Sandpile Research Articles

Scouring effects on lateral cyclic responses of piles in sand

The wind turbine has become an efficient way for clean energy. For offshore wind turbine in a sandy area, the monopile is a widely used foundation type under proper water depths. During the life time, monopiles are subjected to millions of cyclic loads from winds and waves and scouring around the pile is a common phenomenon, both of which can influence the operation safety of the offshore turbine. To study the coupled effects of cyclic loading and scouring on the horizontally loaded pile, a series of horizontal monotonic and cyclic loading tests on model piles were carried out in sandy soil. The influence of pile diameter, cyclic loading amplitude, and scour depth on the long-term residual accumulated displacements of a monopile is investigated. The test results show that the deformation mode of pile and the dilatancy of sand result in different static responses of the pile. A quantised work is presented to estimate the accumulated residual displacements of the pile, in which the effects of the three factors can be expressed in a united expression. Since the lateral capacity is a crucial parameter for the normalisation in regression analysis, the confirmation of a lateral capacity should be related to the corresponding concern in practical projects.

A modified p–y model of single pile in coral sand under lateral load

This study addressed the characteristics of lateral pile–soil interactions in coral sand foundation using a series of direct shear, triaxial, and model pile tests. Through the comprehensive analysis of the stress state of the coral sand around pile, it was found that the soil resistance is mainly dominated by frontal squeezing resistance. Accordingly, the framework of the modified p–y model was determined, namely the function type, exponents of depth term, and the mark of entering the plastic state. The modified p–y model adopts a normalized dimensionless form, and it is composed of the first nonlinear segment represented by the power function and the plastic state at large displacements represented by a straight line. The final p–y model was calibrated using the results of the model pile test. Subsequently, the validity of the modified p–y model was verified by the experimental results of this study and other researchers. The soil reactions and pile responses predicted by the modified p–y model were in a reasonable agreement with the measured data. Finally, the modified p–y model was compared with the existing p–y models, thus confirming its rationality and applicability.

A novel method to measure air-immobile regions of the composting pile by inverse calculation combined with gas tracer test

Air-immobile regions in composting piles obstruct O2 mass transport and exacerbate the formation and emission of harmful off-gases. However, effective methods for measuring the parameters of these air-immobile regions are lacking. With quartz sand piles, this study first adjusted the circumstances of a gas tracer test (gas tracer, its injection volume, and chamber type) using the two-region model (TRM). The effects of β (proportional coefficient of gas in the air-mobile region) and ω (mass exchange coefficient) on the breakthrough curves (BTCs) of the gases were then explored. Finally, an inverse calculation method was used to measure the feature parameters of air-immobile regions in two composting piles (temperature-increasing and thermophilic phases) and estimate the O2 concentrations in different composting piles (50, 100, 200 cm whole height; layers of 50, 100, 200 cm height in a 200-cm high pile). The results showed that the optimal conditions were achieved when 100 mL helium (He) as the gas tracer and a cylinder with a height/diameter ratio of 3 as the chamber were used. With the simulating composting piles, increasing β or ω slowed breakthrough and decreased peak concentration in BTCs of a gas tracer. Tracer-inverse calculation protocol can be used to efficiently estimate the volume ratios of air-immobile regions (φ) and first-order mass transfer coefficient (α), with the values of 39%/46% and 0.001/0.006 min−1 in the composting piles during temperature-increasing /thermophilic phase. The TRM also predicted the O2 concentration in the off-gas or air-mobile/immobile regions of the temperature-increasing-phase composting piles.

