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.

In recent years, researchers have taken advantage of the nonlinear characteristics of the underlying soil to mitigate the excessive seismic force demands on the superstructure under earthquake excitation. For this purpose, the conventionally designed foundation can be replaced with rocking foundation. This is achieved by under proportioning the shallow foundation. Although the mechanism of rocking foundations has been well documented, there remains a gap in developing a methodology for reduction of foundation sizes in multi storey Reinforced Concrete (RC) shear wall framed structure. Therefore, this study focuses on the seismic responses of a shallow foundations supporting a multistorey RC shear wall framed structure. The foundation for RC shear wall is proportioned by gradually reducing the earthquake load considered for the foundations to enhance the increased rocking effect and to mitigate seismic force demands. Thereafter, key parameters responsible for seismic behavior of sub-structure are being compared with conventionally designed foundation with increasing foundation rocking, by varying type of underlying soil and with increasing height. Seismic behavior obtained by implementing a series of nonlinear time history analyses indicates that the foundation rocking greatly influences the dynamic properties. With increasing degree of foundation rocking, natural fundamental period of the overall structure gets lengthened, with decreasing peak roof acceleration, thereby mitigating the peak base moment and base shear experienced at the shear wall compared to conventionally designed foundation. On the other hand, it is observed that there is an increase in roof displacement and shear wall settlement at the foundation level. It is found that the foundation of shear wall can be designed by considering 40%, 60% of earthquake loads for zone V and zone II structural designs, respectively without encountering excessive settlements. From the sensitivity analysis it is highlighted that the foundation size and design seismicity impact the base shear contribution ratios between shear wall and column members, fundamental natural period and foundation settlement.

Rocking isolation is an effective method for reducing structural damage during earthquakes and aligns with a seismic design approach that aims to minimize damage to bridges. The seismic responses of rocking structures are significantly influenced by the soil-structure interaction and the soil characteristics. In this research, a shaking table test was conducted on a single-pier rigid-frame bridge model with an uplifting footing, considering soil-structure interaction. This test was used to validate a finite element model (FEM) developed using ABAQUS software. Subsequently, the seismic responses of the rigid- frame bridge with a pile foundation capable of rocking at the pier base were analyzed in detail. Four soil types, including silt, silt clay, sand, and clay, were examined, and two foundation types were considered: a fixed pile foundation and a rocking pile foundation. The results indicate that uplifting the footing can reduce the deck's acceleration and the pier's bending moment, while increasing the bridge's displacement, compared to a bridge with a fixed pile foundation.

Residual liquefaction, a significant issue in marine engineering, results from accumulated pore-water pressure in the seabed due to cyclic shear stresses, which compromises soil stability. This study aims to investigate residual liquefaction around gravity-based marine structures by means of a 2D numerical model. The model employs a two-step procedure: First, the stresses in the soil domain are determined via solving Biot equations, and subsequently the generation and diffusion of accumulated pore pressure in the soil is simulated by means of a pressure diffusion equation with a source term. The model was first validated against analytical solution for pore pressure buildup in the seabed under progressive waves, and against experimental data for residual liquefaction around a buried submarine pipeline. The results showed that the model can satisfactorily capture pore pressure buildup and residual liquefaction in the seabed around structures. Once validated, the model was utilized to model the pore-water pressure buildup and residual liquefaction potential around a caisson breakwater under the action of standing waves and the wave-induced rocking motion of the caisson, separately and in combination. Spatial distribution of liquefaction potential was determined in the seabed soil around the caisson with and without a bedding layer on the seabed. The model results revealed the critical role of the bedding layer in reducing liquefaction susceptibility under standing waves and rocking motion, and highlighted that the rocking motion alone poses a significant risk of inducing residual liquefaction in the seabed around the caisson.

This study investigates the seismic response of a rocking wall frame structure considering dynamic soil-structure interaction (DSSI) through shaking table tests. A comparison with conventional frame structures and structures with fixed-base foundations is made to examine the influence of DSSI effects on various aspects including structural damage distribution, dynamic characteristics, and floor responses. Test results indicate that the presence of a rocking wall reduces structural responses across different site conditions, although the reduction is less significant under soft soil conditions compared to fixed-base foundation conditions. Overall, DSSI diminishes the mitigating effect of the rocking wall on the maximum structural response. Furthermore, a three-dimensional finite element model of the shaking table test is established. The numerical model employs the equivalent linear method to simulate the soil's nonlinear behavior and incorporates the concept of the rocking wall. Comparative analysis between experimental and simulated results demonstrates that the model effectively predicts the dynamic response of the rocking wall frame structure in DSSI systems.

