Centrifuge modeling of batter pile foundations under earthquake excitation

Although batter pile foundations are widely used in civil engineering structures, their behavior under seismic loadings is not yet thoroughly understood. This paper provides insights about the differences in the behavior of batter and vertical piles under seismic soil-pile-superstructure interaction. An experimental dynamic centrifuge program is presented, where the influences of the base shaking signal and the height of the gravity center of the superstructure are investigated. Various seismic responses are analyzed (displacement and rotation of the pile cap, total shear force at the pile cap level, overturning moment, residual bending moment, total bending moment and axial forces in piles). It is found that in certain cases batter piles play a beneficial role on the seismic behavior of the pile foundation system. The performance of batter piles depends not only on the characteristics of the earthquakes (frequency content and amplitude) but also on the type of superstructures they support. This novel experimental work provides a new experimental database to better understand the behavior of batter pile foundations in seismic regions.     

Centrifuge modeling of offshore wind foundations under earthquake loading

The construction of large offshore wind turbines in seismic active regions has great demand on the design of foundations. The occurrence of soil liquefaction under seismic motion will affect the stability of the foundations and consequently the operation of the turbines. In this study, a group of earthquake centrifuge tests was performed on wind turbine models with gravity and monopile foundations, respectively, to exam their seismic response. It was found that the seismic behavior of models was quite different in the dry or saturated conditions. Each type of foundation exhibited distinct response to the earthquake loading, especially in the offshore environment. In the supplementary tests, several remediation methods were evaluated in order to mitigate the relatively large lateral displacement of pile foundation (by fixed-end pile and multi-pile foundation) and excessive settlement of gravity foundation (by densification, stone column, and cementation techniques).     

Centrifuge modeling of the behavior of caisson-type quay walls during earthquakes

A series of 2-D centrifuge modeling tests with an in-flight shaker were carried out in order to model both the deformation characteristics of backfill and the seismic responses of caisson-type walls embedded in soils with various permeabilities. The rotational and translational modes were found to be in phase or various degrees out of phase with each other for quay walls embedded in soils with varying permeabilities. The alternative pumping and suction processes in excess pore water pressure that are caused by a wall's vibrations increase the level of damage because large amounts of backfill are forcedly leaked into the sea. The test results show that the rotational mode makes the dominant contribution to the changes in excess pore water pressure and in the earth pressure in the deep layers of soil, but the translational mode makes the dominant contribution to these pressures in the shallow layers. The average shear wave velocities were found to decrease rapidly to values as low as 1/8th of the velocity measured at the beginning of shaking.     

Centrifuge modeling of seismic behavior of a slope in liquefiable soil

Two centrifuge tests were designed to improve the understanding the response of liquefied sandy slopes beyond initial liquefaction. A distinctive dilative behavior of the soil was observed near the slope where static shear stresses are present. The corresponding drops in the piezometric records and simultaneous negative upslope spikes in the acceleration records were measured in the transducer raw data. This dilative response became stronger as the input acceleration increased and tends to limit the downslope accumulation and thus reducing the permanent lateral displacements. Therefore, the maximum permanent displacement was smaller in the model with the larger input motion, because it developed a stronger dilative response. The dilative response was not observed away from the slope, where no static shear stresses are present.     

Characterization of rocking shallow foundations using centrifuge model tests

This paper presents new results of centrifuge model tests exploring the behavior of rocking shallow foundations embedded in dry sand, which provides a variety of factors of safety for vertical bearing. The results of slow (quasi‐static) cyclic tests of rocking shear walls and dynamic shaking tests of single‐column rocking bridge models are presented. The moment–rotation and settlement–rotation relationships of rocking footings are investigated. Concrete pads were placed in the ground soil to support some models with the objective of reducing the settlement induced by rocking. The behavior of rocking foundation was shown to be sensitive to the geometric factor of safety with respect to bearing failure, L_f/L_c, where L_f was the footing length, and the L_c was the critical soil‐footing contact length that would be required to support pure axial loading. Settlements were shown to be small if L_f/L_c was reasonably large. Placement of concrete pads under the edges of the footing was shown to be a promising approach to reduce settlements resulting from rocking, if settlements were deemed to be excessive and also had impacts on the energy dissipation and rocking moment capacity. A general discussion of the tradeoffs between energy dissipation and re‐centering of rocking foundations and other devices is included. Copyright © 2011 John Wiley & Sons, Ltd.     

第四纪地层中断层同震错动行为的离心机试验研究

运用试验地球物理学的原理和方法来研究认识当地震发生时在第四纪地层中断层同震错动行为的有关特征,为减轻地震灾害相关问题进行基础研究.原创了在试验模型中预制断层的方法来模拟第四纪地层中存在的断层,用离心机模拟试验研究第四纪地层中不同活动年代、不同上断点深度断层的同震错动行为,特别是地表破坏(地表形变和破裂)特征,取得了新的明确认识,给出了不同场地条件下建设工程应对地震地表破裂造成直接破坏的避让距离.因此这项工作不但有着基础科研意义,而且具有对工程建设防震减灾的实际应用意义.     

