Sandpile Research Articles

A physical study of the LLL algorithm

This paper presents a study of the LLL algorithm from the perspective of statistical physics. Based on our experimental and theoretical results, we suggest that interpreting LLL as a sandpile model may help understand much of its mysterious behavior. In the language of physics, our work presents evidence that LLL and certain 1-d sandpile models with simpler toppling rules belong to the same universality class.This paper consists of three parts. First, we introduce sandpile models whose statistics imitate those of LLL with compelling accuracy, which leads to the idea that there must exist a meaningful connection between the two. Indeed, on those sandpile models, we are able to prove the analogues of some of the most desired statements for LLL, such as the existence of the gap between the theoretical and the experimental RHF bounds. Furthermore, we test the formulas from finite-size scaling theory (FSS) against the LLL algorithm itself, and find that they are in excellent agreement. This in particular explains and refines the geometric series assumption (GSA), and allows one to extrapolate various quantities of interest to the dimension limit. In particular, we obtain the estimate that the empirical average RHF converges to ≈1.02265 as the dimension goes to infinity.

Power and energy consumption of skid‐steer rovers turning on loose soil

AbstractThis study highlights two key phenomena affecting power and energy consumption of skid‐steer rovers on loose soil that is not present on the hard ground: soil excavation due to wheel counterrotation and impeded turning when dragging a braked wheel. Experiments in the field and in a controlled laboratory sandbox show that, on sand, power peaks by 15%–20% in a newly identified range of turns with radii between half the rover width, , to , the radius at which the inner wheel does not turn. In this range of turns, the inner wheels rotate backwards but are being dragged forward through piles of sand they excavate by counterrotation. At , turns are shown to take much longer, leading to higher total energy consumption over time. Experiments in a controlled laboratory sandbox isolate the high motor torque and the resistance force experienced when a skid‐steer rover drags a counterrotating or braked wheel, respectively, through loose soil. Other field experiments also demonstrate that paths combining circular arcs and lines can lead to energy savings of up to 15% relative to common ones consisting of point turns and lines; the experimental results suggest the circular arcs should have radii of approximately . The quantitative values presented in this paper are specific to the rover and soils tested, but there are reasons to support the overall conclusions generalizing to all skid‐steer rovers in loose soil.

Evidence of self-organized criticality in time series by the horizontal visibility graph approach

Determination of self-organized criticality (SOC) is crucial in evaluating the dynamical behavior of a time series. Here, we apply the complex network approach to assess the SOC characteristics in synthesis and real-world data sets. For this purpose, we employ the horizontal visibility graph (HVG) method and construct the relevant networks for two numerical avalanche-based samples (i.e., sand-pile models), several financial markets, and a solar nano-flare emission model. These series are shown to have long-temporal correlations via the detrended fluctuation analysis. We compute the degree distribution, maximum eigenvalue, and average clustering coefficient of the constructed HVGs and compare them with the values obtained for random and chaotic processes. The results manifest a perceptible deviation between these parameters in random and SOC time series. We conclude that the mentioned HVG’s features can distinguish between SOC and random systems.

Study on combination of p-y models for laterally loaded pile in offshore wind farm

The p-y curve method recommended by American Petroleum Institute (API) code is a mainstream design method of the laterally loaded large-diameter piles for offshore wind turbines. However, it has been long recognized that the conventional p-y models proposed for piles with a relatively large length to diameter ratio may not be appropriate for the large-diameter piles. In this study, the field tests of laterally loaded pile are analyzed in detail, particularly the bending moment and lateral displacement under multistage cyclic loading. The bending moment and lateral displacement of test pile are calculated by several combinations of clay p-y model and sand p-y model. A modified p-y model for clay is proposed considering the influence of pile diameter, and a modified p-y model for sand is proposed introducing the effect of sand layer depth and pile diameter on initial stiffness. The results indicate that the effect of pile diameter on p-y model for clay is apparent, and the influence coefficient of pile diameter on the critical parameter yc is recommended as 0.2–0.5. For the silty sand close to seabed, the formula of initial foundation stiffness of silty sand recommended by Sorensen appears to be more reasonable, and the initial foundation stiffness of silty sand at depth is suggested to calculate with formula suggested by Kallehave et al.

Dynamic p-y analysis method based on cone penetration test results for monopiles in sand

In this study, a CPT-based dynamic p-y analysis method was proposed for the seismic design of piles in sand. The proposed method is aimed at establishing an effective seismic design method for monopiles by directly incorporating in-situ test results into the design process. For this purpose, the continuous and in-situ soil profiling capability of CPT is utilized, which can further enhance the seismic design of monopiles by minimizing uncertainties involved in soil characterization process based on sampling and lab testing procedure. The proposed method was established based on the pseudo-static analysis with the dynamic p-y curve and equivalent static load. The CPT-based p-y curve was formulated as a function of the cone resistance considering damping effect. The load responses of dynamic load test were compared with results obtained from the proposed method and the finite element analysis. It was shown that the proposed CPT-based dynamic p-y method was effective for the seismic design of monopiles.