Recently, significant progress has been made in conceptually describing the dynamic aspects of coarse particle entrainment, which has been explored experimentally for open channel flows. The aim of this study is to extend the application of energy criterion to the low mobility aeolian transport of solids (including both natural sediment and anthropogenic debris such as plastics), ranging from incomplete (rocking) to full (rolling) entrainments. This is achieved by linking particle movements to energetic flow events, which are defined as flow structures with the ability to work on particles, setting them into motion. It is hypothesized that such events should impart sufficient energy to the particles, above a certain threshold value. The concept's validity is demonstrated experimentally, using a wind tunnel and laser distance sensor to capture the dynamics of an individual target particle, exposed on a rough bed surface. Measurements are acquired at a high spatiotemporal resolution, and synchronously with the instantaneous air velocity at an appropriate distance upwind of the target particle, using a hot film anemometer. This enables the association of flow events with rocking and rolling entrainments. Furthermore, it is shown that rocking and rolling may have distinct energy thresholds. Estimates of the energy transfer efficiency, normalized by the drag coefficient, range over an order of magnitude (from about 0.001 to 0.0048 for rocking, up to about 0.01, for incipient rolling). The proposed event-based theoretical framework is a novel approach to characterizing the energy imparted from the wind to the soil surface and could have potential implications for modelling intermittent creep transport of coarse particles and related aeolian bedforms.

Recent research has shown that full mobilization of foundation bearing capacity may be beneficial in terms of structural integrity-especially in the case of seismic motions that exceed the design limits. Full mobilization of foundation bearing capacity may serve as seismic isolation because it limits the inertia loading transmitted to the superstructure. Although most research has focused on rocking shallow or embedded foundations, a rocking pile group has attracted much less attention. A potential reason is the probability of structural damage below the ground level (at the piles), which may be difficult to repair or even detect. To shed more light on the problem, the present study investigates the seismic performance of a rocking pile group in clay, aiming to assess its efficiency as a seismic isolation alternative. Employing the finite-element (FE) method, an idealized yet realistic example of a single bridge pier supported by a pile group foundation is analyzed. A carefully calibrated and thoroughly validated kinematic hardening constitutive model is employed for the soil, and the concrete damage plasticity model is applied for the structural members. Using a suite of records as seismic excitation, the response of an intentionally underdesigned rocking pile group is compared with that of a conventionally (capacity) designed system. Similarly to what has been shown for shallow foundations, the comparison reveals that the rocking pile group can be beneficial for the seismic performance of the bridge, reducing the flexural demand on the pier at the expense of increased settlement. Interestingly, the rocking pile group exhibits a genuinely ductile response, such that none of the studied ground motions could lead to full mobilization of the bending moment capacity of the piles. Thus, pile structural damage is avoided. The findings of the present study reveal the advantages of exploiting nonlinear soil-foundation response and indicate that there is a great potential to optimize the contemporary seismic foundation design, which conventionally culminates in massive pile group foundations. The rocking pile group concept may be of particular interest for the retrofit of existing bridges that do not meet the requirements of the current seismic design provision because it can reduce or even completely avoid strengthening the foundation. Ultimately the presented findings call for a shift toward performance-based design, with due consideration of geotechnical failure modes.

Rocking shallow foundations interrupt the seismic transmission path from the base of the structure and possess advantages, such as effective seismic isolation, self-resetting capabilities post-earthquake, and low costs. A numerical model of the rocking shallow foundation was developed in OpenSees (version: Opensees 3.5.0) based on field test data using numerical simulation. The effect of different parameters (column height, foundation sizes, top mass, and soil softness and stiffness) on the seismic response characteristics of rocking shallow foundations is investigated, and the seismic response characteristics of rocking shallow foundations are analyzed under the action of sinusoidal waves of different frequencies and various seismic wave types. The results of the study show that, as the height of the column increases, the bending moment decreases and settlement decreases; as the size of the foundation increases, the bending moment increases and settlement increases; as the mass of the top increases, the bending moment increases and settlement increases; and as the soil becomes softer, the bending moment decreases, and settlement increases. Inputting a sine wave that matches the structure's natural oscillation frequency may induce resonance. This phenomenon can significantly amplify the structure's vibrations; thus, it is essential to avoid external excitation frequencies that coincide with the foundation's natural oscillation frequency. Under seismic loading, the rocking shallow foundation can mitigate the bending moment in the superstructure. When the displacement ratio remains within -0.5 to 0.5 percent, the foundation settlement is minimal. However, when the absolute displacement ratio exceeds 0.5 percent, the soil exhibits plastic deformation characteristics, resulting in increased foundation settlement. This study is an important contribution to the improvement of seismic performance of buildings and an important reference for improving seismic design standards and practices for buildings in earthquake-prone areas. In the future, the seismic response characteristics of rocking shallow foundations under bidirectional seismic action will be investigated.

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.

This study established a numerical model for soil-structure interaction (SSI) to examine the effects of the spatial incidence angle of SV waves and soil nonlinearity, utilizing viscoelastic artificial boundaries (VAB) and equivalent nodal force (ENF) method. Both the foundation's and superstructure's torsion and rocking responses were then analyzed. The findings indicate that subjected to spatially oblique incident SV waves, the rectangular foundation primarily has the rocking response while the torsional response is negligible. Furthermore, the maximum torsional and rocking angles about the x-axis at each frame floor are significantly enlarged by comparison with the perpendicular incident case. Moreover, the soil nonlinearity could increase the foundation's rocking angle and enlarge the maximum torsion and rocking responses of the structure's floors. Consequently, structural seismic damage assessment requires considering both the soil nonlinearity and incident seismic wave angles.