# Settlement Prediction of Footings Using \(V_{s}\)
## 1 Introduction  
The design paradigm of civil structures is currently shifting to performance-based design (PBD) instead of the traditional safety factor-based design. In PBD, greater emphasis is placed on controlling structural deformation to assure the serviceability and durability of civil structures [1] rather than using safety factors for design. Specifically, the key design factor of shallow foundation is settlement and not the bearing capacity because shallow foundations are generally constructed on good ground conditions having sufficient bearing capacity. A number of methods have been introduced to predict the settlement of shallow foundations. Most of these methods are based on the theory of elasticity and thus focus on the determination of soil compressibility. In order to determine the compressibility of soil (i.e., stiffness or modulus) the selection of stiffness is commonly made on the basis of penetration resistance. Parameters such as the \(N\) value and \(q_{c}\) value, derived from a standard penetration test (SPT) and cone penetration test (CPT), respectively, are generally utilized to determine the stiffness of soil layers. [PERSON] [2], [PERSON] [3], and [PERSON] [4] suggested methods of settlement estimation for footings based on the SPT-\(N\) value while [PERSON] [5], [PERSON] et al. [6] and [PERSON] et al. [7] suggested methods based on the CPT-\(q_{c}\) value. [PERSON]'s method has been extensively applied by engineers due to its simplicity and intuitive concept based on elasticity theory. The method utilizes CPT tip resistance, \(q_{c}\), to evaluate Young's modulus using soil type-based empirical coefficients. For predicting settlement, the crucial factor is, however, deformation-related stiffness and not strength. Even though modulus determination from SPT-\(N\) or CPT-\(q_{c}\) is generally adopted, the penetration resistance is strongly related to the soil strength and requires additional empirical coefficients to convert soil strength to soil modulus. The coefficient utilized for conversion ranges from 2 to 24 depending on the soil condition [8]. Therefore, it is quite probable that the penetration resistance-based methods could estimate the settlement several times greater or smaller due to the wide range of coefficients depending on soil condition. This is the intrinsic limitation of using strength parameters in the settlement prediction. In addition, these in-situ tests are not applicable under certain ground conditions such as intermediate to hard geomaterials (e.g., weathered soil/rock). As mentioned earlier, most of the penetration resistance-based methods adopt the elasticity theory. These methods, including [PERSON]'s method, assume linear elastic soil deformation using a representative modulus taken from the resistance values. However, observations of settlement on footings and soil behavior show a high degree of nonlinearity, which changes with the stress-strain level. Previous studies have reported that settlement prediction based on nonlinear stress-strain models is reasonably consistent with field observations [9]. Recently, the nonlinearity of soil behavior was considered in settlement predictions according to PBD for enhancing the accuracy of settlement prediction. [PERSON] et al. [10] and [PERSON] [11] proposed a modified [PERSON]'s method using modulus which varied depending on the settlement or strain level rather than using a single representative modulus initially converted from the \(q_{c}\) value. Nevertheless, the penetration resistance based on strength criteria is still commonly utilized in modulus determination using relevant coefficients. The shear wave velocity (\(V_{S}\)) could be an alternative parameter in the settlement prediction to resolve the aforementioned problems. The \(V_{S}\) is directly related to the deformation characteristics of soil (i.e., the maximum shear modulus, \(G_{max}\)). Complete soil deformation characteristics could be established from the \(V_{S}\).