The MV Rena shipwreck: time-critical scientific response and environmental legacies

ABSTRACT

The sinking of the MV Rena on Astrolabe Reef (Otaiti) in the Bay of Plenty, New Zealand, resulted in the release of oil and ship debris, including dangerous goods carried as cargo. Two key questions of concern to the public and environmental managers were posed immediately: what was the impact of the Rena oil spill and how long would it take for the marine environment to recover? The research that began immediately after the ship grounded provided answers, as documented in this special issue.     

THE HYDROGEOLOGY OF GHANA

SUMMARY

Many hydrological systems exhibit long periods of quiescent behaviour, broken only occasionally by short periods of comparatively intense activity. Clear examples arise in stream run-off measurements and in ground water table observations. The number of measurements recorded can then be considerably reduced by reducing the frequency of recording over the quiescent periods. The paper describes an algorithm whereby this reduction is attained in an optimum manner. When recordings can be accepted directly by a computer, the algorithm simply provides a translation programme Whereby the quality of data may be very considerably reduced. Other applications are, however, discussed.

The problems of Optimum representations is first presented, and choices of norm indicated. Using a particular norm, it is shown that the optimum representation is characterised, under certain limiting conditions, by the property that the second moments of the second derivatives are constant over all optimum intervals. This characterisation is used to construct an iterative difference scheme, whereby a certain truncation error is accepted. Sufficient conditions for stability of the scheme are determined and these incorporated into a computer programme. The programme has been tested on a variety of data with satisfactory results. In conclusion, a further development of the method is indicated.     

A posteriori local error estimation and adaptive time-stepping for newmark integration in dynamic analysis

A simple a posteriori local error estimate for Newmark time integration schemes in dynamic analysis is presented, based on the concept of a so called ‘post-processing’ technique. In conjunction with the error estimate, an adaptive time-stepping algorithm is described, which adjusts the time step size so that the local error of each time step is within a prescribed error tolerance. Numerical examples given in the paper indicate that the error estimate is asymptotically convergent, computationally efficient and convenient, and the adaptive time-stepping scheme can predict a nearly optimal step size from time to time, thus making the numerical solution reliable in an efficient manner.     

Influence of a wall system on the interaction between soil and foundation plates

The paper considers the influence of a building wall system on the interaction between the soil and the foundation plate. A simplified semi-analytical finite element method gives an economical solution for large three-dimensional soil-structure interaction problems. The simplified method appears to be sufficiently accurate for engineering purposes. Numerical results presented show significant influence of building walls on the foundation-plate-soil interaction.     

A post-processing technique and an a posteriori error estimate for the newmark method in dynamic analysis

In this paper, we present a post-processing technique and an a posteriori error estimate for the Newmark method in structural dynamic analysis. By post-processing the Newmark solutions, we derive a simple formulation for linearly varied third-order derivatives. By comparing the Newmark solutions with the exact solutions expanded in the Taylor series, we achieve the local post-processed solutions which are of fifth-order accuracy for displacements and fourth-order accuracy for velocities in one step. Based on the post-processing technique, a posteriori local error estimates for displacements, velocities and, thus, also the total energy norm error estimate are obtained. If the Newmark solutions are corrected at each step, the post-processed solutions are of third-order accuracy in the global sense, i.e. one-order improvement for the original Newmark solutions is achieved. We also discuss a method for estimating the global time integration error. We find that, when the total energy norm is used, the sum of the local error estimates will give a reasonable estimate for the global error. We present numerical studies on a SDOF and a 2-DOF example in order to demonstrate the performance of the proposed technique.     

Finite element analysis of progressive failure in long slopes

Progressive failure in long natural clay slopes with an underlying weak shear zone is studied. The clay slope is assumed to be elastic–perfectly plastic, whereas the shear zone may have an elastic–plastic strain softening behaviour. The failure will occur due to the development of large shear deformations in the weak zone. The general behaviour, including the possibility of progressive failure, can be studied by the use of a one-dimensional finite element model. Other interesting matters which can be studied are critical load, critical disturbance and critical length of the slope. Numerical examples show the overall behaviour due to different residual shear strengths of the weak layer, end disturbance or change of pore pressure in the weak layer. Although simple, the proposed finite element model provides a practically applicable tool for the prediction of whether progressive failure will occur and in which manner the local failure will propagate.