Sandpile Research Articles

Two-dimensional study of the inclusions of skirt sand and deep cement piles to improve the load‒displacement behavior of circular foundations on soft clay soil

The bearing capacity of clayey soils is low, and the induced settlements play an important role in estimating the stability of structures built on these weak soils. Therefore, these clayey soils need improved mechanical strength. In this study, a two-dimensional finite element model was used to improve the bearing capacity and settlement of soft clay soil by employing skirt sand piles, and the results were compared with reinforced cement piles. Skirt sand piles consisting of thick sand cores and closed tubes placed under a circular shallow foundation with a steel plate of suitable dimensions, as well as reinforced cement piles of different lengths and in nondrained situations were studied. These calculations were carried out using PLAXIS 2D software, and a series of finite element analyses were performed. The Mohr‒Coulomb and hardening soil models were used to model the fine-grained and granular soils, respectively. A linear elastic model was used to simulate the circular plate and skirt components. Previous experimental studies were used to validate the numerical model. The experimental test and the 2D axisymmetric model agree well. According to the assumptions, the efficiency of skirt sand piles is superior to that of deep cement piles. In addition, increasing the length of SSP skirt sand piles has a significantly greater effect on improving the bearing capacity than increasing the length of deep cement piles. As a consequence, the failure modes of piles with skirt sand were determined. It was found that the failure mode when skirt sand piles were tied into clayey soils occurred in the underlying sandy soil layer as a general shear failure.

Sandpile Solitons in Higher Dimensions

Let $$p\in {\mathbb {Z}}^n$$ be a primitive vector and $$\Psi :{\mathbb {Z}}^n\rightarrow {\mathbb {Z}}, z\rightarrow \min (p\cdot z, 0)$$ . The theory of husking allows us to prove that there exists a pointwise minimal function among all integer-valued superharmonic functions equal to $$\Psi $$ “at infinity”. We apply this result to sandpile models on $${\mathbb {Z}}^n$$ . We prove existence of so-called solitons in a sandpile model, discovered in 2-dim setting by S. Caracciolo, G. Paoletti, and A. Sportiello and studied by the author and M. Shkolnikov in previous papers. We prove that, similarly to 2-dim case, sandpile states, defined using our husking procedure, move changeless when we apply the sandpile wave operator (that is why we call them solitons). We prove an analogous result for each lattice polytope A without lattice points except its vertices. Namely, for each function $$\begin{aligned} \Psi :{\mathbb {Z}}^n\rightarrow {\mathbb {Z}}, z\rightarrow \min _{p\in A\cap {\mathbb {Z}}^n}(p\cdot z+c_p), c_p\in {\mathbb {Z}}\end{aligned}$$ there exists a pointwise minimal function among all integer-valued superharmonic functions coinciding with $$\Psi $$ “at infinity”. The Laplacian of the latter function corresponds to what we observe when solitons, corresponding to the edges of A, intersect (see Fig. 1).

Response analysis of single pile embedded in saturated sand under bidirectional cyclic loading

In this study, the dynamic responses of a single pile in liquefiable sand under bidirectional loading are investigated using fully coupled three-dimensional nonlinear finite element analyses. A multi-surface plasticity model is adopted to simulate the liquefiable sand behaviour. The analysis procedures elaborate the bidirectional shaking patterns of 2-D linear, circular, and oval shape simultaneously. Results reveal that compared to the unidirectional loading, the bidirectional loading reduces the soil liquefaction resistance and increases the depth of liquefied soil layer. The results also showed that the phase difference between orthogonal components of base excitation and the frequency content of the input motion have a significant impact on the dynamic responses of soil and pile. In addition, an increase in the phase difference reduces the excess pore water pressure and the thickness of liquefied layer, and delays the liquefaction occurrence. Moreover, the maximum pile bending moment and its location correspond to the dominance of either inertia or kinematic interaction forces, which are primarily influenced by the frequency content of input motion.

