Design of Piles in Liquefied Soils for Combined Inertial and Kinematic Demands

The design of piles penetrating liquefiable soils poses a number of challenges, including 1) accounting for the effects of liquefaction on lateral soil springs (p-y), 2) estimating liquefaction-induced kinematic demands (lateral spreading displacements) including pilepinning effects, and 3) combining the effects of inertial demands from superstructure and kinematic demands from liquefied ground. This paper illustrates two approaches to address the above questions: A) a simplified decoupled approach adopting equivalent static analysis (ESA), and B) a detailed, coupled approach adopting nonlinear dynamic analyses (NDA). These approaches are presented through example projects showing the limitations and the potential conservatism associated with the simplified decoupled ESA approach, the benefits of using more rigorous coupled NDA approach, and recommendations on how to modify ESA methods, when used, to approximate outputs from advanced NDA for slope instabilityinduced demands on piles. These modifications include using pile-restrained, rather than freefield, soil displacements in the ESA, to reduce conservatism associated with these methods. Introduction Previous earthquakes have shown that liquefaction-induced lateral spreading can cause extensive damage to deep foundations. A number of studies have focused on the response of pile foundations in liquefied soils using physical models, numerical models and case studies (e.g. Martin et al. 2002; Boulanger et al. 2007). However, the guidance varies in terms of how to modify soil springs (p-y) to account for the effects of liquefaction, and how to combine kinematic demands from laterally spreading ground with inertial demands from the superstructure. This paper describes two approaches used in the design of piles in liquefied soils through two illustrative examples. The first example explains a simplified decoupled equivalent static analyses (ESA) approach based on Caltrans (2012) guidelines. The simplified approach is used to assist with the foundation design of a 90-meter long bridge in Northern California supported by large diameter cast-in-drilled-hole (CIDH) piles penetrating potentially liquefiable, loose granular soils. To reduce uncertainty in estimating lateral spreading displacements, 2D dynamic effective-stress analyses were performed as opposed to simplified empirical methods. The kinematic and inertial demands were then combined and applied to the piles pseudostatically. The second example illustrates the detailed fully coupled approach in the foundation design of a cruise ship terminal in the Dominican Republic. The facility is located in a region of Project Engineer, Fugro Consultants Inc., Oakland, CA, USA, akhosravifar@fugro.com Senior Engineer, Fugro Consultants Inc., Oakland, CA, USA, jugalde@fugro.com Principal Engineer, Fugro Consultants Inc., Oakland, CA, USA, ttravasarou@fugro.com high seismicity and subsurface soils include liquefiable medium dense granular strata and soft normally-consolidated clays; hence, the trestle foundations had to be designed for kinematically-induced demands. Two-dimensional nonlinear dynamic analyses (NDA) were performed in FLAC, in combination with the UBCSAND constitutive model that enables dynamic effective-stress modeling of soil liquefaction in addition to embedded pile and superstructure elements. The analyses were used to guide substructure design decisions, including size of piles and final trestle geometry. Example 1: Decoupled Equivalent Static Analysis (ESA) Background The Riverfront Reconnection project consists of an approximately 90-meter long new bridge ramp in Sacramento, California. The ramp structure will be supported on five bents and will be cantilevered over Interstate Highway 5. Each bent will be supported on a single, 2.4-meter diameter CIDH pile. The subsurface soils include approximately 18-meter loose to medium dense non-plastic silts and sands overlying denser strata. The loose to medium dense sand was found to be susceptible to liquefaction using procedures by Idriss and Boulanger (2008) for the 975-year return period PGA of 0.3g and design earthquake magnitude equal to 6.9. The liquefaction-induced horizontal soil displacement associated with the elevation difference at the retaining wall will impose kinematic loads on the foundations and the proposed bridge (Figure 1a). Approach The loads and deformation demands on the bridge foundations associated with liquefactioninduced lateral spreading were computed using the procedures presented in Caltrans (2012). The recommended design procedures are based on conducting Equivalent Nonlinear Static