Displacement Accumulation Research Articles

Centrifuge testing on monotonic and cyclic lateral behavior of large-diameter slender piles in sand

The existing studies have been primarily focused on the lateral behavior of large-diameter stubby pile or small-diameter slender pile in sand, with little attention paid to large-diameter slender pile. This study presents a unique series of centrifuge tests on monotonic and cyclic lateral behavior of heavily instrumented large-diameter slender piles in medium dense sand. Two typical length to diameter ratios (L/D) are considered with the same length (L = 60 m) but different diameters (D = 4 and 6 m). It is found that the lateral behaviors of large-diameter slender pile, including its monotonic p-y response, cyclic accumulation of lateral displacement and cyclic stiffness evolution, are marginally different from those of small-diameter slender piles, but significantly deviate from the large-diameter stubby piles. This may suggest the longstanding argument of ‘diameter effect’ is relatively minor, while the lateral behavior of monopile in sand is more significantly governed by the relative pile-soil stiffness. The API (2011) non-conservatively predicts both stiffness and capacity of the large-diameter slender piles, leading to development of a new p-y formulation. These centrifuge testing results form a unique database to support development of new design methods for large-diameter slender piles, and to verify advanced numerical analyses involving cyclic models.

Capacity of plate anchors in clay under sustained uplift

The use of plate anchors on permanent offshore facilities with taut or semi-taut moorings requires a thorough understanding of their long-term capacity under sustained loading. In this paper, a programme of centrifuge tests and numerical simulations is reported to investigate the capacity of a plate anchor deeply embedded in normally consolidated clay during and after vertical sustained loading. Experimental data show that a sustained load higher than 85% of the ultimate monotonic anchor capacity leads to anchor failure, characterised by acceleration of anchor movement with a large accumulation of vertical displacements towards the soil surface. At sustained loads lower than 85% of the monotonic anchor capacity, the undrained anchor capacity increases due to consolidation and hence strengthening of the soil mobilised by the anchor. The maximum increase in capacity relative to the monotonic capacity is 23% when the sustained load is approximately half the monotonic anchor capacity. A gap-filling technique was proposed and incorporated into large deformation finite element analyses, which are shown to reproduce the experimental observations well.

Centrifuge modelling on monotonic and cyclic lateral behaviour of monopiles in kaolin clay

This paper details a programme of centrifuge tests (100g) on the monotonic and cyclic lateral behaviour of large-diameter semi-rigid monopiles in kaolin clay. Piles of different diameters were used, with a maximum prototype value of 5·9 m. The pile–soil interaction was investigated in terms of the overall load–displacement behaviour, distribution of bending moment and pile deflection, p–y curves and excess pore pressure response. For monotonic loading, procedures were developed to fit the monotonic p–y curves obtained from different pile and soil properties using a hyperbolic tangent model. In addition, an explicit model was derived to assess the development of excess pore pressure within the surficial soil, which was found to approach the vertical effective soil stress at large displacement. For cyclic loading, the accumulation of lateral pile displacement could be accompanied by either increase or decrease in soil resistance, which strongly depends on the loading rate. Strong correlation between the development of peak soil resistance and a dimensionless velocity group was obtained, and was supported by the measured excess pore pressure. Under undrained conditions, the peak soil resistance decreases almost linearly with the accumulation of excess pore pressure.

A novel macroelement model for the nonlinear analysis of masonry buildings. Part 1: Axial and flexural behavior

