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Next, the scope and objectives of the performed research are presented. An outline of the dissertation concludes the chapter.1.1 Passive Earth PressureIn geotechnical engineering practice, earth pressure is categorized as at-rest, active,or passive (Lambe and Whitman 1969). “At-rest” earth pressure occurs when a stiff,massive or otherwise restricted retaining wall does not move relative to the supported soil (the backfill).“Active” earth pressure can occur if a wall moves away from the adjacent backfill,decreasing pressure and inducing extensional lateral strain in the soil (Kramer 1996). If a wall moves sufficiently far away, the soil will fail in shear along a surface (the failure plane), and a wedge will slide down and towards the wall. In that limit state, minimum active earth pressure acts on the wall. As such, active earth pressure is lower than the atrest condition (Figure 1.1). In contrast, “passive” earth pressure occurs if a wall moves towards the adjacent backfill, increasing pressure and inducing compressive lateral strain (Kramer 1996). If the wall moves sufficiently toward the backfill, the soil will fail in shear along the failure plane, a wedge will slide up that slope, and maximum passive pressure acts on the wall. As expected, passive pressure is higher than the at-rest condition, and often exceeds the active pressure by a significant factor (Figure 1.1). Mobilization of the maximum passive pressure also typically requires greater displacement than that of the minimum active earth pressure (Figure 1.1). Passive earth pressure can provide stability in a range of applications. On theshallow side of a retaining wall (Figure 1.2), passive pressure resists sliding andoverturning (Lambe and Whitman 1969). A bulkhead or sheet pile (Figure 1.3) may be anchored to a wall which mobilizes passive pressure (Lambe and Whitman 1969).Abutment backfills (Figure 1.4) provide passive resistance to earthquake-induced bridge deck displacements (Caltrans 2004, AASHTO 2007, Shamsabadi et al. 2007,Bozorgzadeh 2008, Lemnitzer et al. 2009).
Acting on the cap of a pile group (Figure1.5), passive pressure also increases the lateral stiffness and capacity (Gadre and Dobry 1998, Cole and Rollins 2006, Rollins and Cole 2006). Conversely, passive earth pressure may exert detrimental loads. An integral abutment (Figure 1.6) may transmit forces to the bridge deck and foundation from passive pressure due to thermal expansion (Duncan and Mokwa 2001, Shah 2007). Due to lateral offset from a seismic fault rupture, buried tunnels and pipelines may also experience passive pressure loads (Wang and Yeh 1985, Lin et al. 2007, Abdoun et al. 2008).1.1.1 Passive Earth Pressure TheoriesBased on limit equilibrium and simplifying assumptions, the Coulomb, Rankine and Log Spiral methods (Lambe and Whitman 1968, Terzaghi et al. 1996) are commonly used to predict passive earth pressure. These predictions require accurate values for parameters including the soil friction angle φ, cohesion c, soil unit weight γ, the supported soil height H, wall-soil interface friction δ, and other geometric properties of the wall and backfill as discussed below.1.1.1.1 Rankine TheoryRankine’s theory (1857) offers a simple prediction of the peak passive earthpressure. This theory applies to smooth (δ = 0) vertical walls, and assumes that thefailure plane (mentioned above) forms at the inclination where the Mohr-Coulomb failure criterion (Lambe and Whitman 1969) is met, at an angle of 45 + φ/2 from the vertical (Figure 1.7). According to Rankine theory (1857), the earth pressure is assumed to act at an angle β from the horizontal, which is equal to the slope of the backfill. Based on these assumptions, the passive pressure resultant force Pp can be estimated using the following equations: where Kp is the coefficient of maximum passive earth pressure. The Rankine solutionyields:For cohesive backfills, Eq. (1.1) can be extended to:In most practical cases, the smooth wall (δ = 0) assumption is not accurate, and asa result the Rankine passive pressure prediction tends to under-estimate the actualavailable resistance (Kramer 1996, Terzaghi et al. 1996). However, due to its simplicity it is often used.1.1.1.2 Coulomb TheorySimilar to the Rankine theory, Coulomb (1776) assumed that the failure wedgeformed along a planar surface, but extended the prediction to include δ, and wallsinclined at an angle θ from the vertical (Figure 1.8). By employing force equilibrium on trial failure wedges (Figure 1.8), and finding