The seismic responses of abutment rock mass of two arch dams were analysed by F.E.H. The influence of boundary conditions of the calculation model on the dynamic response of the abutment were studied. The results agreed quite well with those of in-situ, measurements and model tests.
La reponse sismique de la foudation d'aboutement en deux barrages en voûte est analysee par la methode d'element fini. L'influence des conditions frontières du calcul modele sur les proprietes dynamiques de la masse de rocke a ete etudies. Les resultats du mesurage de sur place correspond bien à celui de l'essai modele.
Die Erdbebenreaktion der seitlichen Gesteinsauflager in zwei Bogenstaumauern wird durch F.E.H untersucht. Der Einfluss der Randbedingungen des numerischen Modells auf die dynamische Eigenschaft wird bewertet. Die Resultate stimmen mit der Feldsvermessungen und der Hodellversuchen ueberein.
Engineering structures such as dams, bridges, mines, etc., located in areas of high seismic risk must be such 'designed as to safely resist dynamic excitation by earthquakes. The amplitude of ground motion at the top of a canyon could be 1–3 times greater than that at the toe. Obviously, this amplification behavior is unfavorable for the aseismic stability of the slope of rock mass. Therefore, to study the dynamic behavior and seismic response of rock mass is important and to find out a method to evaluate them is imperative.
This paper conducted a study on the dynamic behavior of rock mass by finite element method (F.E.H), and calculated the seismic responses of abutment foundations for two arch dams. The results were compared with those obtained from in-situ measurements of ambient vibrations and geomechanic model tests.
With certain restraint conditions on the boundary of rock mass given, the canyon can be idealized as an assemblage of finite elements as shown in Fig.1. The applicability of this model depends on the simulation of the boundary, topographic and geological conditions, and on the degree of absorption of the reflected waves. The effects of the boundary on the dynamic behavior of rock mass will be described later.
The equations of motion of a discretized system can be written as
(Equation in full paper)
where H, C, K are the mass, damping, and stiffness matrices of the system respectively; V is the vector of relative displacement of the nodal point;. the vector Vg includes 3 components of earthquake acceleration imposed upon the rigid base, and r is an influence coefficient matrix.
Two typical methods were used to solve the equations. One is the "response spectrum" method. It was assumed that only a limited number of lower modes of the system evaluated by the subspace iteration method was excited and only the maximum value of each component was estimated on the basis of the definition of standard spectral accelerations.
Another procedure for solving the equations is the response history method. The complete history of displacement and acceleration of each degree of freedom can be obtained by a step-by-step direct integration scheme. By selecting the time step ∆t properly, the higher modes of the system can be considered.
8-node 3-D solid elements were used. The finite element models are shown in Fig.1 and Fig.2 model I (Fig.1) is the model of the abutment of Longyangxia arch dam located on the Yellow river in Northwest China. The dam is 178m high and the canyon wall is of nearly the same height as the dam. The main fault F7 and the variation of elastic modulus of the rock with
(Figure in full paper)
elevation were simulated in the model. Model II (Fig.2) is the model of the left abutment of the Ertan arch dam located in Southwest China. The dam is 240m high and the canyon is much higher than it.
The calculation were performed by using the program SAP5. The details of the formulation are described elsewhere (Bathe & Wilson 1976) and need not be repeated here.
In order to check the results obtained by F.E.M, a comparison with those obtained from in-situ measurements of ambient tests in the sites of Longyangxia and Ertan (Zeng & Li 1985) and from geomechanic model tests. The excitation of the tests were analysed by a stochastic procedure. The transfer function of each point of rock mass was obtained by in-situ measurements or by model tests in which excitation was effeated by random or impulsive loading. The power spectral density function such as standard white noise and filtered white noise with predominant frequency (fg) of 2.5,5, and 10Hz were input. Then the seismic response of rock mass can be estimated in the frequency domain.
