Alexander M. Puzrin

A thermomechanical framework for constitutive models for rate-independent dissipative materials

Abstract A formulation of elastic–plastic theory for rate independent materials is described, based on the use of thermodynamic potentials. The four energy functions commonly used in thermodynamics (internal energy, Helmholtz free energy, enthalpy and Gibbs free energy) are used to provide descriptions depending on which combinations of the stress, strain, temperature and entropy are taken as the independent variables. Much use is made of Legendre transformations to establish the links between the different energy functions. Dissipative behaviour is introduced through the use of kinematic internal parameters, and their conjugate variables, which are termed generalised stresses. A dissipation function or a yield function is used to describe the irreversible behaviour, and these are related by a degenerate case of the Legendre transformation. A central theme is that the constitutive behaviour is entirely determined by the knowledge of two scalar potentials. A systematic presentation is made of 16 possible ways of formulating constitutive behaviour within this framework. From four of these forms it is possible to establish the incremental response entirely by differentiation of the two potentials and by standard matrix manipulation. Examples are provided of the forms of the potentials for certain simple cases. The paper builds on previous work by Ziegler and other authors, and extends and generalises work by Collins and Houlsby to include thermal effects.

Microbial Fuel Cell Biosensor for In situ Assessment of Microbial Activity

Microbial fuel cell (MFC)-based sensing was explored to provide useful information for the development of an approach to in situ monitoring of substrate concentration and microbial respiration rate. The ability of a MFC to provide meaningful information about in situ microbial respiration and analyte concentration was examined in column systems, where Geobacter sulfurreducens used an external electron acceptor (an electrode) to metabolize acetate. Column systems inoculated with G. sulfurreducens were operated with influent media at varying concentrations of acetate and monitored for current generation. Current generation was mirrored by bulk phase acetate concentration, and a correlation (R(2)=0.92) was developed between current values (0-0.30 mA) and acetate concentrations (0-2.3 mM). The MFC-system was also exposed to shock loading (pulses of oxygen), after which electricity production resumed immediately after media flow recommenced, underlining the resilience of the system and allowing for additional sensing capacity. Thus, the electrical signal produced by the MFC-system provided real-time data for electron donor availability and biological activity. These results have practical implications for development of a biosensor for inexpensive real-time monitoring of in situ bioremediation processes, where MFC technology provides information on the rate and nature of biodegradation processes.

A new versatile expression for yield and plastic potential surfaces

Abstract In any elasto-plastic constitutive model there are three main ingredients, namely a yield surface, a plastic potential surface and a hardening/ softening rule. In this paper a versatile mathematical expression is presented which can be used to describe the yield and plastic potential surfaces. The expression is defined completely by a maximum of only four parameters. These parameters can easily be obtained from observable soil behaviour in simple triaxial tests. A major advantage of the expression is that by suitable adjustment of the parameters a wide range of surface shapes can be achieved. For example, it is possible to reproduce the so called “bullet shape” typical of the plastic potential used in the original Cam clay model and the “tear shape” yield surfaces employed in the more recent models. In fact the expression is capable of accurately reproducing the shapes of many of the yield and plastic potential surfaces currently in use. The expression is also shown to be in good agreement with experimental data.

The growth of shear bands in the catastrophic failure of soils

This paper is an attempt to apply the Palmer–Rice fracture mechanics approach to the shear band propagation in sands and normally consolidated clays. This approach, proposed 30 years ago for overconsolidated clays, had a tremendous advantage of treating a shear band evolution as a true physical process and not just as a sufficient mathematical condition for its existence. Extension of this approach to a wider variety of soils requires for non-elastic soil properties (e.g. isotropic hardening plasticity, strain softening, lack of tensile strength, dilatancy, active and passive failure modes, etc.) to be taken into account. This paper demonstrates how the energy balance and process zone approaches can be applied to the simple problem of the shallow shear band propagation in an infinite slope built of such a soil. The energy balance approach appears to be the most conservative one. It allows for catastrophic and progressive types of soil failure to be properly identified, and dramatically effects the results of the slope stability analysis.