Analyses (ESA) where the foundation is loaded by a laterally displacing soil mass in conjunction with inertial loading from the superstructure. Analyses were conducted using the software LPILE 6.0 for four cases: • Case 1 – No Liquefaction: lateral pile analyses were conducted for a loading scenario with 100% of inertial loads estimated using spectral elastic analyses. • Case 2 – With Soil Liquefaction: lateral pile analyses were performed for a loading case considering 100% kinematic + 50% elastic inertial loads. A reduction factor equal to 0.5 is applied on the inertial loads to account for the fact that individual peaks of the contributing dynamic loads and kinematic demands generally occur at different times. Kinematic loads associated with liquefaction-induced soil movement were developed based on the results of dynamic effective-stress analyses. Kinematic soil demands were imposed by means of depth varying “free-field” soil displacements. These springs in liquefied layers were factored using excess pore pressure-dependent p-multipliers to reduce the ultimate capacity along the length of liquefiable soils. • Case 3 – No Liquefaction/Plastic Demands: lateral pile analyses were conducted using superstructure plastic demands provided by the structural engineer. • Case 4 – With Soil Liquefaction/Plastic Demands: In the liquefied case, soil springs were factored with p-multipliers similar to Case 2 above. Similarly, kinematic soil demands were imposed by means of depth varying “free-field” soil displacement in the liquefied case. Finally, plastic demands were applied at the shaft head. Similar to Case 3 this case was analyzed to ensure that CIDH piles are capable to resist ultimate plastic demands from the superstructure in terms of shear forces and bending moments along the piles. Unlike Case 2, no reduction in inertial plastic demands were applied as proposed by Khosravifar et al. (2014). This was considered as an upper bound scenario. Free-field liquefaction-induced soil displacements The existing simplified empirical methodologies available to estimate liquefaction-induced lateral spreading include considerable uncertainty and are not appropriate for the geometry and boundary constraints of this project. Therefore, two-dimensional effective-stress dynamic analyses were conducted in FLAC to refine the estimates of liquefaction-induced displacement demands in the vicinity of the proposed foundations (Figure 1b). FLAC analyses were also used to estimate average excess pore-water pressure (PWP) ratios in the sand layers to modify p-y curves (p-multipliers) per Caltrans (2012). Three input ground motions were spectrally matched to 975-year target spectra and used as input to the dynamic analyses. Results Figure 2 presents the detailed lateral pile analyses results for Case 2 load combination (100% of the kinematic demands and 50% of inertial demands). The figure presents depth varying: a) idealized p-multiplier used to modify the soil springs in sandy layers, b) horizontal kinematic soil demand and estimated pile deflection, c) soil reaction, d) shear force demand, e) bending moment demand. The estimated pile head deflection is approximately 7 cm for a case where soil displacement is about 0.3 meter at depths of 9 to 12 meters. The total additional force transferred on the soil as a result of the pile deflection is estimated equal to approximately 3 MN over a vertical length of about 5.5 meters from the top of the shaft. Given the close proximity of the pile to the retaining wall, and the large magnitude of the additional force (e.g., larger than the estimated at-rest soil pressure), it was recommended that foundation isolations be used to reduce the potential of additional loading on the wall. Example 2: Fully Coupled Nonlinear Dynamic Analysis (NDA) Background The Amber Cove Cruise Ship Docking Facility is located in Maimon Bay near Puerto Plata, Dominican Republic. The docking facility was designed to accommodate two cruise ships and includes a main pier (400 m long supported on 30 bents), trestle (200 m long supported on 17 bents), and mooring and berthing dolphins. Each bent is supported by a 1-by-3 pile group of open-ended steel pipes with outer diameter of 0.76 m spaced at 3.5 m center-tocenter. The project is located in a highly seismically active area, just within 15 km of the Mouchoir Bank subduction source to the north and additional local faults with large magnitude potential (M~7.5). Probabilistic seismic hazard analyses (PSHA) were conducted which incorporated local faults to develop design acceleration response spectra for the project location (Fugro, 2013). The estimated PGA was an outstanding 0.98g at rock for the MCE design level.