Analysis of the Ground Response - part 1
Geology of the Managua area
Ground movements that develop in a soil deposit during an earthquake can be attributed in many cases mainly to the vertical propagation of shear waves from the underlying rock formation. Analytical methods developed to determine the ground response to seismic excitements under these conditions incorporate the non-linear characteristics of the shear-strain relationship [Schnabel et. al., 1972] [Seed et. al., 1970].
The application of analytical methods, in which the restriction of vertical propagation of the wave is implicit, is justified in the following considerations [Martínez, 1977]:
- The strong earthquakes that affect the area of the city occur at very short distance, practically under the city. And the depth is greater than the diameter of the area where an earthquake would cause worse damages, and it is also bigger than the distance between any sites within that area and the superficial features of any fault which could originate a strong earthquake [Faccioli et. al., 1973]. Therefore the seismic waves impact in short angle with the vertical.
- Propagation of seismic waves have the tendency to become vertical as the waves are refracted toward less dense materials, which almost invariably are nearer to the surface, diminishing this way their speed.
- It is assumed [Tsai, 1969] that the superficial waves, of long period, cause that the soil deposits become agitated approximately in phase, as if they were subjected to the excitement of plane volumetric waves impacting vertically.
The election of the method depends on the configuration of the soil deposit [Seed, 1974]. For those cases in which all the frontiers of a stratified or homogeneous deposit are essentially horizontal, the ground can be taken as a series of semi-infinite strata. This way, the analysis becomes a one-dimensional problem. This technique is also known as model of the vertical shear beam [Dowrick, 1995].
On the other hand, if the deposit presents irregular or inclined interfaces between each layer, it is required to apply a procedure that takes care of the two-dimensional aspects of the problem. An appropriate method is that of Finite Elements.
The analysis of the ground response as a one-dimensional system is applicable to the study of the behaviour of the soils of Managua since the materials of the Managua Group that overlays to the Las Sierras Group, are presented in well-defined layers and their limits are essentially horizontal.
Two analysis methods based on these conditions exist, one based on the continuous solution of the wave equation in the field of the frequency, and another in which the soil deposit is represented by a series of concentrated masses connected to springs [Seed, 1974].
Both methods give the same results [Seed, 1974], and it has been proven that their results are in reasonable agreement with field observations [Schnabel et. al., 1972] [Seed, 1974].
Whichever it is the method applied, it will be possible to make reasonably good evaluations of the characteristics of the ground surface movement if the soil properties have been correctly evaluated and the movements of the base have been assessed with certain precision.
The analytic procedure based on this method, incorporating the non-linear behaviour of the soil, supposes the following steps [Schnabel et. al., 1972] [Seed et. al., 1970]:
- To evaluate the characteristics of the movements that could develop in the rock underlying the site and to select an accelerogram with those characteristics to be used in the analysis. The maximum acceleration, the predominant period and the effective duration are the parameters of the earthquake that are more important to consider.
- To determine the configuration and extension of the strata that composes the deposit, from the surface to the basement.
- To evaluate the dynamic properties (shear module and damping) of the different types of soils, and how these properties vary with the strain.
- To calculate the soil deposit response to the movements at the basement. The Fourier spectrum of the basement movement is multiplied for the transfer function that transforms the harmonic movements of induction at the bedrock into movements on the surface [Dowrick, 1995]. The resulting Fourier spectrum is inverted to know the amplitude of the movements on the ground surface [Seed, 1974].
The dynamic analysis was carried out by means of the program SHAKE91. It is based on the continuous solution of the wave equation, adapted to use with transitory movements by means of the Fast Fourier Transform algorithm.
The program uses soil properties linear equivalent with an iterative procedure to obtain properties compatible with the deformations developed in each stratum [Schnabel et. al., 1972].
Another advantage, derived from the technique of the transfer function, is that the movements in the basement can be easily estimated from the movements in the surface, which are usually those that are registered. Then it constitutes a useful source of induction data in the bedrock of another place [Dowrick, 1995].