Micromechanical analysis of the particle corner breakage effect on pile penetration resistance and formation of breakage zones in coral sand

Although particle corner breakage has proven to be the major breakage mode of irregular grains, most pile–soil interaction analysis has focused on particle fracture breakage, thus the microscopic mechanism of sharp settlement/stress change for piles in coral sand remains unclear. This particle corner breakage–based study features laboratory pile penetration tests as well as DEM simulations. In the laboratory tests, in-situ sand samples that avoid slipping loss of corner debris are obtained and adopted. During DEM simulations, the cluster method is adopted with the linear parallel bond model. Unlike with classical friction resistance of piles, the particular shrinkage of friction resistance of piles in coral sand can be seen as resulting from a dual effect of corners. An additional increase in confining pressure was not efficient at improving the ultimate friction-bearing capacity of piles in crushable angular grains. As indicated by a diagram describing relationships between corner breakage and effective contacts, the force transmission in soil is newly generated, allowing interpretation of the sharp decrease of pile friction-bearing capacity. Findings indicate that higher grain angularity increases particle breakage within a narrower shear zone in soil samples. Finally, a particular relationship between particle breakage mode and the breakage zone around the pile tip is derived. This study sheds light on the microscopic mechanism of pile penetration in crushable granular soils, offering guidance for evaluating the ground-bearing capacity of angular granular soils.

Natural time analysis of acoustic emissions before fracture: Results compatible with the Bak-Tang-Wiesenfeld model

Natural time analysis has been recently applied for the elaboration of data recorded by means of the Acoustic Emission (AE) sensing technique while specimens and structures are mechanically loaded at levels approaching those causing macroscopic fracture. In terms of the variance , the entropy in natural time S, as well as the entropy in natural time under time reversal , a complex behavior was observed, which could be understood by the Burridge-Knopoff train model and the Olami-Feder-Christensen earthquake model. Here, the AE data recorded when notched fiber-reinforced concrete specimens were subjected to three-point bending until fracture, are analysed in natural time. The analysis leads to , S, and values that are compatible with those obtained by a centrally fed Bak-Tang-Wiesenfeld sandpile model, which was theoretically studied in natural time almost a decade ago.

Energy fluctuations in one dimensional Zhang sandpile model

We consider the Zhang sandpile model in one-dimension (1D) with locally conservative (or dissipative) dynamics and examine its total energy fluctuations at the external drive time scale. The bulk-driven system leads to Lorentzian spectra, with a cutoff time T growing linearly with the system size L. The fluctuations show 1/f α behavior with α ∼ 1 for the boundary drive, and the cutoff time varies non-linearly. For conservative local dynamics, the cutoff time shows a power-law growth T ∼ L λ that differs from an exponential form ∼exp(μL) observed for the nonconservative case. We suggest that the local dissipation is not a necessary ingredient of the system in 1D to get the 1/f noise, and the cutoff time can reveal the distinct nature of the local dynamics. We also discuss the energy fluctuations for locally nonconservative dynamics with random dissipation.

Self-Organized Criticality of Precipitation in the Rainy Season in East China

Based on daily precipitation data from 1960 to 2017 in the rainy season in east China, to a given percentile threshold of one observation station, the time that precipitation spends below threshold is defined as quiet time τ. The probability density functions τ in different thresholds follow power-law distributions with exponent β of approximately 1.2 in the day, pentad and ten-day period time scales, respectively. The probability density functions τ in different regions follow the same rules, too. Compared with sandpile model, Γ function describing the collapse behavior can effectively scale the quiet time distribution of precipitation events. These results confirm the assumption that for observation station data and low-resolution precipitation data, even in China, affected by complex weather and climate systems, precipitation is still a real world example of self-organized criticality in synoptic. Moreover, exponent β of the probability density function τ, mean quiet time τ¯q and hazard function Hq of quiet times can give sensitive regions of precipitation events in China. Usual intensity precipitation events (UPEs) easily occur and cluster mainly in the middle Yangtze River basin, east of the Sichuan Province and north of the Gansu Province. Extreme intensity precipitation events (EPEs) more easily occur in northern China in the rainy season. UPEs in the Hubei Province and the Hunan Province are more likely to occur in the future. EPEs in the eastern Sichuan Province, the Guizhou Province, the Guangxi Province and Northeast China are more likely to occur.

