Rankine Earth Pressure Research Articles

Numerical Simulation of Double-row Piles in Deep Foundation Pit Excavation

This paper aims to investigate the stress and deformation characteristics of double-row piles in deep foundation pit excavation by selecting representative strata in the Changchun area. The changes in bending moment, displacement, and earth pressure of double-row piles during the excavation are established using the FALC 3D software. The findings indicate that the deformation of the front pile is larger than that of the back pile, and the earth pressure distribution of the fornt pile deviates from the conventional Rankine earth pressure theory. Moreover, there are noticeable variations in earth pressure at the soil layer interface of the rear pile.

A simplified calculation method for high-steep soil slope stability due to groundwater rise from irrigation

The groundwater is the critical factor impacting the stability of high-steep soil slopes (HsSS) on the loess tableland. In view of the shortcomings of the current commonly used calculation methods for HsSS, based on the Rankine earth pressure, the equilibrium conditions, and the strength failure criterion, a simplified calculation method for HsSS stability is proposed considering the typical characteristic that the failure surface of the high-steep slope is a double-segment line, and the critical groundwater level of the slope of the tableland edge was determined based on the HsSS stability model. The results are consistent with slope and modified the shortcomings of the existing model, such as the relatively concentrated and smaller of the stability coefficient. The critical groundwater level prediction model was applied to the Heifangtai tableland to verify the feasibility of the prediction model and point out the three high-risk points along the Heifangtai tableland.

Large Scale Model Test Study of Foundation Pit Supported by Pile Anchors

Due to the special time–space and environmental effects of the foundation pit, there are many unstable factors in the construction process of the field test. The indoor model test can avoid many uncertainties in the construction process due to its operability, which can reduce the interference with the test results and improve the accuracy of the test. In order to further discuss the force-bearing characteristics and deformation laws of loess pits’ support structure in Northwest China, a large model test of foundation pit supported by a pile anchor with a geometric similarity ratio of 1:10 was designed and completed. The force and deformation characteristics of the support structure were systematically studied by simulating the conditions of additional load at the pit edge, soil layered excavated, and anchors tensioned. The test results show that: for the pile-anchor support structure, the anchors have significant limiting effects on the displacement of the piles. Especially, when the position of the first row of anchors is closer to the pile top, the displacement of the pile is smaller. The stress state of the piles was changed by the prestressed anchor. The passive stress state of piles is changed from one side of tension and the other side of compression to the active stress state of “S” shape, which makes the distribution of the bending moment of piles more reasonable. The measured earth pressure in the process of soil unloading has a nonlinear distribution, which is different from the classical Rankine earth pressure distribution; specifically, the passive earth pressure in front of the pile is more obvious. In addition, the prestress applied to the anchors has a more significant effect on the internal forces of the other anchors. Compared with sequential tensioning, the prestress loss caused by interval hole tensioning is significantly reduced. The greater the number of spaced holes, the smaller the prestress loss and the better the anchoring effect of the anchor. The results of the study can provide reference for similar model tests, and also for related engineering applications.

Cantilever Soldier Pile Design: The Multiobjective Optimization of Cost and CO2 Emission via Pareto Front Analysis

In the context of this study, it is focused on the design of cantilever soldier piles under the concept of Pareto optimality with multiobjective analyses of cost and CO2 emission considering the change in the excavation depth, the shear strength parameters of the foundation soil strata, and the unit costs and unit emission amounts of structural materials. Considering this aim, the harmony search algorithm was used as a tool to achieve the integrated effects of the solution variants. The lateral response of the soil mass was determined based on the active Rankine earth pressure theory and the design process was shaped according to the beams on the elastic foundation soil assumption. Moreover, the specification envisaged by the American Concrete Institute (ACI 318-11) was used to control the structural requirements of the design. Pareto front graphs and also design charts were created to achieve the eco- and cost optimization, simultaneously, for the design with arbitrarily selected cases to compare the results of the multiobjective analysis to minimize both the cost and the CO2 emission.

