ABSTRACT
Earth retaining structure may be analysed in many different ways and a variety of methods are available to the designer. Each has a valuable place in the ‘tool box’ and it is up to the engineer to appreciate the assumptions and limitations of each in order to select the most appropriate for a given task. They range from the very simple (perhaps requiring only hand calculations) to the very complex (requiring signicant computational power). Demand for the latter has arisen from the need to demonstrate that displacements around excavations are within acceptable limits. Because each method is applicable to more than one type of earth retaining structure, this chapter presents an overview of the main types of analysis that are available. Subsequent chapters will focus on specic wall types and will show the application of these methods-which include
• Rules of thumb • Evidential methods • Closed-form solutions • Upper and lower bound solutions • Limiting equilibrium • Discrete-spring models • Continuum models
8.1 RULES OF THUMB
In general, a so-called ‘rule of thumb’ is an easily applied procedure for making some determination. Rules of thumb are common in geotechnical design. They permit the preliminary identication of key dimensions or proportions of foundations, excavations, tunnels and walls. The preliminary design of some types of earth retaining structure can be carried out using such rules, which are based on historical experience and do not require formal calculations. Examples include
• Tentative dimensions for mass concrete walls to ensure that the resultant (of wall weight and external soil pressure) falls within the middle third of the base
• Initial sizing of base and stem elements of semi-gravity T and L cantilever walls
• Penetration depth for embedded cantilever walls (e.g. penetration ≥ 2 × retained height)
• Preliminary proportioning for reinforced soil walls (in which, for example, the length of reinforcement is related to overall retained height)
• Driveability of sheet-piles based on cross-section area • Piping/heave in a cofferdam using blocks and submerged unit weights
These methods originate from a variety of sources. Take, for example, the ‘middle third’ rule, which is based on the structural mechanics of columns. It has been known for a long time that the transverse stress distribution on a column depends not only on the magnitude of the axial force carried by the column but also its line of action-specically, its eccentricity about the principal axes x-x and y-y. For a rectangular cross-section b × d, it can be demonstrated that (e.g. Morley 1912) the transverse normal stresses are everywhere compressive if the line of action passes through the kernel or core of the section-a rhombus dened by points at ±b/6 and ±d/6 on either side of the centroid (see Figure 8.1). An important consequence of this in masonry columns is that tension cannot develop and all joints will thus remain closed and able to mobilise shearing resistance across the full area of contact.
