Keywords: shear-wedge model, embankment, soil inelasticity, stiffness degradation, strength degradation, radiation damping.

The earth embankments of bridges usually have a length that is several times larger than the dimension of the trapezoidal cross section of the embankment. Typical approach embankments extend 150m or more earth end abutment of the bridge. Due to this geometry several researchers have adopted a two-dimensional plane-strain idealization to derive response quantities.

In 1936 Mononobe [1] was the first to consider that earth dams and embankments are deformable bodies, and introduced the ingredients of what has come to be called the "shear-wedge" model. However, it was not until twenty years later that this model was fully explored and achieved the status of engineering theory, following the work of Hatanaka [2] and Ambrasseys [3]. Hatanaka [4] confirmed that bending-type rocking deformations are negligible compared to those in simple shear. The developed shear-wedge model was exploited in the 1960s and 1970s to interpret the results of full-scale tests, to perform parameter studies aimed at gaining a better understanding of the problem. The 1960s also witnessed the first implementation and subsequent wide-spread use of the finite-element method in studying the seismic response of the earth dams [5,6,7]. However, at least two finite-difference studies [8,9] had earlier recognised the 2-D nature of dynamic deformations experienced by infinitely long embankment dams subjected to vertical S-waves, under plane-strain conditions.

The "shear-wedge" or "shear-beam" concept has served as the foundation for many of the newly developed models, and will thereby take major place in the subsequent presentation. In its original (pre-1980) form the shear-beam model involved the following major simplifying assumptions: (a) only horizontal lateral displacements and simple shearing deformations take place, (b) displacements and shear stresses and strains are uniformly distributed along horizontal planes across the embankment, (c) the embankment consists of a homogeneous material which behaves as a linear visco-elastic solid and described by a constant shear modulus, damping ratio, and mass density, and (d) the embankment is either infinitely long and is subjected to a synchronous rigid-base lateral motion.

A number of analysis methods of varying degrees of accuracy and efficiency have been developed for the response of bridge earth embankments. However, the "shear-wedge" model involves complicated material and geometric nonlinearities, such as soil inelasticity, stiffness and strength degradation with cycling loading and radiation damping. In this work, the nonlinear response of shear-wedges is described through a hysteretic model of the Bouc-Wen type. The numerical study has preliminary addressed (a) the lateral monotonic, (b) the dynamic - sinusoidal type - response of wedges and (c) the dynamic response due to Ricker and Tsang pulses. Numerical examples are presented that illustrate the non-linear behaviour and versatility of the unified approach. The model is shown to be capable of simulating complex nonlinear characteristics of the wedge response. The results highlight the significant role of soil yielding in the overall response of the wedge and as a result the greater role of the wedge with respect to the bridge superstructure. The predictions of the method compare adequately with results from the two-dimensional finite element analysis using ABAQUS.

1

Mononobe, H.A. et al. "Seismic stability of the earth dam", Proc. 2nd Congress on Large Dams, Washington DC, IV, 1936.

2

Hatanaka, M., "3-Dimensional consideration on the vibration of earth dams", J. Jap.Soc.: Civ. Engrs. 1952, 37, 10.

3

Ambraseys, N.N., "On the shear response of a two-dimemsional truncated wedge subjected to an arbitrary disturbance", Bull. Seism. Soc. Am., 1950, 50(1), 45-46.

4

Hatanaka, M., "Fundamental consideration on the earthquake resistant properties of the earth dam", Bull. No.11, Disaster Prevention Research Inst., Kyoto Univ., 1955.

5

Chopra, A.K., "Earthquake response of earth dams", J. Soil Mech. And Found. Div., ASCE 1967, 93, SM2.

6

Clough, R.W. and Chopra, A.K., "Earthquake stress analysis in earth dams", J. Engrg. Mech., ASCE 1966, 92, EM2.

7

Chopra, A.K., Dibaj, M., Clough, R.W., Penzien, J. and Seed, H.B., "Earthquake analysis of earth dams", Proc. 4th World Conf. on Earthq. Engrg., Santiago, 1969.

8

Ishizaki and Hatekeyama, "Consideration on the dynamical behaviour of earth dams", Bull. No. 52, Disaster Prevention Research Inst., Kyoto Univ., 1963.

9

Medvedev, S. and Sinitsym, A., "Seismic effects on earth fill dams", Proc. 3rd World Conf. Earthq. Engrg., New Zealand, 1965, Paper IV/M/18.

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