DEM Analysis and Simplified Calculation of Passive Earth Pressure on Retaining Walls Backfilled with Sand Considering Strain-Softening Behavior

Common calculation methods of passive earth pressure, such as the Rankine or Coulomb earth pressure theory, assume that the width of the fill behind the wall is sufficient for the development of the slip surface and that after the passive earth pressure reaches the limit state, its value remains unchanged with the increase of displacement of the retaining wall. Nevertheless, cases with narrow backfill width should be considered when retaining walls must be built close to existing stabilization walls in urban areas or near rock faces in mountainous areas. Furthermore, for sand, especially dense sand, when the displacement of the retaining wall is large, a strain-softening behavior similar to the triaxial test will appear, resulting in a decrease in passive earth pressure. In this regard, a practical model for strain-softening of dense sand is proposed firstly and verified by the discrete element method (DEM) using the Particle Flow Code (PFC-2D) software. Then, based on the sliding surface shape obtained by DEM, a simplified method for determining the passive earth pressure distribution of retaining walls using limit equilibrium analysis was proposed. Finally, the passive earth pressures calculated by the proposed method agree well with those from PFC results, and the effects of the width of the backfill and displacement of retaining wall on the distribution of active earth pressure were discussed.

Estimating critical height of unsupported trenches in vadose zone

Workers are often required to enter unsupported trenches during the construction process, which may present serious risks. Trench failures can result in death or damage to adjacent properties; therefore, trenches should be excavated with extreme precaution. Critical height (i.e., maximum depth that can be excavated without failure) is the most important design consideration for ensuring the stability of unsupported trenches. Because excavation work is often done in the vadose zone, the influence of matric suction should be taken into account when estimating the critical height of an unsupported trench. In this study, an attempt was made to estimate the critical heights of unsupported trenches using three distinct approaches: (i) analytical method based on the extended Rankine earth pressure theory, (ii) finite element coupled stress – pore-water pressure analysis, and (iii) limit equilibrium method (i.e., Bishop’s simplified and Morgenstern–Price method). It was assumed that the trenches were excavated in an engineered sand (Unimin 7030) and Indian Head till, which represent cohesionless and cohesive soils, respectively, considering various practical scenarios. Geotechnical modeling software, GeoStudio (ver. 2016; SIGMA/W and SLOPE/W), was used for both finite element analysis and the limit equilibrium method.

Study on Model and Tests of Sheet Pile Wall with a Relieving Platform

A new type of retaining wall, the sheet pile wall with a relieving platform, is introduced in this paper. Based on the prototype retaining wall with a height of 12 meters, the model tests with a geometric similarity ratio of 7 are designed and we focus on the model production and analysis on the test results. Some comparative analyses between the measured values and the calculation values by using the theoretical calculation method and finite difference method are carried out, including Earth pressure behind the wall, prepile resistance force, the bending moment, and the deformation of rib pillars in the retaining wall. The results show that Earth pressure behind the wall has a linear increase with the depth and lies between Rankine Earth pressure and Earth pressure at rest. Moreover, the prepile resistance force can be approximated by the m method, and the bending moment can be also used for approximate calculation by the m method and is larger than the results calculated by the finite difference method. It is also observed that there is a zero‐displacement point on the pile bottom, and the Earth pressure above the point behind the pile develops from Earth pressure at rest to the active Earth pressure; the Earth pressure under the point behind the pile develops from Earth pressure at rest to the passive Earth pressure. Therefore, the Earth pressure behind the bottom wall is larger than the calculated value by the Rankine theory. Finally, the displacement of the rib pillars is greater than the calculated results using the finite difference method and exceeds the standard requirements, owing to the failure of the retaining wall, and the unloading board needs to be constructed to improve the retaining wall’s behaviour. These findings verify the model’s credibility and provide an underpinning for studying the behavior of the retaining wall.

