Karoo Aquifers Deformations, Hydraulic and Mechanical Properties
Report No 936/1/04
Aquifers in the Karoo formations of South Africa are usually considered as unreliable sources of water, as illustrated by the difficulties experienced by towns such as Dealesville, Dewetsdorp and Philippolis with water supply schemes based on boreholes. However, as pointed out by (Botha et al., 1998) in a previous study for the Water Research Commission these aquifers must contain considerable volumes of water, otherwise it will be difficult to explain the large quantities of water pumped daily from mines and buildings located in and on the formations respectively. One reason advanced by Botha and his co-workers for this seeming discrepancy is that the behaviour of a stressed Karoo aquifer is determined by its very complex geometry, consisting of multi-porous rocks interspersed by a few bedding-parallel fractures. To neglect this geometry in the management and operation of these aquifers, which incidentally is not discussed in textbooks on groundwater resources, can only cause severe damage to the aquifer or even ruin it completely. Indeed, there is sufficient reason to believe that the inability of previous investigators to take the internal geometry of Karoo aquifers into account must be regarded as the main reason for the difficulties experienced with these aquifers, and why people distrust them. The real problem with these aquifers might thus be more a management problem than a shortage of water.
2 BACKGROUND TO THE STUDY
A common view of the Karoo formations in the past was that the rocks are very tight and that the formations can only store water in vertical and sub-vertical fractures. However, the investigations of Botha and his co-workers have shown that this is not the case. Vertical and sub-vertical fractures do occur quite frequently in these formations, but they only serve as preferential flow paths during the recharge of the aquifers and not as storage units. The major storage units of water in Karoo aquifers are the formations themselves, while the bedding-parallel fractures serve as the conduits of water in these aquifers. A borehole in a Karoo aquifer therefore only has a significant yield if it intersects one (or more, but usually only one) bedding-parallel fracture. Although these fractures often extend over large areas, they can only store a limited volume of water, because of the sizes of their apertures, which are of the order of 10 mm. The apertures, nevertheless, are large enough to allow them to transmit water rapidly to any point in the aquifer where the fracture is present and there is a demand for water.
The American hydrologist O.E. Meinzer already argued in 1928 that aquifers (be it only confined aquifers) are compressible from observations of the following phenomena (Meinzer, 1928).
Nevertheless, the compressibility of an aquifer is habitually neglected in groundwater investigations, because the magnitudes of these phenomena are small and difficult to observe in practice. However, this does not imply that compressibility can be neglected in the case of water-yielding fractures with apertures of similar dimensions. Such fractures could still deform even though the deformation might not be recognized during normal field investigations of an aquifer. Indeed, there are strong indications that the bedding-parallel fractures in the Karoo formations are particularly susceptible to such deformations. For example, the complaint: ‘my borehole has dried up’, often heard from people who depend on Karoo aquifers for their water supply, may be the result of a bedding-parallel fracture that collapsed locally. The hydraulic tests, discussed in Botha et al. (1998), also indicated that deformations might affect the yield of a borehole in the Karoo formations adversely.
Since deformations seemed to play such an important role in Karoo aquifers and very little information was available in the existing literature on groundwater resources at the time that the project of Botha and his co-workers ended, the Water Research Commission was again approach for funds to investigate this phenomenon in more detail.
3 OBJECTIVES OF THE STUDY
The aims of the present study as set out in the original proposal to the Water Research Commission were as follows:
The first step taken in this investigation was to expand the three-dimensional model developed for Karoo formations during the project ‘The analysis and interpretation of aquifer tests in secondary aquifers’ for the Water Research Commission to account for deformations. The computer program developed for this purpose was originally based on a three-dimensional Cartesian description of the aquifer, as it was anticipated that suitable computer resources might become available nationally during the duration of the project. Unfortunately, the latter expectation did not materialize and the program had to be scaled down to radial-symmetric, cylindrical coordinates.