A thermomechanical framework for rate-independent dissipative materials with internal functions

Abstract This paper builds on previous work by Houlsby and Puzrin (Int. J. Plasticity 16 (2000) 1017) in which a framework was set out for the derivation of rate-independent plasticity theory from thermodynamic considerations. A key feature of the formalism is that the entire constitutive response is determined by knowledge of two scalar functions. The loading history is effectively captured through the use of internal variables. In this paper, we extend the concept of internal variables to that of internal functions, which represent infinite numbers of internal variables. In this case the thermodynamic functions are replaced by functionals. We set out the formalism necessary to derive constitutive behaviour within this approach. The principal advantages of this development is that it can provide realistic modelling of kinematic hardening effects and smooth transitions between elastic and elastic–plastic behaviour.

Fundamentals of kinematic hardening hyperplasticity

Abstract We present a hyperplastic (thermomechanical) framework for the modelling of kinematic hardening of plastic materials. The advantage of this approach is that it allows a compact development of plasticity theories, which are guaranteed to obey thermodynamic principles. Starting with a model which employs a single kinematically hardening yield surface, we generalize this first to multiple surfaces and then to the case of an infinite number of yield surfaces. At each stage of generalization, the link with conventional plasticity is demonstrated, and examples of one- and multi-dimensional hyperplastic models are presented, together with their interpretation in terms of conventional plasticity theory.

Rate-dependent plasticity models derived from potential functions

In this paper we describe a method for the derivation of the constitutive behavior of rate-dependent materials from two potential functions. Once the potentials have been specified an entirely standardized procedure can be adopted to derive the response, and no additional assumptions are necessary. There is some freedom in the choice of which potential functions to specify: the first is one of four energy potentials, and the second, which specifies the dissipative behavior, is either the force or flow potential. The method allows alternative models to be quickly compared and set within an appropriate hierarchy. This work extends previous work on rate-independent materials, for which the force potentials take a special form. We illustrate the method with four examples of different viscoplastic models.

THE BEARING CAPACITY OF A STRIP FOOTING ON CLAY UNDER COMBINED LOADING

In this paper we seek closed-form solutions for the problem of failure of a strip foundation on undrained clay subjected to combined vertical, moment and horizontal loading. The motivation for the study comes from the offshore oil and gas industry, where the understanding of problems of foundations under general loading is important. The contact between the foundation and the clay is unable to sustain tension, and this feature of the problem considerably complicates the solution. It is found that the bound theorems of plasticity theory are insufficient to solve the problem, and a solution can only be found by adopting certain further hypotheses. Although the existence of an exact solution cannot be proven, apparent upper and lower bounds to a plausible solution are obtained. In order to derive these solutions, a new scaling procedure is introduced, which plays the same role for upper bounds as does the effective width method for lower-bound footing collapse loads.

Landslide monitoring using a road-embedded optical fiber sensor

A novel technique for the determination of a creeping landslide boundary is demonstrated. It is based on application of distributed optical fiber strain measurements using Brillouin Optical Time Domain Analysis (BOTDA) technology. A road crossing the St. Moritz landslide boundary was instrumented with a fiber optic cable, which turned the road, effectively, into a large scale strain gauge. The obtained monitoring data was in good agreement with visual observation and also followed the trends of the geodetical data. The presented validation of this technology allows for a conclusion that distributed fiber optic strain sensing is a promising new tool in landslide surveillance. At present, until methods and standards in this field are established and reliable, combination with traditional methods is necessary. Ongoing measurements during 2008 may strengthen the conclusions of this paper.

Geomechanics of Failures

Settlements.- Interaction between Neighbouring Structures: Mexico City Metropolitan Cathedral, Mexico.- Unexpected Excessive Settlements: Kansai International Airport, Japan.- Leaning Instability: The Tower of Pisa, Italy.- Bearing Capacity.- Bearing Capacity Failure: Transcona Grain Elevator, Canada.- Caisson Failure Induced by Liquefaction: Barcelona Harbour, Spain.- Excavations.- Braced Excavation Collapse: Nicoll Highway, Singapore.- Tunnel Excavation Collapse: Borras Square, Spain.- Tunnel Face Instability: Floresta Tunnels, Spain.