Evaluation of cyclic behavior of dense sands under multidirectional loading using centrifuge tests

The seismic performance of nuclear power plant (NPP) structures constructed on compacted, coarse-grained soil depends on the soil’s cyclic shear stress – shear strain – volumetric strain response. NPPs founded on a thick deposit of dense coarse-grained soil may experience nontrivial settlements due to small, but accumulated volumetric strains during an earthquake. Studies that have investigated the seismic response of granular are primarily limited to unidirectional loading. However, since seismic events are multidirectional in nature, design based on unidirectional studies may lead to underestimation of vertical strains, and nontrivial settlements that can impact structures. While correlations to estimate vertical strains from drained and undrained cyclic element tests are available, they do not all explicitly incorporate multidirectional shaking. Moreover, typical drainage conditions in the field may be partially drained while shaking-induced vertical strains accumulate. This work forms a unique database of dynamic centrifuge “case-histories” that provide insight into the shear and volumetric response of dense coarse-grained soils under unidirectional and bidirectional loading under partially drained conditions. Dynamic centrifuge tests were performed on thick (up to 20m) layers of saturated dense Ottawa sand (D = 95%) with models representing both free-field and a soil-structure (near field) system excited using unidirectional and bidirectional historical broadband motions.\nFree-field centrifuge experiments highlight that shear response in each orthogonal direction is not affected by multidirectionality. Thus, site shear response can be estimated for use in one-dimensional non-linear site response analysis. In contrast, centrifuge tests illustrated that volumetric strains (v) and excess porewater pressures (evaluated in terms of excess porewater pressure ratio, ru) are affected by multidirectionality irrespective of density, with the ratios of bidirectional to unidirectional v and ru ranging from 1 to 4. Consequently, multidirectional factors relationships for v and ru are proposed as a function of FSliq. Furthermore, Energy-based intensity measures (Arias and Housner intensities) provided nearly unique estimates of excess PWP and (v) for both 1D and 2D motions, indicating that they capture multi-directionality effects, while vectored peak accelerations and velocities (PGA and PGV) yielded different relationships for 1D and 2D motions.\nA semi-empirical hyperbolic (GQ/H), simplified model based on ground motion intensity parameters (e.g., Housner Intensity), and shear wave velocity (Vs) is proposed to estimate vertical strains in dense coarse-grained soils under free field conditions. Comparison of GQ/H model predictions and estimates based on undrained cyclic shear tests indicated that the latter consistently overpredicts the measured settlements in the dense sand profiles. In contrast, the approach based on drained cyclic shear tests reasonably agrees with both measured settlements and GQ/H-v model. Further comparison of recorded near field settlements from centrifuge test data indicate that the (GQ/H) simplified free model underestimates settlements beneath the structures tested here. \nLastly, a semi-empirical near field model to estimate vertical strains beneath structures is proposed. This model also includes ground motion intensity measures to account for duration (e.g., Housner intensity) in conjunction with a rocking stiffness parameter (originally proposed by Gazetas 1991) derived from shear wave velocity Vs. The vertical strain model requires estimates of Housner Intensity by means of nonlinear site response analysis. The proposed vertical strain models reasonably capture free field and near field settlements on dense sands recorded in dynamic centrifuge tests. \nThe aforementioned two semi-empirical models are used in conjunction to estimate settlements of structures founded primarily on dense sands during shaking.

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