A memory-enhanced p-y model for piles in sand accounting for cyclic ratcheting and gapping effects

The analysis of cyclically loaded piles is acquiring ever greater relevance in the field of geotechnical engineering, most recently in relation to the design of offshore monopiles. In this area, predicting the gradual accumulation of pile deflection under prolonged cycling is key to performing relevant serviceability assessments, for which simplified pile–soil interaction models that can be calibrated against common geotechnical data are strongly needed. This study proposes a new cyclic p−y model for piles in sand that takes a step further towards meeting the mentioned requirements. The model is formulated in the framework of memory-enhanced bounding surface plasticity, and extends to cyclic loading conditions the previous monotonic, CPT-based p−y formulation by Suryasentana and Lehane (2016); additionally, detailed modelling of pile–soil gapping is introduced to cope with the presence of unsaturated sand layers or, more generally, of cohesive soil behaviour. After detailed description of all model capabilities, field data from an onshore cyclic pile loading test are simulated using the proposed p−y model, with the most relevant parameters calibrated against available CPT data. Satisfactory agreement is shown between experimental and numerical results, which supports the practical applicability of the model and the need for further studies on a fully CPT-based calibration.

On the Regularity of Optimal Transports Between Degenerate Densities

We study the most common image and informal description of the optimal transport problem for quadratic cost, also known as the second boundary value problem for the Monge–Ampère equation—what is the most efficient way to fill a hole with a given pile of sand?—by proving regularity results for optimal transports between degenerate densities. In particular, our work contains an analysis of the setting in which holes and sandpiles are represented by absolutely continuous measures concentrated on bounded convex domains whose densities behave like nonnegative powers of the distance functions to the boundaries of these domains.

Optimization of inter-helix spacing for helical piles in sand

The optimization of the inter-helix spacing is a key issue of the axial bearing capacity of helical piles. In this paper, based on the cavity expansion, an analytical approach considering the small-strain stiffness, strength, compressibility and stress level of sand around the helical pile was proposed to analyze the influence zone of the helices to determine the optimal inter-helix spacing in sand. The calculation results of the proposed method were verified using the centrifuge test data and finite element analysis for helical pile in Congleton HST95 sand. They were also compared with those using the Meyerhof pile foundation theory. The results show that the optimal inter-helix spacing based on Meyerhof pile foundation theory differs significantly from the measurement. The range of the influence zone for the helices in sand calculated by the cavity expansion theory matches with the data from literature. The calculation results with the proposed method are consistent with the range of the optimal spacing ratio inferred in the centrifuge tests. The results based on the two-dimensional (2D) finite element model (FEM) are also basically consistent with the calculated analytical solution.

A self-organized critical model and multifractal analysis for earthquakes in Central Alborz, Iran

This paper is devoted to a phenomenological study of the earthquakes in central Alborz, Iran. Using three observational quantities, namely the weight function, the quality factor, and the velocity model in this region, we develop a modified dissipative sandpile model which captures the main features of the system, especially the average activity field over the region of study. The model is based on external stimuli, the location of which is chosen (I) randomly, (II) on the faults, (III) on the low active points, (IV) on the moderately active points, and (V) on the highly active points in the region. We uncover some universal behaviors depending slightly on the method of external stimuli. A multi-fractal detrended fluctuation analysis is exploited to extract the spectrum of the Hurst exponent of the time series obtained by each of these schemes. Although the average Hurst exponent depends slightly on the method of stimuli, we numerically show that in all cases it is lower than 0.5, reflecting the anti-correlated nature of the system. The lowest average Hurst exponent is found to be associated with the case (V), in such a way that the more active the stimulated sites are, the lower the average Hurst exponent is obtained, i.e. the large earthquakes are more anticorrelated. Moreover, we find that the activity field achieved in this study provide information about the depth and topography of the basement, and also the area that can potentially be the location of the future large events. We successfully determine a high activity zone on the Mosha Fault, where the mainshock occurred on May 7th, 2020 (M_W 4.9).