The devaluation of the South African Rand between the time the proposal was submitted to the Water Research Commission and when the project actually began meant that that there were not sufficient funds to purchase a suitable flow meter. The project team therefore concentrated their efforts on the development of the deformation model. This model showed that deformations might play a much larger role in the behaviour of aquifers in general, and not only Karoo aquifers, than originally thought. This means that one should use a model that also takes the mechanical properties of the aquifer into account and not a model that only depends on the classical hydraulic parameters (specific storativity and hydraulic conductivity), when modelling the flow of groundwater in practice. One approach to determine these parameters (Young’s modulus and Poisson’s ratio) is through electrokinetic surveys. The Water Research Commission was therefore approach with the request, supported by the Steering Committee, to include an investigation of electrokinetic surveys in the project, which the Commission accepted.
Although significant results were obtained with the electrokinetic surveys (Fourie et al., 2000), it later became clear that a full investigation of the method would take a much longer time than originally anticipated and that it could not be completed even during the extension of this project. The surveys could fortunately be continued through grants from the National Research Foundation to the Project Leader. However, this meant that the original objectives of the investigation had to be modified. The results of the electrokinetic surveys will therefore not be included in this report, but a separate report will be submitted to the Water Research Commission after the conclusion of the project.
The deformation model was supplemented with the two-dimensional mass transport model of Verwey and Botha (1992) to study mass transport in an aquifer subject to deformations. However, this showed that there is no significant difference between mass transport in a deformable and a rigid aquifer, provided that the discharge rate of a borehole is not so high as to cause oscillations in the water levels of the aquifer and the mass transport model becomes unstable. This report will therefore concentrate on a discussion of the deformation model.
4 METHODOLOGY USED IN THE INVESTIGATIONS
4.1 The Nature of Deformations
All material bodies on earth, including the earth itself, change their shape, or deform, to some degree when acted on by an external force. Some bodies regain their original shape once the external force is removed, but others retain all or a degree of the deformation induced by the force. Typical examples of the first type of body include the elastic band and the well-known coiled spring. These bodies are consequently known as elastic bodies. The other inelastic bodies all retain some degree of deformation—commonly referred to as residual deformations. A number of inelastic bodies, which retain the full deformation, such as clay, are known as plastic bodies. The deformation of a body is essential caused by the interaction between the molecules in the body, which act even when no external forces are applied to the body. These interactions, which ensure the existence of a solid state and its strength—the ability of the solid medium to withstand applied forces—are conventionally studied in the theory of elasticity. However, the theory of elasticity is not so much concerned with the internal forces themselves, but rather with the effects of the forces.
4.2 Aquifer Deformations
Since real bodies differ considerably in their composition, the internal interactions differ widely from one body to the next. Two approaches are therefore commonly used to study the behaviour of a body in the theory of elasticity—experimental and theoretical. Previous experience has shown that a combination of the two approaches provides the best way to study the behaviour of deformable bodies. Although an attempt was made to develop equipment and observational techniques for this purpose, the progress was slower than expected. The present study therefore had to be limited to a more theoretical approach.
Previous studies on the deformations of aquifers have in the past always been based on the generalized linear law of Hooke, which is one of the keystones of the theory of elasticity (Biot, 1956; Hsieh, 1996; Burbey, 1999). This law, unfortunately, does not allow one to study residual information, which could be important in Karoo aquifers. Since the linear law of Hooke cannot account for residual deformations, a new non-linear form of the law was introduced to study residual deformations in aquifers.
There are no analytical solutions available for the coupled flow and momentum equations that arise from the application of both the linear and non-linear forms of Hooke’s law to the flow of groundwater through deformable aquifers, at least not to the knowledge of the authors. The finite element method (Botha and Pinder, 1983; Huyakorn and Pinder, 1983) was therefore used to approximate the equations and a computer program was developed for the numerical computations of solutions.