AbstractIn the numerical modelling of the nonlinear response of masonry buildings by equivalent‐frame models based on macroelements representative of the in‐plane response of structural members, it is important to correctly capture compressive behavior, lateral stiffness, and strength of the structure. The macroelement model currently implemented in the TREMURI computer program, thanks to the presence of nonlinear interfaces lumped at the element extremities, allows studying the coupled axial and in‐plane bending response, with the inherent limitation of approximating the stiffness associated with at least one of these behaviors. The simplified compressive law does not capture the displacement accumulation during cyclic loads; moreover, second‐order effects are not modelled. The article presents an improved macroelement model, able to simulate the in‐plane cyclic response of masonry walls. The model overcomes some of the limitations of the currently available macroelement. As regards the compressive and flexural behavior, a new compressive law is introduced, together with a methodology to capture the correct flexural stiffness of the panel and to model the second‐order effects. The improved model was then implemented in the TREMURI program and validations of the new features are shown, together with a simulation of an experimental test on a single wall characterized by flexural behavior. A companion article presents the shear formulation and shows the ability of the new macroelement of accurately predicting the nonlinear response of masonry structures at the building scale through the simulation of a larger number of experimental tests.

Effect of Horizontal Multidirectional Cyclic Loading on Piles in Sand: A Numerical Analysis

Foundations of offshore and nearshore wind energy production systems are subjected to multidirectional and cyclic loads, due to the combined action of wind and waves and in the particular case of mutualized anchor foundations for floating wind turbines, to the phase shift between the loads generated in the adjacent anchored turbines. This article presents a three-dimensional numerical model developed with FLAC3D to analyse the impact of the change in direction of the horizontal load during the cycles. The typical case of a 1.7 m diameter and 10 m-long pile founded in a dense homogeneous sand is considered. A specific procedure has been implemented to apply force-controlled cycles with a change in lateral load direction. The results are compared to mono-directional lateral cyclic loads with the same average and cyclic forces. The results of the parametric study highlight the effect of the average value and amplitude of the cyclic loading on the accumulation of pile head horizontal displacements during the cycles. When a multidirectional cyclic loading is applied, it also leads to an accumulation of the deviated horizontal displacements, and the resulting accumulated horizontal displacements are larger than for a mono-directional cyclic loading of the same amplitude.

Limit states and safety factors under repeated loading

Verification of the structures operating possibility using numerical modeling beyond the elastic limit requires standardization of safety factors and calculation methods used to get them. In the framework of the discussion on the improvement of the strength standards of the aviation and nuclear industries for structures operating under low-cycle mechanical and reversible dilatation (temperature, hydrogen) external influences, the article discusses the limiting states; the deformation properties of materials necessary for their calculation; safety factors for loads and durability; calculation methods. The article divides limit states of structures under low-cycle actions into two groups: typical, corresponding to a qualitative change in the deformation type, and individual, determined by allowable displacements and cracks for a particular structure. The following types of deformation are considered: inelastic deformation only at the running-in stage (that changes to elastic after the auspicious residual stresses develop and cyclic hardening of the material); alternating flow (that continues with the number of cycles); progressive accumulation of strains and displacements; combined deformation (when both strain span and strain increment are non-zero in a stable cycle). The types of deformation differ in possible consequences for the structure and the initial data for the calculation: mechanical properties of the material required for modeling different types of deformation should be determined by fundamentally different tests. An analysis of individual limit states without taking into account differences in the types of deformation - and thus typical limit states - may be incorrect. The main focus of the article is on typical limit states. The limit states vary depending on the stage of operation at which inelastic cyclic deformation is allowed. Inelastic deformation expands allowable load range, the expansion due to the inelastic deformation at the running-in stage only is usually more significant than additional expansion due to the continuous inelastic deformation; besides, the inelastic deformation only at the running-in stage does not demand analysis of low-cycle fatigue and accumulated strains. Further expansion of the permissible load range, as well as solution of safety problems based on risk assessments, requires a more complete study of the deformation properties of materials at the pre-fracture stage, where cyclic softening predominates.

