## 1 Introduction
The above information has been assumed in structural design and analysis of the foundation for many years. Earlier discussions of the contact pressures under the foundation can be found in Barden [9] based on the approximate calculation method. A number of studies were carried out taking the foundation-soil system as a two-dimensional structure subjected to combined static loads and/or dynamic load. Until recent years, the effects of the three-dimensional geometry of the foundation-soil system were found to be important in affecting the actual responses of the structure system [10; 11]. Therefore, it is worthwhile to investigate the principles of foundation settlements and distribution of contact pressure with 3D solutions. At present, the foundation settlements and soil reactions of arbitrarily loaded foundations can be easily estimated using either numerical or physical models. While the physical model is usually scaled, thus resulting in stress levels incomparable to the real foundation, rigorous numerical methods such as the 3D FE analyses can provide a more convenient and effective solution to engineering problems. [PERSON] et al. [12] and [PERSON] et al. [13] have demonstrated the advantages of employing analytical and numerical analyses for certain foundation problems. As the resulting coefficient of subgrade reaction (i.e., the soil spring constant, \(k_{s}\)) plays a key role in the structural design of foundations, numerous soil spring models have been developed since 1950. Besides the beam on elastic foundation model ([PERSON]'s model), the so called two-parameter soil spring model proposed by [PERSON] [14], which can account for the elastic shear influence on the surrounding soil, has been adopted and modified by numerous researchers [15; 16; 17; 18]. Such models have disadvantages in modeling layered soil profiles. From the 3D FE analysis, the soil reactions and soil springs underneath the raft were found to be dependent upon foundation size and the characteristics of the soil [19]. Other research conducted on soil springs using FE analysis can be found in [PERSON] [20] and [PERSON] [21]. Based on the 3D FE analysis, [PERSON] and [PERSON] [22] compared the applicability of two-parameter foundation models under certain load conditions. Additionally, [PERSON] et al. [23] proposed a two-dimensional soil spring model modified from [PERSON]'s analog model using Midas-GTX analysis. Besides the alternative foundation models on soil springs, it has been suggested by [PERSON] [24] that the rigorous computer-based method, e.g., the 3D FE analysis, is becoming a very convenient tool for engineers in dealing with foundation design. In recent years, 3D FE analysis has been popularly adopted as a design tool in engineering practice for foundation designs of high-rise buildings [25; 26; 27]. With the above information, this study intends to examine the load-response mechanism of a surface raft foundation model in clay and in sand subjected to vertically uniform loads using the 3D FE analysis. It should be pointed out that a surface raft, or a raft with very shallow embedment, is used to sustain mainly vertical structural load. The lateral resistance of such foundations is generally ignored in the design purpose. For simplicity, the small-strain level shear wave velocities (\(V_{s}\)) of the soils were assumed within a range (\(V_{s}\) = 120-180 m/s) in order to simulate the type-III soils (basin soils) at local sites. For clay, the Poisson's ratio was assumed to be 0.4. For sand, the Poisson's ratio was assumed to be 0.3. Elastic moduli were thereafter obtained. For more realistic solutions, nonlinear soil responses were modeled based on the Mohr-Coulomb model. Undrained shear strength of the clay soils was assumed based on correlations with the shear wave velocity of the soil. Drained internal friction angles were assumed for sand using empirical relations based on shear wave velocity and SPT-N value. A surface square raft foundation model was presumed to be located at various sites in the soils.