Centrifuge Modeling of Fault Propagation through Alluvial Soils

Introduction. The behavior of alluvial deposits this machine is illustrated in Figure 1. It subjected to fault movements in the underlying has been employed in a number of investigations to bedrock is of major concern for critical structures date, including piles (Scott eta!., 1977; Scott, located within fault zones. An understanding of 1979), ocean floor anchors (Tagaya et al., 1977), fault propagation through soils would assist in slipping on a fault (Liu et al., 1978), and offdesign of such structures, but could also be shore gravity structures (Prevost et al., 1981). utilized in geological interpretation of fault displacement history. On the premise that alluvial Model Scaling fault morphology contains shear patterns •characteristic of modes and rates of fault displacements, a If the ratio of linear prototype dimensions to study was undertaken involving centrifugal and those of the centrifuge model is h, then the ratio numerical models of reverse faulting. This paper of area is h2 and volume h3. Forces in the describes the centrifuge model testing performed to prototype are h2 times those in the model, so that backup simultaneous numerical studies (Geognosis stresses are unchanged. Deformation in the Report, 1980), which will be described elsewhere. prototype is h times larger than in the model, but A comprehensive model test series under earth strains are the same. Thus, the presence of the gravity conditions (lg) involving reverse and same material in both prototype and model results normal faulting under different angles has recently in identical stresses and strains at homologous been undertaken by Cole (1979). However, model points. For dynamic problems it is of interest tests performed under lg-conditions are limited that time in the prototype is h times the model to rather thin soil layers because of their intime, but velocities are unchanged. Energy in the ability to simulate realistic gravity stress prototype is h3 times the energy in the model, but conditions. Furthermore, it is not possible to energy density is the same. simulate faulting fast enough to include inertial The friction angle of a soil being dimensioneffects with such models. less, is the same in both model and prototype. Cohesion, which is a stress, is also the same. The Centrifugal Model Testing of Soils relative contributions of the two quantities to a soil's response depends on the acceleration field. Because of the general dependence of the mechanA particular soil's behavior at lg (prototype) ical properties of soil on the ambient stress may be dominated by cohesion, whereas, at 100 g conditions, and the importance of gravity-induced (centrifugal model), the response may be mostly due stresses, scaling of geotechnical models can only to friction. be satisfied under special conditions. It is inconvenient or impossible to construct a model Test Apparatus soil material, and a real soil is usually employed in model tests. In that case, the scaling condiThe test apparatus shown in Figure 2 was detions require that the soil model be subjected to a signed to incorporate the field variables of angle higher gravitational acceleration than the protoof faulting, amount and rate of bedrock displacetype. The ratio of the accelerations in model and ment and the depth of alluvial deposit. The depth prototype structures is inversely proportional to of alluvium is constrained by the physical dimenthe ratio of their linear dimensions. To obtain sions of the centrifuge bucket and the payload. the necessary accelerations, a centrifuge is It was considered necessary that the model width required. should at least equal the soil depth to reduce A number of centrifuges have been built and used boundary effects. An 8-inch width and a 7-inch for soil testing. There are three in the United depth were chosen as the length of the model (19 Kingdom, two at Cambridge and one at Manchester, inches) was maximized, again because of boundary with radii up to 5 m and acceleration capabilities effects. up to 200 g. In the Soviet Union, a recent paper Considering that at the chosen testing accelera(Polshin et al., 1973) refers to the employment tion o'f 50g, 60 pounds of soil "weigh" 3,000 of "several dozen" centrifuges for soil testing pounds, it was necessary to simulate reverse purposes. So far, only a few small centrifuges faulting by dropping the downthrown side instead of have been used for such tests in the United States, pushing the upthrown side up. Such a faulting mode although the technique was apparently originated allows use of the centrifugal acceleration field to here (Bucky, 1931). propel the soil mass. A false bottom, representing A few years ago, a small (9-foot diameter, the downthrown section of bedrock, is mounted on maximum payload about 100 pounds at 150 g) centriroller bearings which run down hardened steel fuge was obtained from NASA surplus for use in soil ramps. Tests on a 45ø-angle of "bedrock" rupture mechanics studies at Caltech. The rotating arm of are reported here. However, the apparatus permits other fault angles to be used. Whether or not similar faulting patterns develop l_Dames & Moore, Los Angeles in the soil for both modes of bedrock motion 2California Institute of Technology, Pasadena (upthrown upward, or downthrown downward) is an interesting question. For small rupture velocities Copyright 1981 by the American Geophysical Union. both modes should theoretically be identical, due