Study of small-scale structures and their significance in unravelling the accretionary character of Singhbhum shear zone, Jharkhand, India

Localized strain within tabular ductile shear zones is developed from micro- to meso- to even large scales to form complex structures. They grow in width and length through linkage of segments with progressive accumulation of strain and displacement, and finally produce shear zone networks characterized by anastomosing patterns. Singhbhum shear zone (SSZ) represents a large composite zone characterized by a collage of different dismembered lithotectonic segments, with heterogeneous structural features, within a matrix typical of a shear zone. Structural features indicate that the material properties of protoliths have a great role in controlling the mechanics of deformation. Meso- and micro-scale structural studies of the east-central part of the SSZ reveal ‘tectonic complex like’ (? deeper level equivalent of melange type complex) assemblage of dismembered lithoteconic units. Shear-induced foliations, S, C and C′, were developed while the main mylonitic foliation is represented by C-plane. Apart from that, shear lenses are exceptionally well developed in both meso- and micro-scale in most of the units, particularly in schistose rocks. They were formed from different processes during progressive simple shear, which includes (1) anastomosing C-planes, (2) intersection between C- and C′-planes, (3) disruption of stretched out longer limbs of asymmetric folds, and (4) cleavage duplex. Fabrics recorded in rocks indicate that there was a progressive change in the development of predominantly flattening fabric (coaxial pure shear) in the northern part (outside the SSZ), to simple-shear non-coaxial type deformation producing shear fabric, dominating over the flattening fabric, in the southern part (within the SSZ) that is in close proximity with the Singhbhum Craton. Although an overall plane strain simple shear model is apparent, occasional presence of extensional features along two directions of the mylonitic foliation, demonstrative of three-dimensional deformation (simple shear and flattening: X > Y > 1 > Z), may indicate the stretching nature of the SSZ. From the orientation of oblique grain shape fabric [ISAmax (θ < 45°)], there is slight deviation from simple shear, i.e., a sub-simple nature of plane strain shear could be inferred. However, in conformity with simple shear model the ubiquitously developed stretching lineation shows consistency in orientation being parallel to the movement direction. There is no evidence of transpression. Shear sense indicators invariably indicate up-dip ductile thrust movement with vergence top-to-the south. Microstructural deformational characteristics indicate that peak temperature attained during the deformation in shear zone was ~600 °C. Prolonged period of metasomatism, induced by fluid influx, played an important role in strain softening during the development of SSZ.

Displacement Accumulation and Sampling of Paleoearthquakes on Active Normal Faults of Crete in the Eastern Mediterranean

AbstractActive normal faults on the Mediterranean island of Crete form prominent limestone scarps together with basin and range topography. These faults mainly strike E‐ESE and N‐NNE in southern and northern Crete, respectively, with fault sets commonly intersecting and northerly trending faults being a factor of 3 more abundant. Lengths, displacements, and displacement rates have been analyzed for 84 active faults sampled over 2 ± 0.5 Ma (long‐term) and 16.5 ± 2 ka (short‐term) time‐intervals, with half showing no resolvable short‐term activity. Active faults record earthquake processes on timescales of thousands to million years and constrain sampling biases, which can lead to under and over estimates of fault parameters. The available data provide no evidence for fault propagation and support a model in which fault lengths were established early in the development of the fault system. Short‐term displacement rates (0.09–1.2 mm/year) are generally higher than long‐term rates (0.002–0.7 mm/year), with a factor of 4 disparity in the average recurrence intervals for the two time periods (∼2.5 Kyr vs. ∼11 Kyr). We attribute these differences to “clustering” of surface‐rupturing (e.g., &gt;Mw6) earthquakes on individual faults over millennial timescales, and to preferential sampling of the most seismically active faults during the short‐term. Displacement rates are comparable when averaged for each time interval on the longest faults (&gt;10 km), indicating that for these faults earthquake “clustering” spans time‐intervals of &lt;∼16.5 Kyr. Paleoerthquakes &gt; Mw6 on Crete are at least three times more frequent than historical earthquakes since ∼1920, possibly because multi‐fault surface‐rupturing earthquakes are double counted in the paleo‐record.