Convergence of a sandpile on a triangular lattice under rescaling

We present a survey of results on convergence in sandpile models. For a sandpile model on a triangular lattice we prove results similar to the ones known for a square lattice. Namely, consider the sandpile model on the integer points of the plane and put $n$ grains of sand at the origin. Let us begin the process of relaxation: if the number of grains of sand at some vertex $z$ is not less than its valency (in this case we say that the vertex $z$ is unstable), then we move a grain of sand from $z$ to each adjacent vertex, and then repeat this operation as long as there are unstable vertices. We prove that the support of the state $(n\delta_0)^\circ$ in which the process stabilizes grows at a rate of $\sqrt n$ and, after rescaling with coefficient $\sqrt n$, $(n\delta_0)^\circ$ has a limit in the weak-$^*$ topology. This result was established by Pegden and Smart for the square lattice (where every vertex is connected with four nearest neighbours); we extend it to a triangular lattice (where every vertex is connected with six neighbours). Bibliography: 39 titles.

Convergence of a sandpile model on a triangular lattice

Мы даем обзор результатов о сходимости в песочных моделях. Мы доказываем для песочной модели на треугольной решетке результаты, аналогичные уже существующим для квадратной решетки. А именно: рассмотрим песочную модель на целых точках плоскости, положим $n$ песчинок в начало координат. Запустим процесс релаксации: если в некоторой вершине $z$ число песчинок не меньше ее степени (в этом случае говорим, что вершина $z$ нестабильна), перемещаем из $z$ в каждого из соседей $z$ по одной песчинке; повторяем эту операцию, пока есть нестабильные вершины. Мы доказываем, что носитель состояния $(n\delta_0)^\circ$, на котором процесс стабилизируется, растет со скоростью $\sqrt n$, и после ремасштабирования в $\sqrt n$ раз у $(n\delta_0)^\circ$ есть предел в $^*$-слабой топологии. Такой результат уже был показан У. Пежденом и Ч. К. Смартом для квадратной решетки (каждую вершину соединяем с четырьмя ближайшими соседями), мы распространяем его на треугольную (каждая вершина соединяется с шестью соседями) решетку. Библиография: 39 названий.

Решение одномерной самоорганизованно-критической модели Осло

I study the Oslo model – a one-dimensional conservative strictly isotropic self-organized critical sandpile model. I obtain a complete analytical solution for it, and I also present confirming simulation results. The solution is based on a meso-level model. I consider the processes of this level as anomalous diffusion. To explain it, I consider various random walk mechanisms, one of which essentially takes into account the one-dimensional nature of the model.

Autonomous Dozer Sand Grading Under Localization Uncertainties

Surface grading, the process of leveling an uneven area containing pre-dumped sand piles, is an important task in the construction site pipeline. This labour-intensive process is often carried out by a dozer, a key machinery tool at any construction site. Current attempts to automate surface grading assume perfect localization. However, in real-world scenarios, this assumption fails, as agents are presented with imperfect perception, which leads to degraded performance. In this work, we address the problem of autonomous grading under uncertainties. First, we implement a simulation and a scaled real-world prototype environment to enable rapid policy exploration and evaluation in this setting. Second, we formalize the problem as a partially observable markov decision process and train an agent capable of handling such uncertainties. We show, through rigorous experiments, that an agent trained under perfect localization will suffer degraded performance when presented with localization uncertainties. However, an agent trained using our method will develop a more robust policy for addressing such errors and, consequently, exhibit a better grading performance.

Experimental Analysis of the Behaviour of Piled Raft Foundations in Loose Sand

This paper presents the experimental analysis that was conducted on small-scale 1g physical models of piled raft foundation structures with a group of 2 × 2 piles in loose sand. The purpose of the piles was to reduce the settlement of the raft. The test program included twelve experiments, three of which were conducted on a raft alone and nine on piled rafts at pile distances of 3d, 4d, and 5d and pile lengths of 10d, 20d, and 40d, where d is pile diameter. The test results show that the current conventional approach to design of piled raft foundations, at a high safety load factor in piles that assume to take the whole external applied load, is very conservative. Instead, it is more economical to apply a low bearing capacity factor for piles as settlement reducers and maximize use of raft bearing capacity to carry part of the external load.

