# OTHER TYPES OF MODELS

Occasionally, other methods are used to model groundwater flow regimes for engineering purposes. Examples are graphical models; physical models; and analogue models.

5.6.1 Graphical Models

Flow net analyses are a graphical representation of a solution of a given two-dimensional groundwater flow problem and its associated boundary conditions. A flow net (Figure 5.2) is a network of ‘flow lines’ and ‘equipotentials’ that, when developed correctly, provide a graphical solution to a steady-state groundwater flow regime in two dimensions.

• • Flow lines represent the paths along which water can flow within a two-dimensional cross section.
• • Equipotentials are lines of equal total head.

Consideration of Darcy’s law (Section 3.3.2) shows that groundwater flows from higher total head to lower total head. Because each equipotential represents constant total head, there can be no flow along an equipotential. Therefore (under isotropic conditions), each flow line and equipotential must intersect at right angles. Practical guidance on constructing flow nets is given in Cedergen (1989), including their application under anisotropic permeability conditions. Hand sketching of flow nets can be used to obtain solutions to certain flow problems, considered either in plan or in cross section, for isotropic or anisotropic conditions.

A typical problem where flow nets are used is illustrated in Figure 5.2 for seepage into an excavation where the presence of partial cut-off walls alters the groundwater flow paths (see

Figure 5.2 Flow net into an excavation, where groundwater flow is affected by low-permeability cut-off walls forming a cofferdam, (a) Conceptual model on which the graphical model is based, (b) Graphical model in the form of a flow net.

Williams and Waite, 1993). Experience has shown that for such a problem, if a hand-drawn flow net is constructed by someone competent in the technique, the calculated flow rate and head distribution from the flow net will agree very closely with the results of numerical modelling. This illustrates that there is no fundamental difference between hand-drawn flow nets and two-dimensional numerical modelling - each approach develops a solution to the same mathematical problem, but using different methods.

5.6.2 Physical Models

Very rarely, physical models are used to analyse groundwater flows. Such models are simplified scaled physical representations of a groundwater flow problem - such as seepage through a dam or into an excavation cofferdam. Typical examples include ‘sand tank’ models, where granular materials are placed within a tank and groundwater is added or removed to create the desired groundwater flow patterns. Physical models require careful design to take account of scale effects to achieve a representative model, and are rarely used outside teaching and research.

5.6.3 Analogue Models

Analogue models are an application of the fact that several physical processes (which can easily be physically realized and measured) are controlled by mathematical relationships that are analogous to groundwater flow (see Table 5.1). This means that physical models of these analogous processes can be used to predict and interpret certain groundwater flow cases. In the past, analogue models were used more commonly to analyse complex problems, but in recent times, advances in numerical modelling methods have made these techniques largely obsolete.

Examples include:

• • Electrical resistance or resistance-capacitance analogues. Such models, as described in Rushton and Redshaw (1979), are based on the analogy between electrical flow and groundwater flow. In the past, before the widespread availability of numerical models, these methods were used more commonly to analyse complex problems. A rare recent electrical analogue application from the 1980s is described by Knight et al. (1996).
• • Viscous flow analogues. Commonly known as Hele-Shaw models. This analogue approach uses the slow flow of a viscous fluid in the narrow space between two parallel plates to simulate groundwater problems. This approach is rarely used outside teaching and research.

# THE ROLE OF GEOLOGICAL STRUCTURE IN MODELS

Chapter 3 described how the boundaries and structure of aquifers and aquitards can complicate the flow of groundwater. The presence of recharge boundaries or multiple layered aquifers will have a significant effect on the groundwater lowering requirements for an excavation.