Stability of submarine landslides by in situ observation

With the continuous expansion of human activities to the ocean and the development of marine engineering, the stability of submarine landslides has attracted increasing attention. Monitoring data of the stability of submarine landslides under the action of strong wind and waves remain lacking because of limited observation technology and complex real sea conditions. This paper reports the long-term and continuous stability monitoring of submarine landslides under the action of wind and waves in the seabed of the Zhujiajian landslide area of Zhoushan by using a self-developed observation equipment. Effective data were collected, and variations in the pore pressure and displacement of seabed under the action of wind and waves were analyzed. Then, problems related to the change of displacement of seabed under the action of waves were explored. A typhoon event occurred during the observation period, and the significant wave height increased significantly from about 0.1 m under calm sea conditions to 0.5 m. The excess pore pressure in the sediment of 1 m under the seabed fluctuated obviously under the action of waves, with an amplitude of 2–4 kPa. By contrast, the amplitude of excess pore pressure oscillation was about 0.5 kPa under calm sea conditions, and the wave enhancement significantly increased the excess pore pressure oscillation in shallow sediments. The displacement of 0.5 mm occurred from 12 m to 13.5 m under the seabed, and the rapid accumulation or large fluctuation of lateral displacement occurred at different depths during the three periods when the significant wave height peaked.

A non-linear static approach for the prediction of earthquake-induced deformation of geotechnical systems

This paper illustrates an original and simple method to predict earthquake-induced deformations of geotechnical systems. The method is an extension of static non-linear analysis, and is conceived to predict the behaviour of geotechnical systems, like supported and unsupported excavations, that during the seismic motion accumulate displacements in a single direction. The seismic capacity of the system is described by its capacity curve, obtained either from a numerical push-over analysis or through a simplified procedure. The corresponding seismic demand is described by a combination of the elastic response spectrum, including basic information on the maximum amplitudes of the seismic motion, and a cyclic demand spectrum, that provides additional information about the equivalent number of cycles that contribute to the accumulation of displacements. In the paper, the method is described in detail and is validated through different procedures, namely: comparisons with experimental results obtained in the geotechnical centrifuge; comparison with results of advanced numerical analyses; extensive comparison, using a large database of seismic records, with the results of non-linear time-domain analyses. In its final part, the paper provides guidance for the practical use of the method for design.

Lateral response of rigid monopiles subjected to cyclic loading: centrifuge modelling

In this study, a total number of 20 centrifuge tests were carried out to investigate monopile behaviour under lateral cyclic loading. The instrumented model pile simulates an offshore wind turbine foundation with an embedment ratio of 5 installed in sand layers with two relative densities of 80% and 50%. The influence of the directional characteristic and amplitude of cyclic load on pile lateral behaviour was studied. The data analysis focused on the influence of cyclic load on the accumulation of lateral displacement and evolution of secant stiffness of the foundation system. The most damaging cyclic load type (which can cause the most accumulated pile displacement) is identified as two-way loading, and it was observed that cyclic load always increases the pile secant stiffness. A new model for the prediction of evolution of accumulated displacement and change in secant stiffness has been formulated. An example of the procedure developed is presented for a typical field monopile subjected to cyclic loading. Lastly, the performance of the new model is demonstrated and predicted results are compared with field test data.

A Review on Conventional and Innovative Pile System for Offshore Wind Turbines

This paper includes a brief review of analytical, experimental and numerical studies carried out on conventional and innovative piles subjected to monotonic and cyclic lateral loads. State-of-the-art developments and the important approaches relevant to the field of laterally loaded pile was discussed. The observations from small-scale experiments confirmed that monopiles embedded in cohesionless soil undergoes progressive accumulation of displacement and the rate of accumulation does not approach zero even after 10,000 cycles. The accumulated rotation of the foundations under the offshore loading conditions mainly depends on the characteristics of cyclic loading such as the magnitude of maximum and minimum load during a cycle. The review of existing works showed that there are hardly any studies addressing the effect of gentle seabed slope and also the effect of multi-directional loading on the magnitude of accumulated rotation of rigid monopiles. It is critically suggested to consider the influence of strong vertical loads and moments on stiff monopiles installed on gentle seabed slopes. The current study reveals the use of finned and helical piles in improving the lateral resistance and reducing the pile head deflections. However, further investigations are required to validate their performance in varying soil conditions and also to optimize and ease the design through the development of cyclic p–y curves.