the surface that yields the critical(minimum) passive resistance, the Coulomb (1776) method provides the followingequation: Equation (1.4) can be used in Eq. (1.1) to calculate the peak passive pressure resultant Pp.The Coulomb Theory provides a convenient equation to accountfor δ, and inclined walls. However in cases with large δ, a curved portion of the failure surface has been observed after experiments (Cole and Rollins 2006). As a result, the Coulomb prediction tends to over-estimate the passive resistance in such cases (Kramer 1996, Duncan and Mokwa 2001, Cole and Rollins 2006).1.1.1.3 Log Spiral TheoryFor a rough wall (δ > 0), due to the shear stresses on the wall-soil interface, themajor principal axis may be shifted, resulting in a curved failure surface near the wall(Kramer 1996). This curvature can be accounted for by using a log spiral function todescribe the failure surface shape near the structure (Figure 1.9), with a relatively straight section closer to the backfill surface, depending on the value of δ (Terzaghi et al. 1996). By employing a graphical solution (Terzaghi et al. 1996), or a numerical analysis technique such as a spreadsheet (Duncan and Mokwa 2001), the force equilibrium can be solved in order to obtain the critical (minimum) peak passive resistance using such a curved wedge shape. Charts are also available which list Kp values based on this method, which can in turn be used with Eq. (1.1) to compute the peak passive pressure resultant (e.g., Caquot and Kerisel 1948). As discussed in further detail below, the log spiral method has been shown to provide a more accurate (lower) prediction than the Coulomb theory, particularly when δ > φ/2 (Kramer 1996, Duncan and Mokwa 2001). However, this method can be much more complex and time consuming to use, and is often avoided for these reasons.1.1.2 Passive Pressure Mobilization with DisplacementWhile the Rankine, Coulomb and Log Spiral theories provide estimates of the peakload resistance, no information is provided about the associated force-displacementrelationship. In many practical cases, this relationship plays a major role. Examplesinclude bridge abutment deflection (Caltrans 2004, Bozorgzadeh 2007, Shamsabadi et al. 2007, Lemnitzer et al. 2009), and lateral resistance of shallow foundations and pile caps (Gadre and Dobry 1998, Cole and Rollins 2006, Rollins and Cole 2006).Compared with experimental data, hyperbolic models (Figure 1.10) have been shown to provide a good representation of the passive load-deflection behavior up to the peak resistance (Duncan and Mokwa 2001, Shamsabadi et al. 2007). Shamsabadi et al. (2007) proposed a model based on a secant stiffness K. Employing the parameters shown in Figure 1.10, the derived Hyperbolic Force-Displacement (HFD) model of Shamsabadi et al. (2007) is described by: where F is the resisting force, y is the horizontal displacement, Fult is the maximum passive resistance, and K is the secant stiffness at Fult /2 (Figure 1.10). Shamsabadi et al. (2007) also offer a flowchart for an iterative procedure to calculate the forcedisplacement curve based on soil properties which can be measured in the lab. Alternatively, Duncan and Mokwa (2001) employed a hyperbolic model (Figure 1.10) defined by the initial stiffness (Kmax) according to the following equation: where Rf is a failure ratio (refer to Duncan and Mokwa 2001 and Cole and Rollins 2006 for further description). Duncan and Mokwa (2001) also offer a spreadsheet (PYCAP) which can calculate the force-displacement curve based on soil properties and recommended parameters. 1.1.3 Experimental StudiesDuncan and Mokwa (2001) performed two passive pressure load tests on a 1.1 meter tall, and 1.9 meter long, and 0.9 meter wide anchor block, first with natural sandy silt (ML) and sandy clay (CL) backfill, and next with crusher run aggregate (GW-GM and SW-SM) backfill. From those tests, Duncan and Mokwa (2001) concluded that the Log Spiral predictions, together with the Brinch-Hansen (1966) correction for 3D effects (on the sides of the anchor block where additional shear resistance occurs) provided the best prediction for the peak passive resistance. The hyperbolic model of Eq. (1.6) was found to provide a good approximation of the load-deflection curve (Duncan and Mokwa 2001). Duncan and Mokwa (2001) also reported that as load was applied in those tests, the anchor block moved slightly upwards as it displaced into the adjacent backfill soil, resulting in low mobilized wall-soil friction δmob controlled by vertical equilibrium requirements