Many researchers have computed the bearing capacity of the strip and circular footings resting on the soil with the low and medium friction angle (ϕ ≤ 35°) by employing the finite-element method (FEM). It is reported that the numerical instability occurs with the high value of ϕ. Thus, based on the suggested values of soil dilation angle (ψ) in this study, the numerical computation can be achieved for all ϕ. Therefore, this paper presents the computation of the vertical bearing capacity factors N_c, N_q, and N_γ of a rough conical footing placed on the soil with friction angle ranging from ϕ = 5° to 45° by using the FE-based viscoplastic strain method under the Mohr–Coulomb (MC) yield criterion. The numerical simulations are solved using in-house MATLAB codes. The effects of the cone apex angle (β) and ϕ on the bearing capacity are examined thoroughly by the computation of factors individually and compared with the available solutions. The current solutions are found to be in good agreement for N_c, N_q, N_γ values; however, the discrepancies are also observed and presented. Therefore, the bearing capacity factor charts are established, and, consequently, the ultimate load of the footing can be determined by using the superposition assumption in Terzaghi’s equation.

The DNVGL-RP-F105 guidelines provide essential techniques for the preliminary design of undersea pipelines. However, its approximations for static displacement and the natural frequency of the pipe are restricted to cases where the ratio of the pipe’s diameter to its length (L/D) is less than 140. This limitation poses challenges for longer spans, which, although rare, can sometimes be unavoidable. This study introduces a novel analytical method, rooted in the energy method and cable theory, for computing the static deformation and natural frequency of long free-span underwater pipelines. We conducted a comprehensive verification of our proposed method by comparing its outcomes with those of 212 finite element analysis simulations. The results reveal excellent predictions for long spans. However, for shorter spans, traditional methods remain more accurate. Additionally, we explored the influence of pipeline’s diameter, thickness, and boundary conditions on both static displacement and frequency, providing valuable insights for design considerations. We found that the boundary conditions’ impact on the fundamental frequency becomes negligible for long spans, with up to a 10% difference between pinned–pinned and fixed–fixed conditions. In essence, this research offers a vital enhancement to the existing DNV guidelines, becoming particularly beneficial during the preliminary design phases of pipelines with L/D ratios exceeding 140.

This paper presents the computations of vertical bearing capacity factors $N_c$ , $N_q$ , and $N_{\gamma }$ , of the smooth and rough strip, circular and ring footings resting on soil with a friction angle ($\varphi$ ) ranging from 5° to 45° using a finite element viscoplastic strain method obeying the Mohr-Coulomb yield criterion. The numerical difficulty could be improved to some extent by using the proper magnitude of soil dilation angle ($\psi$ ) in the analysis of high non-associative flow. The effects of domain and mesh size are presented thoroughly. The factors are calculated individually and found to be in close agreement with the existing solutions. However, differences are also reported and discussed. The magnitude of bearing capacity factors increases with increasing $\varphi$ . Moreover, the factors with a rough base are significantly greater than the smooth base at high values of $\varphi$ . Moreover, this work also indicates that the shape factors may depend on $\varphi$ .

Unlike the flat base foundations, the determination of the bearing resistance of the cone‐shaped footing in finite element analysis (FEA) might not be carried out without considering the interface model. In addition, the simulations of the FEA is hardly achieved with a large system due to the assembly technique. So, the alternative should be considered. Therefore, this paper proposes a new method for computing the , and factors of the bearing capacity of the rough and smooth cone‐shaped foundations by combining the skew boundary condition as the interface model incorporated with the viscoplastic strain method‐based meshfree obeying the yield equation of the Mohr‐Coulomb (MC). Thus, the factors can be determined exclusively and reported to reach a close agreement with the published data; nevertheless, the discrepancies are also provided. The plastic flow of the soil mechanics is discussed thoroughly. In addition, the effects of soil friction angle (ϕ) and cone‐shaped angle (β) on the factors are inspected systematically. Accordingly, the conservation of the Terzaghi's superposition assumption is confirmed, and the bearing capacity factor charts can be established for various combinations of 5^o – 45^o and 30^o – 180^o. Therefore, it may conclude that the results produced by these techniques and the techniques themselves may be applied confidently for solving geotechnical problems, especially for computing the bearing resistance of the soil.