An investigation into the Winkler modeling of the cyclic response of rigid footings

The response of shallow foundations under lateral cyclic loading is generally nonlinear and involves rocking, sliding, settlement, and may also involve foundation uplift and soil yielding. Unlike pile foundations, the nonlinear Winkler model is not widely used for modeling cyclic soil–footing–structure interaction (SFSI) problems. Nonetheless, it has some important features that make it more attractive than conventional finite element approaches, and is a recommended approach in the FEMA 356 design guideline. This paper explores the strengths and limitations of the FEMA 356 nonlinear Winkler modeling approach, when used in predicting the cyclic response of various recent SFSI experiments. The results of the study show that the model is capable of satisfactorily predicting all the different cyclic response quantities apart from permanent horizontal displacements. This should therefore be noted when using the approach in design.     

Centrifuge modeling of interaction between reverse faulting and tunnel

In this study, a series of centrifuge tests, modeling reverse fault rupture with 60° dip angle, were conducted in a dry sandy soil with a tunnel embedded in the soil layer. The test results showed that the tunnel and soil responses depended on the tunnel position, soil relative density and tunnel rigidity. Tunnels appeared be able to deviate the fault rupture path, while this deviation may be associated with significant rotation and displacement of the tunnel. However, a deeper tunnel was able to diffuse the shear deformation to a wider zone with an unsmooth surface displacement which may cause severe damage to the surface structures. Finally, the tunnel rotation, the location of the fault outcropping, the vertical displacement of the ground surface, the effect of tunnel rigidity on fault rupture path and surface displacement and the effect of soil relative density on fault–tunnel interaction were reported and discussed in this study.     

Centrifuge modeling of seismic response of layered soft clay

Centrifuge modeling is a valuable tool used to study the response of geotechnical structures to infrequent or extreme events such as earthquakes. A series of centrifuge model tests was conducted at 80g using an electro-hydraulic earthquake simulator mounted on the C-CORE geotechnical centrifuge to study the dynamic response of soft soils and seismic soil–structure interaction (SSI). The acceleration records at different locations within the soil bed and at its surface along with the settlement records at the surface were used to analyze the soft soil seismic response. In addition, the records of acceleration at the surface of a foundation model partially embedded in the soil were used to investigate the seismic SSI. Centrifuge data was used to evaluate the variation of shear modulus and damping ratio with shear strain amplitude and confining pressure, and to assess their effects on site response. Site response analysis using the measured shear wave velocity, estimated modulus reduction and damping ratio as input parameters produced good agreement with the measured site response. A spectral analysis of the results showed that the stiffness of the soil deposits had a significant effect on the characteristics of the input motions and the overall behavior of the structure. The peak surface acceleration measured in the centrifuge was significantly amplified, especially for low amplitude base acceleration. The amplification of the earthquake shaking as well as the frequency of the response spectra decreased with increasing earthquake intensity. The results clearly demonstrate that the layering system has to be considered, and not just the average shear wave velocity, when evaluating the local site effects.     

Centrifuge modeling of a dry sandy slope response to earthquake loading

This paper presents results of a series of centrifuge models of dry, sandy slopes excited by earthquakes and cyclic waves under 50g centrifugal acceleration to investigate the dynamic performance of slopes. Test results of four model slopes with different profiles stimulated by the adjusted El Centro earthquakes with various peak accelerations reveal the response amplification mechanism of the slope. By calculating the response spectra of recorded acceleration time histories, it was observed that the different frequency contents of the input event were amplified to different degrees. The model slope showed a completely different response under the cyclic wave with a constant frequency and amplitude in that the spectral amplification factor curves had no prominent peak values. These findings suggest that dynamic centrifuge tests excited with a real ground motion are able to better reflect the response characteristics of a slope rather than the tests with cyclic loading.     

Seismic response of retaining walls with cohesive backfill: Centrifuge model studies

Observations from recent earthquakes show that retaining structures with non-liquefiable backfills perform extremely well; in fact, damage or failures related to seismic earth pressures are rare. The seismic response of a 6-m-high braced basement and a 6-m free-standing cantilever wall retaining a compacted low plasticity clay was studied in a series of centrifuge tests. The models were built at a 1/36 scale and instrumented with accelerometers, strain gages and pressure sensors to monitor their response. The experimental data show that the seismic earth pressure on walls increases linearly with the free-field PGA and that the earth pressures increase approximately linearly with depth, where the resultant acts near 0.33 H above the footing as opposed to 0.5–0.6 H, which is suggested by most current design methods. The current data suggest that traditional limit equilibrium methods yield overly conservative earth pressures in areas with ground accelerations up to 0.4g.     

