Model Uncertainty in Shallow Foundation Design
Although the bearing capacity problem has been studied for about one hundred years and is perhaps the best understood of all design aspects related to foundation engineering (Baars 2018), a considerable degree of dispersion still exists between the calculated and measured capacity (Phoon and Tang 2019a), and full-scale load test verification remains limited. To account for this dispersion (or uncertainty) in a rational manner, FHWA mandated the use of LRFD for all new bridges after September 2007. Generally, there are two ways to implement a LRFD approach - i.e. theoretical (e.g. Flonjo and Amatya 2005; Foye et al. 2006; Fenton et al. 2008) and empirical or data- based (e.g. Phoon et al. 2003a, b; Paikowsky et al. 2010). The theoretical method is based on the bearing capacity equation in which the inherent uncertainty of soil properties (e.g. cohesion, friction angle and relative density) and model uncertainty in the bearing capacity factors are evaluated separately, as shown in Foye et al. (2006). Later, a more complex procedure was presented in Fenton et al. (2008) where an acceptable failure probability was calculated as a function of the spatial variability of the soil and by the level of “understanding” of the soil properties in the vicinity of the foundation. The empirical method is associated with the use of database calibration where the uncertainties associated with the soil parameters and design equations are characterized by the probabilistic distribution of the capacity model factor. Because of its simplicity, this method is widely used throughout North America. For ULS design of shallow foundations used in highway bridge structures, the most comprehensive database calibration was carried out by Paikowsky et al. (2010) with two databases (i.e. UML-GTR ShalFound07 and UML-GTR RockFound07). Based on the derived model statistics, resistance factors for LRFD of shallow foundations were calculated. Furthermore, Agaiby and Mayne (2016) discussed the methodology for the sizing of shallow foundations for Georgia bridge structures and mapped ASD to LRFD with regards to bearing pressure and movement.
SLS design check usually requires the calculation of foundation movement and determination of tolerable movement criteria (e.g. DiMillio 1982; Moulton 1986; Agaiby and Mayne 2016; Allen 2018). SLS received less attention in the LRFD literature (Phoon and Kulhawy 2008) compared to ULS because it is more difficult to (1) calculate foundation settlement accurately (in which the uncertainty is much higher than that of capacity calculation, as most analytical models did not incorporate all of the important influential factors, such as the in-situ stress state, soil behaviour, foundation- soil interface characteristics and construction effects; e.g. Callanan and Kulhawy 1985; Akbas and Kulhawy 2010; Phoon and Tang 2019a) and (2) establish appropriate criteria for tolerable movement, as it is affected by many factors, such as the type and size of the structure, the properties of the underlying soil and the rate and uniformity of the movement (Zhang and Ng 2005). To conduct an SLS design check, theoretical or empirical methods can be applied. Fenton et al. (2005) presented a theoretical LRFD method for verifying the performance of shallow foundations against excessive settlement in which resistance factors to achieve a certain level of the reliability as a function of soil variability and site investigation intensity are determined analytically using random field theory. Examples of empirical (database calibration) LRFD methods were given by Samtani and Kulicki (2019,
- 2020). Besides the aforementioned semi-probabilistic LRFD approach, full- probabilistic approaches have been studied by Youssef Abdel Massih et al.
- (2008) and Soubra and Youssef Abdel Massih (2010) for bearing capacity and Akbas and Kulhawy (2009c) and Ahmed and Soubra (2014) for settlement.
Despite the significant advances in the RBD of shallow foundations over the past decades, there is still some room for improvement. For example, among the 172 axial compression tests adopted by Paikowsky et al. (2010) for calibration, 138 load tests were conducted on foundations with equivalent widths smaller than 0.1 m. A scaled model test in a controlled preparation of uniform soil sample possibly does not lead to representative model statistics that could be affected by test scale and natural variability of soil properties (Lesny 2017). At present, the evaluation of calculation methods for the uplift capacity of shallow foundations is very limited, except for the study conducted by Stas and Kulhawy (1984). The limit state design of shallow foundations subjected to uplift received very limited coverage in the current European standards (Bogusz 2016). The following section will make an attempt to address these potential shortcomings and bridge these important gaps between research and practice.