We present a 3D-DDA formulation that uses an explicit time integration procedure and an efficient contact detection algorithm optimized to minimize the computational effort. The advantages of the explicit formulation are that the global stiffness matrix does not need to be assembled and the linear equations do not need to be solved by matrix inversion. Consequently, the computational effort and memory requirement can be reduced considerably, which is important for efficient solution of large 3D problems. In addition, the computational efficiency is increased by eliminating unnecessary contact computations using a grid based nearest neighbor search. The grid divides space into a number of cells of equal size and each object is then associated with the cells it overlaps. As only objects overlapping a common cell can possibly be in contact, in-depth tests are only performed on objects found sharing cells with the block tested for collision. The contacts between the blocks are detected by using Fast Common-Plane (FCP) approach. The halfedge (HE) data structure approach is used to handle the navigation into the topological information associated with polyherdral objects (vertices, edges, faces). The halfedge data structure allows for quick traversal between faces, edges, and vertices due to the explicitly linked structure of the network. Examples are provided which demonstrate the capabilities of new algorithm and the size of problem that can be analyzed. Copyright 2013 ARMA, American Rock Mechanics Association.

We present a three dimensional fluid-structure coupling between SPH and 3D-DDA for modelling rock-fluid interactions. The Navier-Stokes equation is simulated using the SPH method and the motions of the blocks are tracked by a Lagrangian algorithm based on a newly developed, explicit, 3D-DDA formulation. The coupled model is employed to investigate the water entry of a sliding block and the resulting wave(s). The coupled SPH-DDA algorithm provides a promising computational tool to for modelling a variety of solid-fluid interaction problems in many potential applications in hydraulics, rock mass stability, and in coastal and offshore engineering. © 2013 Taylor & Francis Group.

Observations of the performance of basement walls and retaining structures in recent earthquakes show that failures of basement or deep excavation walls in earthquakes are rare even if the structures were not designed for the actual intensity of the earthquake loading. Failures of retaining structures are most commonly confined to waterfront structures retaining saturated backfill with liquefaction being the critical factor in the failures. Failures of other types of retaining structures are relatively rare and usually involve a more complex set of conditions, such as sloping ground either above or below the retaining structure, or both. While some failures have been observed, there is no evidence of a systemic problem with traditional static retaining wall design even under quite severe loading conditions. No significant damage or failures of retaining structures occurred in the recent earthquakes such as Wenchuan earthquake in China (2008) and, or the large subduction zone earthquakes in Chile (2010) and Japan (2011). Therefore, this experimental and analytical study was undertaken to develop a better understanding of the distribution and magnitude of seismic earth pressures on cantilever retaining structures. The experimental component of the study consists of two sets of dynamic centrifuge model experiments. In the first experiment two model structures representing basement type setting were used, while in the second test a U-shaped channel with cantilever sides and a simple cantilever wall were studied. All of these structures were chosen to be representative of typical designs. Dry medium-dense sand with relative density on the order of from 75% to 80% was used as backfill. Results obtained from the centrifuge experiments were subsequently used to develop and calibrate a two-dimensional, nonlinear, finite difference model built on the FLAC platform. The centrifuge data consistently shows that for the height of structures considered herein, i.e. in the range of 20-30 ft, the maximum dynamic earth pressure increases with depth and can be reasonably approximated by a triangular distribution This suggests that the point of application of the resultant force of the dynamic earth pressure increment is approximately 1/3H above the base of the wall as opposed to 0.5-0.6 H recommended by most current design procedures. In general, the magnitude of the observed seismic earth pressures depends on the magnitude and intensity of shaking, the density of the backfill soil, and the type of the retaining structures. The computed values of seismic earth pressure coefficient (∆Kae) back calculated from the centrifuge data at the time of maximum dynamic wall moment suggest that for free standing cantilever retaining structures seismic earth pressures can be neglected at accelerations below 0.4 g. While similar conclusions and recommendations were made by Seed and Whitman (1970), their approach assumed that a wall designed to a reasonable static factor of safety should be able to resist seismic loads up 0.3 g. In the present study, experimental data suggest that seismic loads up to 0.4 g could be resisted by cantilever walls designed to an adequate factor of safety. This observation is consistent with the observations and analyses performed by Clough and Fragaszy (1977) and Fragaszy and Clough (1980) and Al-Atik and Sitar (2010) who concluded that conventionally designed cantilever walls with granular backfill could be reasonably expected to resist seismic loads at accelerations up to 0.4 g. Finally, numerical models using FLAC finite difference code were quite successful and able to produce a reasonably good agreement with the results of the centrifuge experiments. However, while the finite difference models were able to capture the main aspects of the seismic response observed in the centrifuge experiments, the results of the analyses were highly sensitive to the selection of soil and interface parameters. Therefore, numerical models used for future designs should be carefully calibrated against experimental data to provide reliable results.

Observations of the performance of basement walls and retaining structures in recent earthquakes show that failures of basement or deep-excavation walls in earthquakes are rare even if the structures were not designed for the actual magnitude of the earthquake loading. For instance, no significant damage or failures of retaining structures occurred in the recent Wenchuan earthquake in China (2008) or in the subduction earthquakes in Chile (2010) and Japan (2011). To develop a better understanding of the distribution and magnitude of the seismic earth pressures on cantilever retaining structures, a series of centrifuge experiments were performed on model retaining and basement structures with medium dense cohesionless backfill. This paper provides a general overview of the research program and its results. Two sets of centrifuge-scale experiments were carried out on the centrifuge at the Center for Geotechnical Modeling at UC Davis. Three different types of prototype retaining structure were modeled in this research effort as follows: (1) a nondisplacing cross-braced (basement) structure with a stem stiffness of 5.92 × 1010 lb-in.2 per ft width (5.57 × 1005 kN-m2 per m width) and 1.04 × 1010 lb-in.2 per ft width (9.79 × 1004 kN-m2 per m width); (2) a nondisplacing U-shaped cantilever structure with a stem stiffness of 5.92 and 1.04 × 1010 lb-in.2 per ft width (9.79 × 1004 kN-m2 per m width); and (3) a free standing, cantilever retaining wall with a stem stiffness of 2.4 × 1010 lb-in.2 per ft width (2.26 × 1005 kN-m2 per m width). Overall, for the structures examined [i.e., wall heights in the range 6.1-9.15 m (20-30 ft)], the centrifuge data consistently show that the maximum dynamic earth pressure increases with depth and can be reasonably approximated by a triangular distribution. This suggests that the result of the dynamic earth pressure increment acts near 0.33H above the footing as opposed to 0.5-0.6 H recommended by most current design procedures. The current data also suggest that cantilever walls can resist ground accelerations up to 0.4 g if designed with an adequate static factor of safety.

We present a three dimensional fluid-structure coupling between SPH and 3D-DDA for modelling rock-fluid interactions. The Navier-Stokes equation is simulated using the SPH method and the motions of the blocks are tracked by a Lagrangian algorithm based on a newly developed, explicit, 3D-DDA formulation. The coupled model is employed to investigate the water entry of a sliding block and the resulting wave(s). The coupled SPH-DDA algorithm provides a promising computational tool to for modelling a variety of solid-fluid interaction problems in many potential applications in hydraulics, rock mass stability, and in coastal and offshore engineering.