Centrifuge modeling of loose fill embankment subjected to uni-axial and bi-axial earthquakes

The seismic risk is fairly high in Hong Kong even though it is located in an intreplate area with low to moderate seismicity. This is because of its high seismic vulnerability due to the presence of many steep loose fill slopes with a marginal static factor of safety, and a high consequence ‘value’ as a result of the dense population and intense economic activity in Hong Kong. In order to investigate the seismic stability and potential flow liquefaction of loose fill slopes, dynamic centrifuge tests in uni-axial and bi-axial directions were performed on saturated model embankments made of loose completely decomposed granite (CDG). Three windowed sinusoidal waves with peak shaking amplitudes ranging from 0.08 g to 0.3 g (prototype scale) were adopted. During the strong uni-axial shaking of 0.3 g, the measured maximum excess pore pressure ratios ranged from 0.70 to 0.85 and a relatively small crest settlement of 5.8 mm (0.22 m prototype) was measured. No soil liquefaction or flow slides were observed. Comparing the results between the strong uni-axial and bi-axial shaking, the maximum pore pressure ratios measured from the bi-axial test varied from 0.75 to 0.87, which were marginally larger than those obtained from the uni-axial test. Although the measured crest settlement during the bi-axial shaking was about 27% larger than that of the uni-axial test, soil liquefaction and flow slide did not occur. These test results suggest that loose CDG fill slopes are likely to be stable under the proposed design PGA ranging from 0.08 to 0.11 g in Hong Kong.     

Centrifuge modelling of flexible retaining walls subjected to dynamic loading

This paper outlines the results of an experimental program carried out on centrifuge models of cantilevered and propped retaining walls embedded in saturated sand. The main aim of the paper is to investigate the dynamic response of these structures when the foundation soil is saturated by measuring the accelerations and pore pressures in the soil, displacements and bending moment of the walls. A comparison among tests with different geometrical configurations and relative density of the soil is presented. The centrifuge models were subjected to dynamic loading in the form of sinusoidal accelerations applied at the base of the models. This paper also presents data from pressure sensors used to measure total earth pressure on the walls. Furthermore, these results are compared with previous dynamic centrifuge tests on flexible retaining walls in dry sand.     

Performance of a transparent Flexible Shear Beam container for geotechnical centrifuge modeling of dynamic problems

A transparent Flexible Shear Beam (FSB) container was designed and constructed to simulate the dynamic response of a stratum of soil under horizontal, one-dimensional (1-D) earthquake shaking in a geotechnical centrifuge. A stack of four rectangular, acrylic frames separated by layers of flexible, high-strength rubber was used to form the transparent container. The fundamental natural frequency of the container was estimated to be similar to a layer of sand in its softened or liquefied state. The suitability of the container in simulating 1-D site response with minimal boundary effects was evaluated by monitoring the uniformity of the induced accelerations and settlements across the soil specimen. Further, the measured lateral displacements were compared with equivalent-linear site response analyses. The new FSB container was found to provide satisfactory boundary conditions for studying complex Soil–Structure-Interaction problems, while simultaneously enabling researchers to visualize deformations of the soil and buried structures during shaking.     

Centrifuge modeling of the seismic responses of sand deposits with an intra-silt layer

Three dynamic centrifuge model tests were conducted at an acceleration of 80g to simulate the seismic responses of level sand deposits: an intra-silt layer was embedded in two of these sand deposits at different depths. The effects of a low-permeability intra-silt layer on the build-up and dissipation of excess pore-water pressure, surface settlement, and the related liquefaction mechanism were investigated. An intra-silt layer modifies the seismic response of the sand deposit, reduces the extent of liquefaction, and thus decreases surface settlement. The depth of the intra-silt layer is one of the factors influencing the seismic responses of the sand deposits. The magnitude of the surface settlement is proportional to the degree of liquefaction in the sand deposit. The high positive hydraulic gradients appearing in both the intra-silt layer and in the sand deposit lying on the intra-silt layer can break a thinner or weaker top layer and result in sand boiling. Our visual animation of the ratio of the excess pore-water pressure and the lateral displacement revealed that the liquefaction front travels upward during shaking and the solidification front travels upward after shaking.     

A new method for formulation of dynamic responses of shallow foundations in simple general form

A single uniform rectangular area, either homogeneous or heterogeneous, is considered in a soil medium (fundamental cell). Two governing ordinary differential equations in special form are developed for the fundamental cell. The ground supporting a partially embedded foundation is divided into a number of coarse rectangular areas (secondary cells). Each secondary cell is treated as either a single fundamental cell for homogeneous ground or a stack of fundamental cells for inhomogeneous ground. Differential equations for the assembly of secondary cells are formed with those for the fundamental cells. These equations lead to the soil responses in each cell expressed in simple closed form. They also lead to the convenient treatment of soil with appropriate Winkler-type models along the foundation faces and concentrated forces acting at the foundation corners. With them, the foundation responses are finally expressed in simple closed form. The approach is demonstrated for various cases and confirmed to produce the results reasonable enough for civil engineering use.     