Family Conflict in Edward Albee’s Selected Dramas

This research aimed to identify the kinds o family conflict that appear in Edward Albee’s dramas and to know the causes and impacts of the dramas using theory of family conflict by Ursula Lehr and descriptive qualitative method. In The Sand box drama the types of family conflict are conflict with own parents, conflict with own children, conflict with husband/wife, and self-conflict. Other causes were because mommy’s selfish characteristic and always wanted to be a dominant person, while grandma was experiencing her second childhood phase. The impacts of The Sandbox drama are the fight between the characters in the drama and the loss of harmonization in the family. In who’s Afraid of Virginia Woolf? Drama, there are conflicts with other people, conflict with husband/wife, and self-conflict. The main causes were Martha and George as a marriage couple that always wanted to drop down on and insulted each other. The impacts are the loss of harmonization in the family, another couple (Nick and Honey) got into their problem fought to each other.

Heat Recovery from a Wastewater Treatment Process—Case Study

This article presents the potential of heat recovery from wastewater with an example of a wastewater treatment plant (WWTP) in Mokrawica, which is located in the West Pomeranian region of Poland. A thorough literature review discusses the relevance of the topic and shows examples of heat recovery conducted with heat pumps. Raw and treated wastewater are mostly used as heat sources, with the latter achieving higher thermal capacities. Heat recovery from a biological treatment process is rarely implemented and requires more detailed studies on this subject. The proposed methodology for estimating possible heat recovered from wastewater, requiring heating and cooling capacities, as well as the coefficient of performance (COP) of a heat pump, is based on only three parameters: wastewater volumetric flow, wastewater temperature, and the required temperature for heating or air-conditioning. The heat recovery potential was determined for different parts of WWTP processes, i.e., the sand box, aeration chamber, secondary sedimentation tank, and treated sewage disposal. The average values of 309–451 kW and a minimum of 58–68 kW in winter were determined. The results also indicate that, depending on the location of the heat recovery, it is possible to obtain from wastewater between 57.9 kW and 93.8 kW of heat or transfer to wastewater from 185.9 to 228.2 kW. To improve biological treatment processes in the winter season, wastewater should be preheated with a minimum of 349–356 kW that can be recovered from the treated wastewater. The heat transferred to the wastewater from the air-conditioning system amounts to 138–141 kW. By comparing the required cooling and heating capacities with the available resources, it is possible to fully recover or transfer the heat for central heating, hot water, and air conditioning of the building. Partial preheating of wastewater during the treatment process requires further analysis.

Combinatorial aspects of sandpile models on wheel and fan graphs

We study combinatorial aspects of the sandpile model on wheel and fan graphs, seeking bijective characterisations of the model’s recurrent configurations on these families. For wheel graphs, we exhibit a bijection between these recurrent configurations and the set of subgraphs of the cycle graph which maps the level of the configuration to the number of edges of the subgraph. This bijection relies on two key ingredients. The first consists in considering a stochastic variant of the standard Abelian sandpile model (ASM), rather than the ASM itself. The second ingredient is a mapping from a given recurrent state to a canonical minimal recurrent state, exploiting similar ideas to previous studies of the ASM on complete bipartite graphs and Ferrers graphs. We also show that on the wheel graph with 2n vertices, the number of recurrent states with level n is given by the first differences of the central Delannoy numbers. Finally, using similar tools, we exhibit a bijection between the set of recurrent configurations of the ASM on fan graphs and the set of subgraphs of the path graph containing the right-most vertex of the path. We show that these sets are also equinumerous with certain lattice paths, which we name Kimberling paths after the author of the corresponding entry in the Online Encyclopedia of Integer Sequences.

Experimental and Semitheoretical Analyses of Uplift Capacity of Belled Pile in Sand

Although belled piles have been widely applied to structures subjected to large horizontal loads, such as coastal structures, high chimneys, and transmission towers, their uplift capacity characteristics under various conditions have not been investigated in detail. In this study, model tests were performed in circular and half-circular chambers to determine the uplift capacity of belled piles in sandy ground under conditions such as relative density, penetration depth, and pile-tip inclination angle. Furthermore, image analysis was conducted by monitoring the model tests in a half-circular chamber to verify the shape of the failure surface. A semitheoretical model to predict the uplift capacity of belled piles in sandy ground was developed using the pile-tip failure angle and failure surface curve in accordance with the relative density, penetration depth, and pile-tip inclination angle based on the limit-equilibrium equation of a previous conventional pile. The values calculated using the proposed model were in good agreement with those obtained from experimental model tests.