Effects of seabed geotechnical properties on scour mechanism at the pile in non-cohesive soils: Experimental study

The influence of the seabed geotechnical properties on the scour development mechanism of the pile is ignored in the majority of the studies, which leads to a low accuracy of the scour depth prediction equation. This paper presents an experimental study on scour of the pile in sand with different seabed geotechnical properties (i.e. the friction angle, the density and the seepage force of the sand). The seabed stress equation, scour mechanism and scour depth prediction equation of the pile are found. The pile scour depth decreases with an increase in the relative densities of sand. The sand friction angle is the main micro parameter of the scour mechanism, and the seabed stress has a positive correlation with the relative density of sand. The seepage force of the sand has little effect on the scour depth of the pile. A scour protection method regarding reducing the scour depths of the pile by increasing the sand density is given. Finally, the effect of seabed consolidation on the scour depth of the pile is discussed.

Combined Effects of Soil Stress History and Scour Hole Dimensions on Laterally and Axially Loaded Piles in Sand and Clay under Scour Conditions

Removal of soil around a bridge foundation due to scour results in a reduction of the lateral and vertical foundation capacity due to the loss of soil support. The common approach in modeling the scour phenomenon of removal of soil springs without modifying the parameters of the remaining soil fails to consider the change of stress state of the remaining soil and the formation of scour hole geometry around the pile foundation. In practice, both of these factors impact the mechanical properties of the remaining soil and the resulting expected structural response of the pile under loadings. This paper proposed a methodology to comprehensively evaluate the combined effects of stress history and scour hole dimensions on piles under scour conditions in uniform soil. It enabled the examination of the lateral and axial behaviors of a loaded pile subject to scour and is applicable for both cohesive and cohesionless soils. The methodology was validated with results from field tests for no-scour scenarios and verified with existing numerical models for scour scenarios. Quantification of the soil effects was investigated through lateral pile deflection and load-settlement curves for lateral and axial behaviors, respectively. Load-settlement curves demonstrated that including the effect of stress history results in increases of up to 34.1% and 61.1% in estimated pile settlement for sand and clay, respectively, leading to potential unconservative designs if soil effects are not properly included in the analysis.

Sandpile cascades on oscillator networks: The BTW model meets Kuramoto

Cascading failures abound in complex systems and the Bak–Tang–Weisenfeld (BTW) sandpile model provides a theoretical underpinning for their analysis. Yet, it does not account for the possibility of nodes having oscillatory dynamics, such as in power grids and brain networks. Here, we consider a network of Kuramoto oscillators upon which the BTW model is unfolding, enabling us to study how the feedback between the oscillatory and cascading dynamics can lead to new emergent behaviors. We assume that the more out-of-sync a node is with its neighbors, the more vulnerable it is and lower its load-carrying capacity accordingly. Also, when a node topples and sheds load, its oscillatory phase is reset at random. This leads to novel cyclic behavior at an emergent, long timescale. The system spends the bulk of its time in a synchronized state where load builds up with minimal cascades. Yet, eventually, the system reaches a tipping point where a large cascade triggers a “cascade of larger cascades,” which can be classified as a dragon king event. The system then undergoes a short transient back to the synchronous, buildup phase. The coupling between capacity and synchronization gives rise to endogenous cascade seeds in addition to the standard exogenous ones, and we show their respective roles. We establish the phenomena from numerical studies and develop the accompanying mean-field theory to locate the tipping point, calculate the load in the system, determine the frequency of the long-time oscillations, and find the distribution of cascade sizes during the buildup phase.

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COVER ILLUSTRATION The self-organized criticality hallmarked by avalanche events whose sizes follow a power-law distribution is a statistical physics notion exemplified by the archetypical sandpile model. The critical brain hypothesis proposes that efficient neural computation can be achieved through critical brain dynamics. This idea was explored in the study using large-scale brain dynamics recorded by resting-state fMRI data. It was shown that subjects could be divided into three groups: those with more ordered or disordered brain dynamics, and those with critical dynamics between order and disorder, characterized by a power-law distribution of neural avalanche activities. Furthermore, in subjects with critical dynamics, their complexity of functional connectivity, as well as their coupling between structural and functional networks, is maximized. Finally, it was discovered that subjects with dynamics that are closer to criticality have higher fluid intelligence and working memory scores. These findings reveal the important role of large-scale critical dynamics in brains in cognitive performance and demonstrate the possibility to map cortical states on a spectrum of neural dynamics, ranging from subcriticality to supercriticality.

