Describing failure in geomaterials using second-order work approach

Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work,involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.

Weibull Statistics Strength Investigation of Synthetic Link Chains Made from Ultra-Strong Polyethylene Fibers

Chains are typically used for tension load transfer. They are very flexible and allow easy length adjustment by hooking at the links. Steel is the traditional material for chains. Recently, synthetic link chains made from ultra-strong polyethylene fibers, branded as Dyneema®, are commercially available. These chains offer a highly improved strength to weight ratio. So far, one type of such chains is available, and it has a Working Load Limit of 100 kN. 50 of such chains, containing 6 links were tested to fracture. The strength of each chain and the location of the failed link were documented during testing for later interpretation. Weibull statistics was applied in order to extrapolate towards the allowable load for very low failure risks (high reliability). Two approaches were used. One extrapolation was based on all results;the other was applied after recognition that the end links failed under a slight negative influence by the connection to the testing equipment. Thus, in fact two populations are mixed, the chains with failing end links and the chains with failing central links. So considering the population without the failing end links is more representative for pure chain behavior without clamping effects. The results from this latter consideration showed a higher Weibull exponent, thus a more realistic extrapolation behavior. Both methods indicate that the reliability at the working load limit of 100 kN is very good.