Analyses on finite earth pressure and slope safety factors

This paper analyzes recent geotechnical engineering studies such as the finite earth pressures, slope safety factors and critical slip surfaces. However, current methods for calculating the finite earth pressure are not appropriate since they predict that the earth pressure decreases to zero as the soil mass width decreases, which violates the soil mechanics laws. The Rankine earth pressure theory can still be used to calculate the finite earth pressure. The slope safety factor is defined according to the strength reserve with no need to distinguish between the force and the sliding force. The shear strength definition shows that the soil shear strength should be used to calculate the safety factor for a given soil slope slip surface. However, a slope cannot necessarily be adjusted to develop its maximum anti-sliding ability. Furthermore, the critical slip surface corresponding to the minimum safety factor may not be the first surface to slide. Thus, this investigation helps discriminate the key concepts for understanding geotechnical mechanics. 摘要 结合岩土工程近年来的发展, 该文针对有限土体土压力、边坡安全系数及临界滑动面的计算方法中存在的问题进行分析探讨, 发现现有的计算有限土体土压力的方法存在缺陷, 由此计算的土压力会随着土体宽度的减小而趋近于0, 违背土力学常识。有限土体土压力应当采用Rankine土压力理论进行计算。采用基于强度储备定义的安全系数, 可以无须区分“抗滑力”和“滑动力”。对于给定滑动面, 取滑动面上土体的抗剪强度来计算安全系数是由抗剪强度的定义本身所决定的, 但土体并不一定能够调整到“最大抗滑能力”。最小安全系数对应的临界滑动面不一定是最先发生滑动的破坏面。该研究对理解相关概念、提高岩土力学的认知水平具有一定意义。

Earth pressure profiles in unsaturated soils under transient flow

Assessing the effect of heavy precipitations on earthen structures warrants studying earth pressure profiles in unsaturated soils under transient flow. This paper presents an analytical framework to determine the changes in at-rest, active, and passive earth pressures of unsaturated soils due to transient infiltration. A closed-from solution for one-dimensional transient unsaturated flow is incorporated into a suction stress-based representation of effective stress to obtain the tempo-spatial changes in matric suction, suction stress, and effective stress. The profiles are used to extend Hooke's law and Rankine's earth pressure theory, leading to the determination of unsaturated at-rest, active, and passive earth pressures at different depths and times. The analytical framework is used in a set of parametric study for three hypothetical soils of clay, silt, and fine sand. The results reveal the nonlinear characteristics of earth pressure profiles during transient infiltration for all three soils, whereas a linear trend is generally seen under steady-state flow conditions. Further, the depth of tension crack under transient flow is different than the one resulted from steady-state analysis. A transition from tension to compression stress is seen near the soil surface. This observation can be particularly important for fine-grained soils, implying that the depth of tension zone is affected by suction stress changes. Findings of this study can contribute toward a better understanding of service state behavior and forensic studies of earthen structures under heavy precipitations.

Passive Earth Pressures on Retaining Walls for Pit-in-Pit Excavations

The technique of pit-in-pit excavations is increasingly used in China to provide an efficient solution of maximizing the utilization of underground space while minimizing the amount of solid waste due to excavations. One of the critical steps toward the successful implementation of the pit-in-pit excavation technique is to rationally estimate the passive earth pressure, which is typically done using approaches such as numerical modeling, field monitoring, or traditional Coulomb or Rankine earth pressure theories. This paper presents a simplified approach for computing passive earth pressures for pit-in-pit excavations. A trapezoidal-shaped failure wedge is formed between two levels of retaining walls. A complete symmetric soil arch is used to describe the stress field of soils in the rectangular zone, whereas a half arch with one base acting on the wall and another base acting on the inclined shear surface is proposed for soils in the triangular zone. The soil arching effect is explicitly considered to derive the earth pressure for both cohesionless and cohesive soils at any intermediate passive state. A parametric study is conducted to demonstrate that the mobilized passive earth pressure increases nonlinearly with the magnitude of wall movement and soil shear strength parameters. The allowable spacing between two walls is also defined to produce a design chart. In the end, the proposed model is assessed against experimental measurements from model-scale tests.