A simple rotational spring model for laterally loaded rigid piles in sand

Monopiles are the most popular foundation for offshore wind turbines. These foundations typically have a low length to diameter ratio and undergo a rigid body rotation when subjected to lateral load. This paper presents results from an extensive numerical investigation involving 3D finite element analyses to demonstrate that the lateral moment-rotation response of a monopile in sand can be represented using a single non-linear rotational spring located at a depth of about 0.75 times the pile embedment. Expressions for the elastic rotational stiffness of a monopile under very low rotations are developed and these combined with observations from measured non-linear variations of rotational stiffness, that are supported by the numerical analyses, are used to develop a simple approximate expression that can be used to determine the response of a monopile to a monotonic lateral load in sand.

Stochastic sandpile on a cycle

In the stochastic sandpile (SS) model on a graph, particles interact pairwise as follows: if two particles occupy the same vertex, they must each take an independent random walk step with some probability 0 < p < 1 of not moving. These interactions continue until each site has no more than one particle on it. We provide a formal coupling between the SS and the activated random walk models, and we use the coupling to show that for the SS with n particles on the cycle graph , the system stabilizes in O(n 3) time for all initial particle configurations, provided that p(n) tends to 1 sufficiently rapidly as n → ∞.

Discussion of “Investigation of Cyclic Loading of Aged Piles in Sand’’ by David Igoe and Kenneth Gavin

Discussion of “Investigation of Cyclic Loading of Aged Piles in Sand’’ by David Igoe and Kenneth Gavin

Lateral responses of monopile-supported offshore wind turbines in sands under combined effects of scour and earthquakes

Offshore wind turbines (OWTs) supported by monopiles can be vulnerable to scour and liquefaction triggered by waves and earthquakes. However, the combined effects of scour and earthquakes on the monopile-supported OWTs in sands are not fully appreciated. This study proposes a practical method to evaluate the post-scour seismic responses of piles in sands and applies it to analyze the monopile-supported OWTs. This method introduces a new concept that relates scour-hole geometric conditions to soil liquefaction potential. Using the proposed method, a parametric study was conducted to evaluate the effects of scour-hole dimensions, sand relative densities, and input ground motions on the lateral responses of OWTs. The results showed that scour shifted the fundamental frequency of the OWT system into the rotor frequency range, causing resonance. An increase in scour depth increased the dynamic responses of the monopile and tower, which was less significant in liquefied than in non-liquefied condition. • A practical method is proposed to simulate dynamic soil-pile interactions in sands under scoured conditions. • Computer scripts are developed to analyze post-scour seismic responses of monopile-supported offshore wind turbines (OWTs). • A parametric study was conducted in time domain to investigate lateral responses of a selected monopile-supported OWT. • Contributions of inertial and kinematic interactions to dynamic responses of OWT were assessed by cross-correlation analyses. • The scour effect on the dynamic responses of OWT was more remarkable in the non-liquefied case than in the liquefied case.

Self-organized quantization and oscillations on continuous fixed-energy sandpiles.

Atmospheric self-organization and activator-inhibitor dynamics in biology provide examples of checkerboardlike spatiotemporal organization. We study a simple model for local activation-inhibition processes. Our model, first introduced in the context of atmospheric moisture dynamics, is a continuous-energy and non-Abelian version of the fixed-energy sandpile model. Each lattice site is populated by a nonnegative real number, its energy. Upon each timestep all sites with energy exceeding a unit threshold redistribute their energy at equal parts to their nearest neighbors. The limit cycle dynamics gives rise to a complex phase diagram in dependence on the mean energy μ: For low μ, all dynamics ceases after few redistribution events. For large μ, the dynamics is well-described as a diffusion process, where the order parameter, spatial variance σ, is removed. States at intermediate μ are dominated by checkerboardlike period-two phases which are however interspersed by much more complex phases of far longer periods. Phases are separated by discontinuous jumps in σ or ∂_{μ}σ-akin to first- and higher-order phase transitions. Overall, the energy landscape is dominated by few energy levels which occur as sharp spikes in the single-site density of states and are robust to noise.