Recent studies have highlighted the potential benefits of allowing inelastic foundation response during strong seismic shaking. This approach, known as rocking isolation, reduces the moment at the base of the column by transferring the plastic joint beneath the foundation and into the soil bed. This mechanism acts as a fuse, preventing damage to the superstructure. However, structures with a low static safety factor against vertical loads (FSv) may experience unacceptable settlements during earthquakes. To address this, shallow soil improvement is proposed to ensure sufficient safety and mitigate risks. In this study, a small-scale physical model of a foundation and structure (SDOF model, n = 40) was placed on dense sandy soil, and seismic loading was simulated using lateral displacement applied by an actuator. A group of short-yielding piles with varying bearing capacities (QU/NU = 0.1-0.8) was installed beneath the rocking foundation. The results of the small-scale tests demonstrate that the use of short-yielding piles during seismic loading reduces the settlement of the shallow foundation by up to 50% and increases rotational damping by 59%. This is achieved through the frictional yielding of the pile wall and the yielding of the pile tip, which dissipate energy and enhance the overall seismic performance of the foundation. The findings suggest that incorporating yielding pile groups in the design of rocking foundations can significantly improve their seismic performance by reducing settlement and increasing energy dissipation, making it a viable strategy for enhancing the resilience of structures in earthquake-prone areas. The optimal bearing capacity ratio (QU/NU = 0.25-0.5) provides a straightforward guideline for designing cost-effective seismic retrofits.

Shallow foundations supporting high-rise structures are often subjected to extreme lateral loading from wind and seismic activities. Nonlinear soil-foundation system behaviors, such as foundation uplift or bearing capacity mobilization (i.e., rocking behavior), can act as energy dissipation mechanisms, potentially reducing structural demands. However, such merits may be achieved at the expense of large residual deformations and settlements, which are influenced by various factors. One key factor which is highly influential on soil deformation mechanisms during rocking is the foundation embedment depth. This aspect of rocking foundations is investigated in this study under varying subgrade densities and initial vertical factors of safety (FSv), using the PIV technique and appropriate instrumentation. A series of reduced-scale slow cyclic tests were performed using a single-degree-of-freedom (SDOF) structure model. This study first examines the deformation mechanisms of strip foundations with depth-to-width (D/B) ratios of 0, 0.25, and 1, and then explores the effects of embedment depth on the performance of square foundations, evaluating moment capacity, settlement, recentering capability, rotational stiffness, and damping characteristics. The results demonstrate that the predominant deformation mechanism of the soil mass transitions from a wedge mechanism in surface foundations to a scoop mechanism in embedded foundations. Increasing the embedment depth enhances recentering capabilities, reduces damping, decreases settlement, increases rotational stiffness, and improves the moment capacity of the foundations. This comprehensive exploration of foundation performance and soil deformation mechanisms, considering varying embedment depths, FSv values, and soil relative densities, offers insights for optimizing the performance of rocking foundations under lateral loading conditions.

In shield tunneling, the joint is one of the most vulnerable parts of the segmental lining. Opening of the joint reduces the overall stiffness of the ring, leading to structural damage and issues such as water leakage. Currently, the Winkler method is commonly used to calculate structural deformation, simplifying the interaction between segments and soil as radial and tangential Winkler springs. However, when introducing connection springs or reduction factors to simulate the joint stiffness of segments, the challenge lies in determining the reduction coefficient and the stiffness of the springs. Currently, the hyperstatic reflection method cannot simulate the discontinuity effect at the connection of the tunnel segments, while the state space method overlooks the nonlinear interaction between the tunnel and the soil. Therefore, this paper proposes a numerical simulation method considering the interaction between the tunnel and the soil, which is subjected to compression rather than tension, and the discontinuity of the joints between the segments. The model structure and external load are symmetrical, resulting in symmetrical calculation results. This method is based on the soft soil layers and shield tunnel structures of the Shanghai Metro, and the applicability of the model is verified through deformation calculations using three-dimensional laser scanning point clouds of sections from the Shanghai Metro Line 5. When the subgrade reaction coefficient is 5000 kN/m3, the model can effectively simulate the deformation of operational tunnels. By adjusting the bending stiffness of individual connection springs, we investigate the influence of bending stiffness reduction on the bending moment, radial displacement, and rotational displacement of the ring. The results indicate that a decrease in joint bending stiffness significantly affects the mechanical response of the ring, and the extent and degree of this influence are correlated with the joint position and the magnitude of joint bending stiffness.

Sources such as wind or severe seismic activity often exert extreme lateral loading onto the shallow foundations supporting high-rise structures such as bridge piers, buildings, shear walls, and wind turbine towers. Such loading conditions may cause the foundation to exhibit nonlinear responses such as uplift and bearing capacity mobilization of the supporting soil (i.e., rocking behavior). Previous numerical and experimental studies suggest that while such inelastic behaviors may engender residual deformations in the soil-foundation system, they offer potential benefits to the overall integrity of structures through dissipating energy and reducing inertia forces transmitted to the superstructure, thereby limiting seismic demand on structural elements. This study investigates the effect of footing shape on the rocking performance of shallow foundations in different subgrade densities and initial vertical factor of safety (FSv). To this end, a series of reduced-scale slow cyclic tests under 1 g condition were conducted using a single degree of freedom (SDOF) structure model. The performance of different footing shapes was studied in terms of moment capacity, recentering ratio, rocking stiffness, damping ratio, and settlement. For three foundations with different length-to-width ratios, the results indicate that increasing the safety factor and length-to-width ratio leads to thinner, S-shaped moment-rotation curves, mainly owing to the enhanced recentering capability and the P-delta effect. Moreover, across all foundation types, the repetition of a limited loading cycles with consistent rotation amplitude does not cause stiffness degradation or moment capacity reduction.