Design Earthquake Records

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Chapter 2 Literature Review

OVERVIEW

As the focus of this thesis was the integrated modelling of structures and foundations, an understanding of previous research in multiple areas of expertise was required. In this review, the following categories have been used to provide an overview of the different research areas:
• Shallow foundation modelling
• Pile foundation modelling
• Structural modelling
• Integrated structure-foundation research
The first aim of grouping research into these categories was to indicate the methods that have been used to model structures and foundation systems when they have been analysed separately. The second aim was to indicate the previous integrated modelling that has been undertaken and what level of complexity has been used to model the structure and the foundation as a combined entity.

EXPERIMENTATION AND MODELLING OF SHALLOW FOUNDATIONS

This section will focus on the stiffness, damping and the bearing capacity of shallow foundations. The complex nature of the interaction between the foundation and the surrounding soil has led to development of simplified models. Three common methods used to model shallow foundations in previous research were:
• Bed of Winkler springs
• Elastic Continuum
• Finite Element
A range of experimental and analytical studies have been undertaken in order to better understand the characteristics of shallow foundations. Many researchers have studied the rocking behaviour of shallow foundations and the impact of non-linear foundation behaviour (Bartlett 1976; Georgiadis and Butterfield 1988; Martin and Lam 2000; Pecker and Pender 2000; Taylor et al. 1981; Taylor and Williams 1979; Wiessing 1979). Using 1g cyclic loading experiments, Bartlett identified that foundation rocking and yielding of clay led to a reduction in the stiffness of the soil-structure interface and lengthened the natural period of the structure. He proposed that this may reduce the force demands imposed on the structure.
Work by Taylor et al. identified the impact of rocking, yield and uplift of a rigid footing on the ductility demand of structures and the potential for reduction in this demand. They postulated that rotational yield of the footing could be allowed under seismic loading without a considerable reduction in vertical load capacity, while developing only small vertical settlements. This resulted in a design philosophy where foundations were allowed to yield under earthquake loading, which could be preferable to the yielding of the structural members. This has also been applied by Taylor and Williams. Faccioli et al. (1998) conducted similar 1 g testing as part of the TRISEE project (3D Site Effects and Soil-Foundation Interaction in Earthquake and Vibration Risk Evaluation).
Zeng and Steedman (1998), Garnier and Pecker (1999), and Gajan et al. (2005) used centrifuge models to analyse the seismic response of footings. Centrifuge models overcome some of the limitations of 1 g tests due to scaling of soil stresses in the models. Gajan et al. carried out an extensive experimental testing program on the moment rotation behaviour of model shallow foundations. Model foundations were subjected to vertical, lateral slow cyclic and dynamic loading at 20g centrifugal acceleration. They identified the large amount of work that was dissipated at foundation level, highlighting the potential for the soil beneath footings to dissipate energy during dynamic loading. However, this had to be balanced against the permanent settlement of the footings due to the softening of the system.

 Bed of Winkler Springs

An early representation of a soil medium proposed by Winkler (1867) assumed a bed of closely spaced discrete linear elastic springs shown in Figure 2-1. This approach was extended by Heyenti (1946) to account for the flexibility of the beam resting on the soil surface. Due to the discrete nature of the springs the displacement at a point was related only to the contact pressure at that point, with displacement of each spring independent of each other. This simplifies the actual situation because of the lack of continuity between each point beneath the foundation.
These values can be combined to determine the overall pressure distribution beneath the rigid foundation. The displacement and rotation of the footing can be determined from these equations using the stiffness of the foundation, which must be converted to the coefficient of subgrade reaction as calculations are in terms of pressure.
The Winkler model has wide use in SSI applications due to its simplicity and the ease at which non-linear aspects can be incorporated into the model with minimal computational effort. Martin and Lam (2000) indicated that the simplified nature of the Winkler spring model makes it easily adaptable to structural code responses for design. It has been extended to dynamic applications with the development of the Beam on Non-linear Winkler Foundation (BNWF) model. Previous study in this area has been summarised by Kutter et al. (2003).
Using results from testing, Bartlett (1976) developed analytical Winkler based models using elastic-perfectly-plastic springs with uplift capabilities. Good comparisons were made between the analytical and experimental results using this approach. Wiessing (1979) also used elastic-plastic springs to represent the compressive behaviour of the soil from his experimental work. Coulomb slider elements were used to capture the uplift of the foundations. Again good correlations were shown between the analytical and experimental work.
Further research incorporating uplift of shallow foundations was undertaken by Yim and Chopra (1984), Chopra et al. (1985), and Nakaki and Hart (1987). Nakaki and Hart used elastic springs and viscous dampers in their Winkler bed model at the base of a shear wall. The others used single degree of freedom cantilever structures on both spring and dashpot beds and two-element foundation systems. The springs provided only compressive resistance and time-history analyses were performed on the overall system.
Harden et al. (2005) used a Winkler foundation system based on the spring setup for soil adjacent to a pile developed by Boulanger et al. (1999). Further details of this setup are provided in Section 2.3.1.2. The response of the soil beneath the foundation was split into near field plastic response and far field elastic response.

