softening associated with shear banding, as well as the effects of confining pressure on the _{0} value and strength anisotropy and others.

**In the sixth lecture**, two different time effects: i.e., **rate-dependent stress-strain behaviour and ageing effects**, are explained based on results from comprehensive series of stress-strain tests. With respect to the rate effects, it is shown that, with a decrease in the inter-particle stability by bounding or unbound-locking and with an increase in its damage by straining, the strength increase with an increase in the constant strain rate becomes weaker, while it could become even negative. As a result, with an increase in the constant strain rate, the strength increases with well-bound geomaterials while decreases with unbound poorly graded round granular materials. These phenomena are complicated but systematic, and it is indispensable to take into account them when analysing the data from laboratory stress-strain tests and field observations. It is also shown that, with bound geomaterials with developing ageing effects, such as relatively young cement-mixed soils, during sustained loading, creep deformation and ageing effects take place simultaneously, both resulting into the development of yield stress. Then, upon the restart of loading, nearly elastic behaviour is exhibited for some large stress range. All these phenomena of rate effects, including creep deformation and stress relaxation, and ageing effects are explained in a unified framework and simulated by a non-linear three-component model.