Application of superabsorbent geotextiles to decontaminate and improve crude oil-contaminated soil

The contamination of soil by various oil products is a severe geo-environmental problem. In this study, some geotextiles were used as superabsorbent geotextiles to decontaminate soil polluted with crude oil. The ability of these geotextiles to absorb oil is better than that of absorbing water. The removal efficiency of the absorbent geotextile was first evaluated by placing the spacer fabrics in different arrangements in contaminated soil samples. Second, the shear strengths of the decontaminated soil samples were evaluated through a series of direct shear tests and compared with those of contaminated soil. The effects of crude oil content, vertical stress, and geotextile arrangement were thoroughly investigated to understand the vivid behavior of the specimen matrix. The results showed that the geometric properties of geotextile and sand, such as the mean size of sand particles, aperture size, fluffs, and piles of geotextile, geotextile roughness, and the two phases occurring in the specimens – wettability and saturation of absorbent layer – are vital in determining the sand-geotextile interface and the behavior of shear strength parameters of the matrix. Ultimately, the results confirmed the efficiency of absorbent geotextile as a potential method for controlling soil contamination and improving the shear strength parameters.

Analysis of laterally loaded piles in sand considering the relationship between the strain wedge model and failure wedge model

This paper proposes an analytical method for laterally loaded piles in sand, in which the strain wedge model and failure wedge model are used together. To determine the process that develops from the strain wedge model to the failure wedge model, a 3D finite element analysis is carried out. Considering the continuity of the soil resistance, the relationship between the strain wedge model and failure wedge model is established. Two failure patterns in which the soil develops from the strain wedge model to the failure wedge model are discussed. The lateral response of the pile and soil is obtained by an iterative calculation. Two centrifuge tests are used to evaluate the accuracy of the new method, showing remarkable agreement.

Experimental study on the lateral cyclic response of the piles in sand

The established foundation type for most offshore wind turbines is monopile. Due to waves and wind, the monopile of such structures experiences cyclic loading that causes the rearrangement of the soil grains around the pile, altering the damping ratio and stiffness of the soil-pile system. In this study, the impact of changing the loading frequency and soil density on the horizontal displacement, stiffness, and damping ratio on piles under cyclic lateral load has been evaluated. A series of experimental tests have been carried out by applying one-way cyclic lateral loading with three frequencies on PVC piles with different length-to-diameter (L/B) ratios in loose and dense sand. The horizontal displacement, stiffness, and damping ratio values were obtained for each test. Also, the constant coefficients of equations proposed by other researchers (to determine deformation, stiffness, and damping ratios) were evaluated. The results are presented that the change of loading frequency has a considerable influence on the absolute values of displacement, stiffness, and damping ratio, however, it has a negligible effect on constant coefficients.

Large diameter laterally loaded piles in sand: Numerical evaluation of soil stress paths and relevance of laboratory soil element testing

This paper uses 3D numerical analyses to investigate the stress path experienced by soil elements around large diameter piles in sand subjected to monotonic drained lateral loading. Inspection of the loading-induced stresses in the soil revealed the multiaxial nature of these stress paths, which are characterised by rotation of one or more principal stress axes. Based on the outcome of the finite element analyses, typical stress paths for different soil elements around the piles are extracted. Such stress paths are then evaluated against those enabled by conventional and advanced laboratory soil element testing. It is found that a combination of tests in the Hollow Cylinder Torsional Apparatus (HCTA) can reproduce most features of the numerically identified stress paths for soil elements around the pile. Unavoidable limitations in laboratory testing are discussed as well as the major challenge in replicating the loading direction with respect to the material axes. Some guidance for the experimental implementation of these stress paths in the HCTA are provided as well as a discussion on the use of conventional experimental equipment, such as the conventional triaxial or simple shear apparatus.

