الفهرس 
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Abstract
The seismic behavior of retaining walls has been the subject of considerable geotechnical research over the last century since the early attempts by Okabe (1926) and Mononobe and Matsuo (1929) by developing the well-known M-O method. Retaining walls are classified, from seismic behavior perspective, into yielding and non-yielding walls. Basement walls are restrained at top and bottom but are relatively free to displace along their entire height depending on the flexure stiffness. Hence, basements walls are neither yielding nor completely non-yielding, and the widely used methods in the literature for yielding (e.g. M-O method) and non-yielding (e.g. Wood, 1973) walls should not be used to evaluate the seismic behavior of basement walls. The seismic behavior of basement walls is further complicated in cases where the basement does not occupy the whole structure’s footprint. In such case, the foundation stresses from the upper foundation level have remarkable effect on the seismic response and behavior of basement walls.
This research study investigates the seismic response of basement walls by numerical analysis. In particular, the study focuses on basement walls occupying part of the structure’s footprint area, i.e. basement walls in structures with two foundation levels. A numerical model is developed to simulate the full seismic interaction between foundation elements, i.e. basement walls and footings, and the surrounding soil, which is considered to consist of dry dense sand. The finite difference method is utilized in the numerical analysis. The developed numerical model is verified by simulating the results of a centrifuge test carried out for a restrained retaining wall in dry sand.
The problem configuration involves a four-story structure with a total width of 20 m, equally distributed over five spans. The structure consists of one basement. Different basement coverage ratios are investigated. A reference case is analyzed where the basement occupies the whole structure’s footprint; i.e. the basement coverage ratio equals 100%. This case is considered for comparison with the results of other cases where the basement occupies part of the structure’s footprint. Basement coverage ratios of 80, 60, 40 and 20% are simulated and analyzed, and the seismic response of the basement wall is compared with the reference case of 100% coverage.
The constitutive behavior of dry sand is represented by the nonlinear dynamic model developed by Byrne (1991). The model accounts for the volumetric-shear strain coupling during seismic events. Byrne (1991) model is an extension to the nonlinear model developed by Martin et al. (1975), but with fewer constants required for characterization of soil behavior.
An extensive parametric study is carried out where the effects of all potential influential parameters are investigated. The effects of each of the peak ground acceleration (PGA) at bedrock, depth of bedrock below bottom of foundations, basement wall thickness and basement clear height are investigated. The seismic excitation is simulated using an artificial earthquake time history applied at the bottom boundary of the model, which corresponds to the top of bedrock. The acceleration records are scaled to correspond to PGA values of 0.10, 0.125, 0.15 and 0.20g. The effect of seismic waves’ propagation is considered by varying the depth of bedrock below the lower foundation level from 10 to 25 m at an interval of 5 m. Basement wall thicknesses of 0.2, 0.3, 0.4 and 0.5 m, and basement clear heights of 3.0, 4.0 and 5.0 m are investigated.
The results are presented and interpreted in terms of the following behavioral aspects:
- Acceleration response of basement wall and footings;
- Seismic earth pressure and seismic thrust responses;
- Seismic bending moment response; and
- Seismic shear force response
The results are presented in the form of charts describing the variation of each of the above quantities with the depth below wall top.
5.2. Conclusions
The study highlights key aspects of the seismic behavior of basement walls, with special focus on basements occupying part of the structure’s footprint. The conclusions of this research study can be summarized as follows:
- The earthquake intensity, represented by PGA at bedrock, and the distance travelled by seismic waves from top of bedrock to the structure are the primary factors governing the acceleration response of basement walls and footings. Amplification of seismic waves is evident in all the analyzed cases, and ranges from 1.15 to 2.3 depending on the PGA and bedrock depth below bottom of foundations. These amplification factors are specific to the soil type and density condition considered in this research study, i.e. dry dense sand, and may not be applicable to other soil types and/or density conditions.
- There is an obvious conjugation/interdependence between the seismic thrust, derived from peak seismic earth pressure, and the peak acceleration response of the basement wall. The results of this research study have enabled developing simple empirical equations to determine the upper and lower bound peak seismic thrust acting on the wall as a function of the peak acceleration response. The developed equations are applicable to basement coverage ratios of 20, 40, 60, 80 and 100%, and include, in an implicit way, the effects of other investigated factors like the wall thickness and basement clear height.
- For basement walls connecting two foundation levels, i.e. basements occupying part of the structure’s footprint, the stresses from the upper footings are shown to have two conflicting effects on the seismic behavior of basement walls. These two effects are the confinement effect and distortion effect. The confinement effect results from the increase in the mean principal stress, while the distortion effect results from the increase in shear stress level. The confinement effect is more dominant for basement coverage ratio of 80%, while the distortion effect is more dominant for basement coverage ratios of 20, 40, 60 and 100%.
- Simple empirical equations are also developed to determine the upper and lower bound peak seismic bending moment and shear force acting on the wall as a function of the peak acceleration response. The developed equations are applicable to basement coverage ratios of 20, 40, 60, 80 and 100%, and include, in an implicit way, the effects of other investigated factors like the wall thickness and basement clear height.
- The seismic bending moment is affected by the wall inertia, which is represented by the wall thickness. Although this conclusion appears logic, the wall inertia effect was not addressed in some of the well-known methods in the literature (e.g. Wood, 1973), which assumes an infinitely rigid wall.
- Soil nonlinearity is a key factor towards understanding and evaluating the seismic behavior of basement walls. The available empirical methods are based on some simplifying assumptions including linear elastic behavior of soil, which ignores stiffness degradation and damping, and underestimates the induced volumetric and shear strains during seismic loading.
5.3. Recommendations for Future Research
The conducted research study identifies some important aspects of the seismic behavior of basement walls connecting two foundations levels, and also basement walls occupying the whole foot print area of the structure in dry cohesionless soils. Further research studies are sought to investigate the following:
1. Other complex systems of non-yielding walls include strutted and anchored in-situ walls. Their seismic response is sophisticated and cannot be evaluated by the methods available in the literature for non-yielding walls.
2. The current study focuses on the interaction with dry cohesionless soils. Further studies are required to investigate the effect of other soil types, e.g. cohesive soils, on the seismic behavior of basement walls. Further research is also required to study the effect of soil saturation and excess pore pressure generation during seismic loading on the overall behavior in terms of hydrodynamic pressures and/or loss of shear strength due to liquefaction.
3. The current study focuses on the acceleration, earth pressure, bending moment and shear force responses of basement walls. Post-earthquake deformation is also an important aspect of the seismic behavior of retaining walls in general and basement walls in particular. In many cases, the seismic design can be governed by serviceability after the end of the earthquake episode.