A direct FEA loading approach for combined failure envelope of foundations in cohesive soil

Offshore foundations are normally subjected to multidirectional combined loading. Their bearing capacities form a n-dimensional hypersurface (n is the number of loads), which is usually termed as failure envelope (Suryasentana et al., 2020). Normally, n = 3, representing a vertical load (V), a horizontal load (H) and a moment load (M) (Achmus et al., 2013; Li et al., 2012; Thieken et al., 2014; Xia et al., 2022). Numerical simulation has been widely adopted to establish the failure envelopes of various foundations (Cheng et al., 2023, 2024; Hakhamaneshi and Kutter, 2016; Jin et al., 2025; Li et al., 2025; Manoharan and Dasgupta, 1995; Wang et al., 2006; Wu et al., 2025), to which ends there are primarily two loading strategies: probe method (Peng and Yin, 2024) and swipe method (Tian et al., 2019). The concept of the probe method is to generate a series of failure loads that lie on the failure envelope by separate simulations, followed by a data fitting process to approximate the failure envelope using a prescribed equation (Peng et al., 2025). In comparison, the swipe method more efficiently establishes a continuous curve on the failure envelope in one simulation by continuously varying the applied external loads, making it more efficient than the probe method as fewer simulations are required. However, it should be noted that this method is only appropriate for combined VH and VM failure in foundations with a small skirt length (e.g., surface footings). For combined HM failure, the method suffers from a significant inaccuracy (Fu et al., 2018; Gourvenec and Randolph, 2003). To address the limitations of the traditional swipe method, Suryasentana et al. (2020) proposed the sequential swipe method, where displacement increments are decomposed into multiple steps. However, the discrete displacements at each stage need to be determined in advance, which adds complexity to the setup in Finite Element Analysis (FEA). Subsequently, Fan et al. (2023) introduced the simplified modified swipe method to streamline this process. Despite this simplification, careful adjustment of the loading amplitude is necessary to prevent excessive mesh deformation or inaccuracies.

In addition, the swipe test suffers from inherent limitations, such as the applied load needs to be sufficiently large throughout the swipe process to elastic unloading (Tan, 1990), and the applied external loads should vary smoothly (Fan et al., 2023) to accurately capture failure envelope.

This study introduces a direct FEA loading method for constructing combined failure envelopes of foundations. This method ensures the smooth variation of the applied load and simplifies the procedure by requiring the definition of only one parameter. The effectiveness and robustness of this method are verified using various types of foundations, including circular surface footings, suction caissons, tripod buckets, and composite pile-bucket foundations, covering a range of shallow to deep foundation categories. Additionally, the sensitivity soil parameters such as the elastic modulus and the undrained soil strength profile, is thoroughly analyzed.