Numerical investigation of the effect of particle gradation on the lateral response of pile in coral sand

This paper addresses the effect of particle gradation on the lateral response of pile in coral sand foundation through numerical method. Firstly, the parameters of Hypoplastic (HP) constitutive model were calibrated by a series of laboratory tests and show obvious difference in value between fine and coarse coral sand. Subsequently, a 50 g centrifuge test and 1g model pile test were carried out to verify the numerical model and calibrated parameters. Afterward, numerical analyses were systematically conducted to investigate the influence of particle gradation, buried depth, and relative density on the lateral response of pile. The lateral load–displacement response, deflection and bending moment of pile, and soil resistance were analyzed and discussed in detail. Numerical results show that the bearing capacity of pile and soil resistance in coarse sand are greater than those in fine coral sand when the relative density is 25 % or 50 %. However, when the relative density is 75 %, the bearing capacity of pile and soil resistance in fine sand present significantly greater values than those in coarse sand under higher lateral displacement level. Moreover, the difference in lateral response of pile between coarse and fine coral sand is more significant in looser sand or shorter pile.

Experimental measurement of particle crushing around model piles jacked in a calibration chamber

During installation of driven or jacked piles in sand, particle crushing occurs in a region below the base of these piles. Quantification of the degree and extent of particle crushing during driving or jacking in sand is necessary to improve current design methods. To study the effects of particle crushing on the capacity of piles jacked in uniform silica sand samples, a model pile was jacked and tested in a half-cylindrical calibration chamber with transparent observation windows in its front wall. Annular samples of crushed sand 3 mm in thickness were recovered after testing from several locations along the shaft and the base of the model piles and used to assess particle gradation changes and to calculate breakage parameters. Relationships between the load mobilized at the base of the model piles and three breakage parameters are proposed. Furthermore, the number of jacking strokes (ranging from 1 to 32 in this research) has a negligible effect on the degree of crushing produced during installation and on the measured stresses at the base of the model pile. Analyses of the digital images captured during pile jacking indicate that the silica sand particles in the path of the model pile crush mainly along irregularities and sharp edges. Different zones are identified below the model pile according to the degree of particle crushing. Digital images taken during static loading of the model pile allowed tracking of the displacement paths of individual sand particles during loading.

Comparison of axial performance of bored and continuous flight augered large-scale model piles in sand

Comparison of axial performance of bored and continuous flight augered large-scale model piles in sand

Under-reamed pile-soil interaction in sand under lateral loading: A three-dimensional numerical study

The studies on the lateral response of under-reamed piles in sand are very limited. Therefore, a 3D numerical model is developed to study the behavior of under-reamed piles in sand under lateral loading. The present numerical model is validated with the results of numerical analyses, small scale model test, centrifuge test, field test, and existing closed-form solution. In the present study, the effects of embedment length of pile, bulb position, number of bulbs, bulb spacing, and soil friction angle are studied. At higher bulb positions, under-reamed piles give a stiffer load-deflection response, thereby producing higher load-carrying capacity and lesser deflection than pile without bulb. The deflection of the under-reamed pile further reduces with more bulbs and lesser spacing. For higher bulb positions, maximum negative (opposing) shear force and the bending moment in the shaft of under-reamed pile are lesser than the pile without bulb. The failure mechanism of soil around under-reamed pile is also studied. From the present study, it is concluded that the provision of a bulb improves both pile capacity and structural response. The results of the present study are presented in non-dimensional form; hence, these will be helpful for the design purpose.

Forecasting Solar Flares by Data Assimilation in Sandpile Models

The prediction of solar flares is still a significant challenge in space weather research, with no techniques currently capable of producing reliable forecasts performing significantly above climatology. In this paper, we present a flare forecasting technique using data assimilation coupled with computationally inexpensive cellular automata called sandpile models. Our data assimilation algorithm uses the simulated annealing method to find an optimal initial condition that reproduces well an energy-release time series. We present and empirically analyze the predictive capabilities of three sandpile models, namely the Lu and Hamilton model (LH) and two deterministically-driven models (D). Despite their stochastic elements, we show that deterministically-driven models display temporal correlations between simulated events, a needed condition for data assimilation. We present our new data assimilation algorithm and demonstrate its success in assimilating synthetic observations produced by the avalanche models themselves. We then apply our method to GOES X-Ray time series for 11 active regions having generated multiple X-class flares in the course of their lifetime. We demonstrate that for such large flares, our data assimilation scheme substantially increases the success of ``All-Clear'' forecasts, as compared to model climatology.