Shear Band Formation in Amorphous Materials under Oscillatory Shear Deformation

The effect of periodic shear on strain localization in disordered solids is investigated using molecular dynamics simulations. We consider a binary mixture of one million atoms annealed to a low temperature with different cooling rates and then subjected to oscillatory shear deformation with a strain amplitude slightly above the critical value. It is found that the yielding transition occurs during one cycle but the accumulation of irreversible displacements and initiation of the shear band proceed over larger number of cycles for more slowly annealed glasses. The spatial distribution and correlation function of nonaffine displacements reveal that their collective dynamics changes from homogeneously distributed small clusters to a system-spanning shear band. The analysis of spatially averaged profiles of nonaffine displacements indicates that the location of a shear band in periodically loaded glasses can be identified at least several cycles before yielding. These insights are important for the development of novel processing methods and prediction of the fatigue lifetime of metallic glasses.

Effects of crosslinking densities on mechanical properties of nitrile rubber composites in thermal oxidative aging environment

AbstractThe effects of crosslinking densities on mechanical properties of nitrile rubber (NBR) composites before and after thermal oxidative aging are investigated. Tensile strengths of NBR composites are enhanced slightly at the initial aging stage, attributing to moderate increment of crosslinking densities. Continuous decrease with further aging is followed, resulting from over‐crosslinking and uneven distribution of crosslinking densities. The digital image correlation method is explored for large‐strain deformation measurement by displacement accumulation and establishing strain model, being promising in practical age detection and measurement of mechanical properties in complex environments. Compression sets are gradually increased with aging because of the destruction of the original crosslinking structures. The molecular chains fracture inhibits elastic recoveries of compressive NBR composites and results in residual deformation in thermo‐oxidative and compressive environment after unloading. This study provides new ideas for exploring mechanical properties of rubber‐based composites before and after thermal oxidative aging.

Coseismic Displacement Accumulation Between 1996 and 2019 Using A Global Empirical Law on Indonesia Continuously Operating Reference Station (InaCORS)

Indonesia archipelago is one of the most populated country with active and complex tectonic zone in the world. Plate boundaries were assembled by four major plate which made the region not only vulnerable to earth-hazard but also prone to semi-dynamic reference frame. However, influence of transient deformation such as coseismic displacement due to large amount of small to intermediate earthquakes (&lt; Mw 6) on the geodetic networks is remain poorly understood. Geospatial Information Agency occupied permanent and continuous GPS networks since 1996 but rapidly increase in 2010. Based on simulated empirical law of coseismic crustal deformation, we estimate the cumulative displacement due to coseismic step on Indonesia Continuous Operating Reference Stations (InaCORS). We utilize the position of the observation network and earthquake hypocentral with estimated moment magnitude. Our result suggesting small to intermediate earthquakes are indispensable for estimating secular motion and potentially contribute the cumulative offset associated with the transient postseismic deformation.

Model of multilevel formation of normal cracks in reinforced concrete elements and structures

This article proposes a model of multilevel formation of normal cracks. It is based on the most important patterns of adhesion of reinforcement with concrete. The occurrence of the first normal cracks of the first level is calculated by the limiting deformations of stretched concrete, which are fixed by the extreme criterion of its strength. The distances between the cracks are determined by the equilibrium of the maximum forces in the stretched concrete and the forces of active adhesion in the area between the cracks. It is proposed to calculate the force of active coupling by the nonlinear function of the average stresses of this coupling, justified by the power of expression. It is substantiated why for bending reinforced concrete elements the distances between normal cracks of new and previous levels will always differ from each other. In the developed model, the width of the most dangerous normal crack opening is calculated from the positions of successive accumulation of reinforcement and concrete mutual displacements.