Although geological structures and boundaries can make dewatering more difficult, conversely, a designer can try to use these features to advantage. For example, if the conceptual model highlights the presence of a more permeable layer within the aquifer sequence, by far the most effective approach is to design dewatering wells to abstract water directly from the

Table 5.1 Conduction Phenomena Analogous to Groundwater Flow

 Variable Groundwater flow Flow of electricity Heat flow Driving potential total hydraulic head [m] voltage [Volt] temperature [K] Flow groundwater flow rate [m3/s] electric current [Ampere] heat [Watt] Physical property controlling flow hydraulic conductivity [m/s] electrical conductivity [S] thermal conductivity [W/mK] Storage parameter specific storage Ss [l/m] capacitance [Farad] specific heat capacity [)/m3K] Relationship controlling flow Darcy’s law Ohm’s law Fourier’s law

Relevant SI units shown in square brackets:) = Joule; К = Kelvin; S = Siemens (formerly mhos).

permeable layer. This will maximize well yields and will induce the adjacent, less permeable layers to drain to the permeable layer. Where the permeable layer is at depth, this approach of pumping preferentially from the most permeable layer is known as underdrainage (see Section 13.6.2 and Figure 13.9).

Sometimes, an understanding of the geological structure can have a very beneficial effect when dealing with groundwater problems. An example is given in the following.

Figure 5.3 shows a 12 m deep excavation being constructed in fractured bedrock of inter- bedded limestone and mudstone, where the bedding of the strata was not horizontal but ‘dipped’ gently to the east - this means that the rock bedding sloped very slightly (2 to 3° below horizontal) eastward. The planned groundwater control included a system of pumped ejector wells (Section 17.2). However, a sensitive archaeological site was present a few hundred metres to the east (within the predicted zone of influence), and there was concern that drawdown from the dewatering pumping could cause adverse impacts (Section 21.4).

Figure 5.3 Effect of large-scale geological structure on groundwater flow around an excavation, (a) Local ground conditions only considered, (b) Regional geology considered.

At the excavation location, the bedrock formed an unconfined aquifer, with groundwater level close to ground level. If similar groundwater conditions were present at the archaeological site, then that site would have been impacted by drawdown of groundwater levels (Figure 5.3a). This could have required mitigation measures, such as artificial recharge, to minimize groundwater lowering beneath the sensitive site. However, a geological desk study (Section 11.6) revealed that as the bedrock aquifer dipped to the east, an overlying aquitard of very low-permeability mudstone layer was observed, gradually increasing in thickness. At the location of the archaeological site, the bedrock aquifer was confined below the mudstone aquitard and was effectively hydraulically isolated from the shallow archaeological site (Figure 5.3b). This indicated that there was a low risk of drawdown impacts affecting the archaeological site; and that expensive mitigation measures were not needed. It is interesting to note that this conclusion would not have been reached based on the investigation boreholes on the excavation site alone, since the confining mudstone layer was absent at that location. This is a powerful illustration of the value that can be gained from an understanding of the wider geological setting of a site.

# FLOW TO WELLS AND SLOTS

Groundwater models can be an interesting field of study in their own right. But our interest in groundwater is more than purely academic; we need to be able to control groundwater conditions to allow construction to proceed. The principal approach is to install a series of wells and to pump or abstract water from these wells - this is the essence of groundwater lowering or dewatering. Hence, the commonly used models that describe flow towards wells must be understood.

Some definitions will be useful. For the purposes of this book, a ‘well’ is any drilled or jetted device that is designed and constructed to allow water to be pumped or abstracted. These definitions are, again, slightly different from those used by some hydrogeologists. In hydrogeology, a ‘well’ is often taken to mean a large-diameter (greater than, say, 1.8 m) well or shaft, such as may be dug by hand in developing countries. A smaller-diameter well, constructed by a drilling rig, is often termed a ‘borehole’, or in developing countries a ‘tube well’.

A well will have a well screen (a perforated or slotted section that allows water to enter from certain strata) and a well casing (which, conversely, prevents water entering from certain strata); see Figure 5.4.

In dewatering terminology, wellpoints (Chapter 15), deep wells (Chapter 16) and ejectors (Section 17.2) are all types of wells, categorized by their method of pumping. A ‘sump’ (Chapter 14) is not considered a well, since it is effectively a more or less crude pit to allow the collection of water.

A ‘slot’ is a linear feature that is used to pump groundwater - a trench drain being an obvious example. An important point is that the geometry of groundwater flow to a slot is notably different from flow to wells, and this affects the methods of analysis that should be used. Flow to slots is of interest to dewatering designers, because it is sometimes useful to simplify a line of closely spaced wells into a slot.