Dimensional analysis of structures with translating and rocking foundations under near-fault ground motions

This paper evaluates the inertial soil–structure interaction (SSI) effects on linear and bilinear structures supported on foundation that is able to translate and rock when subject to near-fault ground motions. Through rigorous dimensional analysis, the peak structural responses (e.g. structural drift and total acceleration) of the soil–foundation–structure interacting (SFSI) systems are characterized by a set of dimensionless Π-parameters, which can decisively describe the interactive behavior of SFSI systems. By comparing the normalized structural responses of various structure–foundation systems with their fixed-base counterparts, the study reveals that SSI effects highly depend on the structure-to-pulse frequency ratio, Π_ω, the foundation-to-structure stiffness ratio, Π_k, damping coefficient of foundation impedance, Π_c, the foundation rocking, and the development of nonlinearity in structures. For linear structures, the SSI effects are insignificant when the structure-to-pulse frequency ratio (Π_ω) is smaller than 1.5 and can amplify the structural responses when Π_ω is higher than 1.5. Foundation rocking can shift and enlarge the response amplification zone of SSI. For nonlinear structures, SSI tends to reduce the structural responses for Π_ω<3 while can increase the ductility demands for Π_ω≥3. The bilinear structures may experience more significant SSI effects than linear structures in certain frequency ranges. The numerical simulations on ten real building cases exhibiting significant rocking and a detailed case study on a nine-story frame structure demonstrate the applicability of dimensional analysis results to predict the SSI effects on realistic building structures. The study demonstrates that the dimensional analysis provides a concise and systematic way of evaluating SSI effects.     

Seismic analysis and design of rigid bridge abutments considering rotation and sliding incorporating non-linear soil behavior

A two-dimensional (2D) finite element analytical model is developed to analyze the seismic response of rigid highway bridge abutments, retaining and founded on dry sand. A well verified finite element code named FLEX is used for this purpose. The proposed model has the following characteristics: (1) The soil (dry sand in this study) is modeled by a 2D finite element grid; (2) The bridge abutment is molded as a rigid substructure; (3) The strength and deformation of the soil are modeled using the viscous cap constitutive model. This model consists of a failure surface and hardening cap together with an associated flow rule. The cap surface is activated for the soil under the wall to represent compaction during wall rocking. In addition, viscoelastic behavior is provided for representing the hysteretic-like damping of soil during dynamic loading; (4) Interface elements are used between the wall and the soil (at the backface of the wall and under its base) to allow for sliding and for debonding/recontact behavior; (5) The finite element grid is truncated by using an absorbing boundary approximation. Using this boundary at both sides of the grid simulates the horizontal radiation of energy scattered from the wall and the excavation. Shear beams are placed adjacent to the lateral boundaries from each side which give the far-field ground motion, for comparison with those computed adjacent to the boundaries. The analytical model is verified comparing predictions to results from dynamic centrifuge tests, with satisfactory agreement. The proposed model is used to study the dynamic response of an 8.0 m high and 3.0 m wide rigid bridge abutment (proportioned using the traditional approach to design) for different sinusoidal and earthquake acceleration input motions. The results from the analysis show that outward tilting of rigid bridge abutments is the dominant mode of response during dynamic shaking and that these abutments end up with a permanent outward tilt at the end of shaking. The results from all the analyzed cases of the 8.0 m high gravity retaining wall together with those from the analysis of the tilting wall centrifuge tests are discussed and used for proposing a practical method for evaluating the seismic response of rigid abutments during earthquakes.     

Seismic response of slender rigid structures with foundation uplifting

The rocking of rigid structures uplifting from their support under strong earthquake shaking is investigated. The structure is resting on the surface of either a rigid base or a linearly elastic continuum. A large-displacement approach is adopted to extract the governing equations of motion allowing for a rigorous calculation of the nonlinear response even under near-overturning conditions. Directivity-affected near-fault ground motions, idealized as Ricker wavelets or trigonometric pulses, are used as excitation. The conditions under which uplifting leads to large angles of rotation and eventually to overturning are investigated. A profoundly nonlinear rocking behavior is revealed for both rigid and elastic soil conditions. This geometrically nonlinear response is further amplified by unfavorable sequences of long-duration pulses in the excitation. Moreover, through the overturning response of a toppled tombstone, it is concluded that the practice of estimating ground accelerations from overturning observations is rather misleading and meaningless.