Utilization of enlarged base to improve the uplift capacity of single pile in sand—model study

Utilization of enlarged base to improve the uplift capacity of single pile in sand—model study

Experimental and Numerical Study on Pressure Distribution under Screw and Straight Pile in Dense Sand

Experimental and Numerical Study on Pressure Distribution under Screw and Straight Pile in Dense Sand

Estimation of the Uplift Resistance for an Under-Reamed Pile in Dry Sand Using Machine Learning

Abstract Under-reamed piles are extensively used to resist uplift forces and settlements. The objective of the present study is to develop various machine learning models (linear and non-linear) and determine the best model to estimate the ultimate uplift resistance of under-reamed piles embedded in cohesionless soil. The machine learning models were developed considering the following input parameters: the density index, dry density, base diameter, angle of an enlarged base with a vertical axis, shaft diameter, and embedment ratio. A linear equation is proposed to estimate the ultimate uplift resistance based on Multivariate Linear Regression analysis with a mean absolute error equaling 0.25kN and 0.50kN for loose and dense sands respectively. The Decision Tree Regression model provides an excellent degree of accuracy with a mean absolute error of 0.02kN and 0.02kN in cases of loose and dense sands respectively.

A test method to study scour effects on the lateral response of rigid piles in sand under real scour conditions

Rigid piles are common foundations for offshore wind turbines. Scour around piles leads to the loss of surrounding soil, which seriously threatens the safe operation of offshore wind turbines. However, most of the existing experimental studies on the scour effects on marine foundations are carried out in the test box without a hydraulic environment, resulting in deviations between the test results and the actual ocean engineering. Therefore, a test method to study scour effects on the lateral response of rigid piles is proposed. The key to this test method lies in the design of four types of parameters: pile, soil, hydraulic (wave and current), and load. Considering the characteristics of scour tests and scour effects tests, the design method of the four types of parameters is proposed. Combined with an example, the test method is described in detail. Subsequently, the defects of this test method are discussed. The research shows that this test method is a good attempt to study the loss of lateral ultimate capacity and the increase of cyclic cumulative deformation of rigid piles under real scour conditions.

Group Efficiency of Tension Double Under-Reamed Piles in Sand

Group Efficiency of Tension Double Under-Reamed Piles in Sand

Experimental and Numerical Investigation of Lateral Loaded Flexible Hybrid Piles in Sand

Experimental and Numerical Investigation of Lateral Loaded Flexible Hybrid Piles in Sand

Universal predictability of large avalanches in the Manna sandpile model.

Substantiated explanations of the unpredictability regarding sandpile models of self-organized criticality (SOC) gave way to efficient forecasts of extremes in a few models. The appearance of extremes requires a preparation phase that ends with general overloading of the system and spatial clustering of the local stress. Here, we relate the predictability of large events to the system volume in the Manna and Bak-Tang-Wiesenfeld sandpiles, which are basic models of SOC. We establish that in the Manna model, the events located to the right of the power-law segment of the size-frequency relationship are predictable and the prediction efficiency is described by the universal linear dependence on the event size scaled by a power-law function of the lattice volume. Our scaling-based approach to predictability contributes to the theory of SOC and may elucidate the forecast of extremes in the dynamics of such systems with SOC as neuronal networks and earthquakes.

Behavior of a vertical pile in loose sand under the effect of an inclined load

The paper investigates the behavior of single vertical steel pipe pile embedded in sand subjected to compressive inclined load through MIDAS GTS/NX 2019 FEM package. The effect of the loading inclination angle and pile length and diameter on the performance of the pile were investigated. Inclined load carrying capacity and pile stiffness were presented. The pile head displacement and pile stiffness are significantly affected by load inclination angle. It was observed that, p-y curves of the pile-soil system are independent of loading inclination angle. In addition, the pile length and diameter are markedly affecting the behavior of the pile.

Finite-size scaling of critical avalanches.

We examine probability distribution for avalanche sizes observed in self-organized critical systems. While a power-law distribution with a cutoff because of finite system size is typical behavior, a systematic investigation reveals that it may also decrease with increasing the system size at a fixed avalanche size. We implement the scaling method and identify scaling functions. The data collapse ensures a correct estimation of the critical exponents and distinguishes two exponents related to avalanche size and system size. Our simple analysis provides striking implications. While the exact value for avalanches size exponent remains elusive for the prototype sandpile on a square lattice, we suggest the exponent should be 1. The simulation results represent that the distribution shows a logarithmic system size dependence, consistent with the normalization condition. We also argue that for the train or Oslo sandpile model with bulk drive, the avalanche size exponent is slightly less than 1, which differs significantly from the previous estimate of 1.11.

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.