The behaviour of layered soil or rock containing a decaying heat source

Solutions are presented for the behaviour of layered soil or rock deposits which contain a heat source. Such a problem arises when high level nuclear waste is placed in deep underground depositaries, as the waste continues to generate heat for many years after placement. This heating of the surrounding soil or rock may lead to expansion and cracking with subsequent contamination of ground water. Results are presented for heat soureces with different decay rates and for heat sources in layers of material with different coefficients of expansion. An example using realistic data for rock is also given. The solution method involves applying Fourier or Hankel transforms to the field quantities and this reduces the two-dimensional or axisymmetric problem to one involving a single spatial dimension. In cases where the soil or rock is horizontally layered, the method has great advantages over other numerical methods such as finite element or finite difference techniques, since little computer storage and data preparation time is required. Solution of the time-dependent problem is carried out by applying Laplace transforms to the field variables, obtaining solutions and then using numerical means to invert the transformed solutions. This enables easy solution of problems involving time-dependent (i.e. decaying) heat sources.     

The behaviour of an elastic non-homogeneous half-space. Part I-line and point loads

In the first part of this paper solutions are developed for the response of a non-homogeneous half-space subjected to either a surface point load or a surface line load. The non-homogeneity considered is a variation in Young's modulus (E) with depth (z) which takes the form E=m_EZ^α where m_E is a constant and α is referred to as the non-homogeneity parameter. The variation of these solutions as the non-homogeneity parameter α varies between the limits of zero (homogeneous soil) to unity (Gibson soil) gives some fresh insight into both these limiting cases.     

Rapid relaxation inversion of CSAMT data

In this paper an inversion algorithm for controlled-source audio frequency magnetotelluric data is presented. This algorithm combines 2.5-D finite element forward modelling with the concepts of rapid relaxation inversion of magnetotelluric data. The inversion uses the same technique to compute sensitivities as the rapid relaxation inversion, and these approximate sensitivities are validated by comparison with exact 2.5-D sensitivities. The comparison shows that the approximate sensitivities are similar in shape to the exact sensitivities when transmitter–receiver offsets are greater than one skin depth in the Earth. The magnitudes of the two sensitivities differ but the variations with depth are similar. Tests of the algorithm on synthetic data and field data provide promising results.     

Bioenergetic modelling of the marine phase of Atlantic salmon (Salmo salar L.)

A bioenergetic model of marine phase, wild Atlantic salmon was constructed to investigate the potential effects on post-smolt growth of predicted changes in oceanic conditions. Short-term estimates of growth in weight were similar to measurements in captivity and simulated growth varied with water temperature and swimming speed as expected. Longer-term estimates of growth in length were less than that achieved by wild salmon, particularly with constant swimming assumed. The model was sensitive to parameters relating to maximum daily food consumption, respiration and the relationships between body energy content, length and weight. Some of the sensitive parameters were based on substantive information on Atlantic salmon and their realistic ranges are likely to be much narrower than those tested. However, other parameter values were based on scant data, farmed Atlantic salmon or other salmonid species, and are therefore less certain and indicate where future empirical research should be focussed.     

Does one size fit all? An evaluation of length–weight relationships for New Zealand's freshwater fish species

Length–weight relationships are a fundamental tool for assessing populations and communities in fisheries science. Many researchers have collected length–weight data throughout New Zealand, yet parameters describing these relationships remain unpublished for many species of freshwater fish. We compiled 285,124 fish records from researchers and institutions across New Zealand to parameterise length–weight equations, using both power and quadratic models, for 53 freshwater species belonging to 13 families. The influence of location and sex on length–weight relationships was also assessed. Location, in particular, generated different length–weight relationships for 65% of the species examined. Length–weight equations were validated by comparing predicted weights against independently measured weights from 25 electrofished sites across New Zealand and the equations were highly accurate (R²>0.99). Recommendations are made about how to robustly apply this new resource which should assist freshwater fisheries researchers throughout New Zealand.     

Estimating periphyton standing crop in streams: a comparison of chlorophyll a sampling and visual assessments

Periphyton standing crop is often measured as chlorophyll a but there is increasing interest in using visual assessments of periphyton cover. Visual methods are rapid and require no sample analysis, but can be regarded as subjective with high inter-operator variability. We investigated variability in periphyton standing crop across operators, rivers and time, as determined visually and from chlorophyll a measurements. We found that visual assessments (comprising percentage cover estimates of up to eight periphyton categories) distinguished sites and occasions as effectively as chlorophyll a. Furthermore, an estimate of chlorophyll a could be derived from the visual assessments. Because our surveys were conducted in only three rivers, general applicability of the derivation of estimated chlorophyll a from the visual assessments warrants further investigation. The current recommendation of 20 views was sufficient for realistic visual assessments of average cover. Overall, our results indicated that inter-operator variability in visual assessments need not be a major concern, given adequate training.     

Green's functions for a fully coupled thermoporoelastic material

The Green's functions for a set of fully coupled linear equations governing thermal consolidation of a homogeneous isotropic material are presented. The Green's functions are evaluated for one, two and three spatial dimensions, and in the Laplace and real-time domains. The Green's functions are employed in a boundary integral analysis of a simple problem to demonstrate the influence of full coupling on the field quantities.     

One-dimensional advective–dispersive transport into a deep layer having a variable surface concentration

Two analytic closed form solutions for the one-dimensional advection–dispersion equation are presented. These solutions take account of changes in surface concentration with time as mass is transported into the soil. The first solution is developed for the case of rapid landfill construction. The second solution considers a time-dependent mass input to the landfill. The use of these solutions is illustrated by a number of examples and it is shown that consideration of the finite mass of contaminant within the landfill can significantly affect the concentration profiles beneath the landfill.     

Finite layer analysis of consolidation. II

The theory developed in Part I of this paper is extended to apply to the consolidation of horizontally layered soils under both axially symmetric and general surface loading. The method again leads to a considerable reduction in the amount of core storage necessary for computer solution and can be implimented on a mini-computer.