Ultimate soil resistance of the laterally loaded pile in uniform sand

Piles have been widely used as foundations to resist lateral loads. For the design of a laterally loaded pile, one of the most important inputs is the ultimate soil resistance ( [Formula: see text] , where Kultis the ultimate lateral soil resistance coefficient, D is the pile diameter, and [Formula: see text] is the vertical effective stress). However, great discrepancy can be found in the existing design equations for piles in sand. To provide new insights and clarify the discrepancy in previous studies, in this study, a series of numerical simulations were performed on piles of different configurations using the finite element model validated by centrifuge pile tests. The computed results suggest that Kultis a function of depth ratios z/ D and z/ L for the flexible and rigid piles, respectively (where z is the absolute depth and L is the embedded pile length), and all existing design equations failed to reproduce the magnitude and distribution of Kult. Additionally, the Kultof horizontally translated fixed-head rigid piles exhibits the same pattern as that of free-head flexible piles, suggesting that the difference between free-head flexible piles and rigid piles is caused by the change of failure modes.

New approach for predicting the load-displacement curve of axially loaded piles in sand

A relationship to predict the load-displacement curve for axially loaded piles in sandy soil is presented by using the tri-linear softening model to describe the shaft load-displacement relationships, as well as a bi-linear model is adopted to characterize the unit end resistance-displacement reaction in the region of the pile's tip soil. Subsequently, an analytical mathematical approach to a single pile-surrounding soil interaction relation is provided as a nonlinear analysis to obtain the load-displacement curves. The mechanical response of piles under compression loading was analysed, and thus, an analytical method is developed to establish a solution for the entire compression process of the piles. A combination of the prementioned models with the pile response under compression loading was employed to establish a fully analytical approach. Furthermore, additional analytical approaches and field-tested pile loading history cases were utilized to prove the degree of exactness of the suggested method by comparing the experimental load-displacement curves with the ones founded by the proposed theoretical method in this work. The results of this study illustrate that the proposed method could be considered as an analytical mathematical technique for utilizing both the tri-linear softening model and the bi-linear elastic-plastic model for the purpose of predicting the load-displacement curves of the axially loaded pile with a 98% degree of accuracy compared to field load tests results.

Ground Improvement - Selected Tunisian Case Histories

This paper presents a detailed analysis of three Tunisian ground improvement case histories. The first case focuses on the cause of disorders that seriously affected the stability of an oil tank, initially built on a superficial soft clay layer improved by sand piles. Due to the underestimated length of sand piles, the oil tank operations stopped after non-admissible consolidation differential settlement. Retrofit solution using micropiles’ reinforcement revealed quite satisfactory to restart the functioning of the oil tank after fifteen years. The second case deals with the reinforcement of compressible silt sand layer by floating stone columns to reduce the long-term differential settlement of a gas storage facility. Recorded measurements during the follow-up of stage construction of the storage facility permitted the assessment of numerical predictions of the settlement of reinforced soil. The third case studies the stability of access ramps of an interchange in Tunis Centre. Built numerical plan strain modelling helped for the prediction of the behaviour of embankment access on improved Tunis soft soil by geodrains. Based on recorded settlements and horizontal displacements, followed the validation of computed consolidation settlement. Adoption of suitable parameters of hardening and soft soil modelling of the behaviour of Tunis soft clay is discussed.

The Effects and Vertical Bearing Capacity of Two Jacked Model Piles in Sand

The effects and vertical bearing capacity of two jacked piles in sand are still not well understood, and the mechanism of the adjacent pile’s uplift caused by the jacking pile in a double pile system is especially unclear, but these facets are important to the stability of the jacked pile. In this paper, a series of tests is performed on jacked model piles in sand, where in the influences of the pile length and the driving pile’s speed on the effects and vertical bearing capacity of two jacked piles were studied. The results revealed that the effects and vertical bearing capacity of the two jacked piles were mainly in relation to pile length and influenced by the driving speed. The horizontal displacement of the top of the first jacking pile during the installation of the post-jacking pile was caused by the difference in the stress state of the first jacking pile between the side of the pile’s face and its back side, in which the uplift displacement of the first jacking pile was also involved. The radial stress of the pile increased nonlinearly with the depth under different pile lengths and gradually converged to the passive earth pressure. The ultimate capacity of the double pile is approximately twice that of a single pile, and the ratio of the ultimate capacity of a single pile to the final jacking pressure was approximately 1.04.