 Elastic Continuum

This model represents a soil profile as a continuous elastic medium, with the continuity of the soil modelled such that a force at a point will be transferred to the surrounding area, its effect decreasing with distance. This concept was proposed by Mindlin (1936) for the situation where a beam is loaded on the soil surface. The approach is still used, even though soil does not behave as a perfectly elastic medium. Douglas and Davies (1964) derived analytical expressions for deflections at the corners of thin vertical elements on a semi-infinite mass which could be used to determine foundation stiffness.
As the foundation material is continuous, the pressure distribution beneath a footing is not constant, and for cohesive material the edges of the footing will have higher stresses due to the sudden change in curvature of the ground surface. Theoretical solutions for a rigid footing on an elastic half space predict that vertical pressures extend to infinity at the footing edges (Mindlin 1936). The significant difference between this and the Winkler spring model is apparent when comparing the pressure distribution beneath a foundation subjected to a vertical load. Constant pressure develops beneath the Winkler spring model due to the constant stiffness of the spring elements.

CHAPTER 1 INTRODUCTION
1.1 Overview
1.2 Objectives and Scope of Research
1.3 Thesis Outline
CHAPTER 2 LITERATURE REVIEW
2.1 Overview
2.2 Experimentation and Modelling of Shallow Foundations
2.3 Experimentation and Modelling of Pile Foundations
2.4 Structural Modelling
2.5 Integrated Structure-foundation Modelling
2.6 Observations and Conclusions
CHAPTER 3 FIXED BASE STRUCTURAL ANALYSIS
3.1 Overview
3.2 Design Earthquake Records
3.3 Structural Design Characteristics and Methodology
3.4 Ruaumoko Structural Model Characteristics
3.5 Structural Designs
3.6 Three Storey Fixed Base Structural Analysis
3.7 Ten Storey Fixed Base Structural Analysis
3.8 Conclusions
CHAPTER 4 SHALLOW FOUNDATION MODELLING
4.1 Overview
4.2 Desired Characteristics of a Shallow Foundation
4.3 Ruaumoko Shallow Foundation Layouts
4.4 Shallow Foundation Characteristics
4.5 Portal Frame Model Analysis
4.6 Conclusions
CHAPTER 5 INTEGRATED STRUCTURE-FOOTING FOUNDATION ANALYSIS .
5.1 Overview
5.2 Foundation Design Methodologies
5.3 Integrated Model Characteristics s
5.4 Elastic Structure-Factor of Safety Design
5.5 Limited Ductility Structure-Factor of Safety Design
5.6 Elastic Structure-Equal Stiffness Design
5.7 Elastic Structure-Pinned Foundation Connection Design
5.8 Discussion
5.9 Conclusions
CHAPTER 6 INTEGRATED STRUCTURE-RAFT FOUNDATION ANALYSIS
6.1 Overview
6.2 Ruaumoko Raft Model
6.3 Raft Foundation Properties
6.4 Integrated Model Characteristics
6.5 Three Storey Integrated Model
6.6 Ten Storey Integrated Model
6.7 Discussion
6.8 Conclusions
CHAPTER 7 PILE FOUNDATION MODELLING
7.1 Overview
7.2 Testing of Column/Pile Units at Iowa State University
7.3 Input Data for Ruaumoko Models
7.4 Ruaumoko Model for Monotonic Loading
7.5 Ruaumoko Model for Cyclic Loading
7.6 Ruaumoko Model for Seismic Loading
7.7 Discussion
7.8 Conclusions
CHAPTER 8 INTEGRATED STRUCTURE-PILE FOUNDATION ANALYSIS
8.1 Overview
8.2 Pile Layout
8.3 Pile Foundation Characteristics
8.4 Pile Foundation Design
8.5 Single Pile Model Analysis
8.6 Integrated Model Characteristics
8.7 Effect of Pile Head Fixity Conditions on Response
8.8 Elastic Structure-Pile Foundation Design
8.9 Limited Ductility Structure-Pile Foundation Design
8.10 Discussion
8.11 Conclusions
CHAPTER 9 CONCLUSIONS
9.1 Foundation Models
9.2 Integrated Structure-Foundation Analysis
9.3 Recommendations for Future Research
REFERENCES
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