A Numerical Analysis to Solve a Geotechnical Problem of a Concrete Pile Subjected to a Static Lateral Load

This work is devoted to a numerical analysis of concrete pile subjected to a static load. As part of the development of methods and procedures to account for the effect of loadings on pile response, a numerical modeling using finite difference codes for 3D analysis has been performed. This paper presents the results of numerical computation in terms of accumulation of displacement at the head of pile and evolution of the lateral friction along the pile by exploring P-Y curves. By using these numerical results it has been possible to solve the geotechnical problem of determining the soil reaction coefficient. This study shows that the reaction coefficient of soil varies with depth. The solutions are based on soil-structure interaction modeling. The good agreement between theoretical and numerical results confirms the validity of the proposed solution.

Analysis Line Approach for Assembly Tolerance Analysis

This work presents the analysis line approach for assembly tolerance analysis. Firstly, the product functional requirements and geometric variations of part positioning features can be converted into small displacements of a series of analysis points along the specified analysis directions. The small displacement torsor (SDT) theory is employed to establish the mathematical relations between the displacements of these analysis points. And then, the variation transfer relations and tolerance accumulation calculations of various orthogonal joints between different parts are studied to determine the maximum displacement of the analysis points on the functional surface. The final displacement accumulation results of the functional surface are compared with the geometric functional requirements of the product, so as to judge whether the product functional requirements are met. Finally, an example is given to demonstrate the effectiveness of the proposed analysis line approach.

The Langevin diffusion as a continuous‐time model of animal movement and habitat selection

Abstract The utilization distribution of an animal describes the relative probability of space use. It is natural to think of it as the long‐term consequence of the animal's short‐term movement decisions: it is the accumulation of small displacements which, over time, gives rise to global patterns of space use. However, many estimation methods for the utilization distribution either assume the independence of observed locations and ignore the underlying movement (e.g. kernel density estimation), or are based on simple Brownian motion movement rules (e.g. Brownian bridges). We introduce a new continuous‐time model of animal movement, based on the Langevin diffusion. This stochastic process has an explicit stationary distribution, conceptually analogous to the idea of the utilization distribution, and thus provides an intuitive framework to integrate movement and space use. We model the stationary (utilization) distribution with a resource selection function to link the movement to spatial covariates, and allow inference about habitat preferences of animals. Standard approximation techniques can be used to derive the pseudo‐likelihood of the Langevin diffusion movement model, and to estimate habitat preference and movement parameters from tracking data. We investigate the performance of the method on simulated data, and discuss its sensitivity to the time scale of the sampling. We present an example of its application to tracking data of Steller sea lions Eumetopias jubatus. Due to its continuous‐time formulation, this method can be applied to irregular telemetry data. The movement model is specified using a habitat‐dependent utilization distribution, and it provides a rigorous framework to estimate long‐term habitat selection from correlated movement data. The Langevin movement model can be written as a linear model, which allows for very fast inference. Standard tools such as residuals can be used for model checking.

Analytical fragility assessment of structures under earthquake and tsunami loads: a case study on the Colombian Pacific coast

This article presents a procedure for the fragility assessment of structures in response to earthquake and tsunami loads using the accumulation of inelastic displacement as a measure of damage. The proposed methodology considers a non-linear static analysis (pushover) for the case of the earthquake and a non-linear static load for the case of the tsunami, taking as starting point the final state of the structure after the occurrence of an earthquake. However, since the impulse force is the critical component of the tsunami load, a simplified approximation in terms of the flood depth is used to estimate the total of the tsunami load. By combining the effect of earthquake and tsunami hazard, a function is obtained relating the spectral acceleration of the earthquake, the flood depth of the tsunami and the drift. Finally, a case study of timber houses located in the municipality of San Andrés de Tumaco at the Colombian Pacific coast is analyzed to assess de proposed methodology. The fragility curve obtained allows a new approach to Multi-hazard risk assessment in areas susceptible to the occurrence of earthquake and tsunami.