Estimation of static earth pressures for a sloping cohesive backfill using extended Rankine theory with a composite log-spiral failure surface

The Rankine earth pressure theory is extended herein to an inclined c–ϕ backfill. An analytical approach is then proposed to compute the static passive and active lateral earth pressures for a sloping cohesive backfill retained by a vertical wall, with the presence of wall–soil interface adhesion. The proposed method is based on a limit equilibrium analysis coupled with the method of slices wherein the assumed profile of the backfill failure surface is a composite of log-spiral and linear segments. The geometry of the failure surface is determined using the stress states of the soil at the two boundaries of the mobilized soil mass. The resultant lateral earth thrust, the point of application, and the induced moment on the wall are computed considering global and local equilibrium of forces and moments. Results of the proposed approach are compared with those predicted by a number of analytical models currently adopted in the design practice for various combinations of soil’s frictional angles, wall–soil interface frictional angles, inclined angles of backfill and soil cohesions. The predicted results are also verified against those obtained from finite element analyses for several scenarios under the passive condition. It is found that the magnitude of earth thrust increases with the backfill inclination angle under both the passive and active conditions.

A Computational Method of Active Earth Pressure from Finite Soil Body

Nowadays, Coulomb and Rankine earth pressure theories have been widely applied to solve the earth pressure on a retaining structure. However, both of the theories established on the basis of the semi-infinite space assumption are not suitable for calculating the earth pressure from finite soil body. Therefore, this paper focuses on a theoretical study about the active earth pressure from finite soil body. Firstly, a common calculation model of finite soil body is established according to the results of previous studies. And then, based on Coulomb’s theory and the wedge element method, an analytical solution of the unit active earth pressure from finite soil body is deduced without an assumption of its linear distribution in advance. Meanwhile, formulas of the active earth pressure strength coefficient and the application point of the resultant force are also deduced. Finally, the influence of parameters such as the frictional angle between the retaining wall back and backfill, slope angle of backfill, dip angle of the retaining wall back, the frictional angle between backfill and rock slope, and uniformly applied load on the backfill surface on the distribution of the unit active earth pressure and the application point of the resultant force is analyzed in detail.

Rankine earth pressure theory considering microstructure of porous materials

Soil as an engineering material has very complex properties, such as non-continuous, non-uniformity and nonlinear mechanical. In a certain extent, macroscopic properties of soil are affected by the changes of the microstructure. And microscopic porosity of soft clay and its influencing factors, the relationship between macro and micro porosity, the average contact area rate and its influencing factors are studied. Some mechanics problems were analyzed by using the relationship between macro-porosity and the average contact area rate. Combining soil lateral stress transfer principle, a calculation theory of earth pressure considering soil contact area was got. The possible reason of the differences between earth pressure and the actual monitoring earth pressure was analyzed by the case.

하천제방의 월류 붕괴 메커니즘 규명을 위한 모형실험

본 연구에서는 월류에 의한 붕괴 메커니즘의 규명을 위해 모형제방(제방고 0.4~0.8m)과 실물제방(제방고 1.0m)을 대상으로 월류 붕괴실험을 수행하였다. 월류에 의한 제방붕괴는 1단계에서는 월류에 의해 비탈표면에서 세굴이 발생되었으며, 월류의 유속은 완만히 증가되었다. 2단계에서는 붕괴단면이 커지고 유속도 급격히 증가되었다. 3단계에서는 월류에 의해 제방 단면이 완전히 붕괴되고 붕괴면적이 넓어져 유속이 상대적으로 감소되었다. 월류에 의한 제방의 붕괴각(<TEX>${\theta}$</TEX>)은 큰 자중, 감소된 전단저항력 및 월류의 흐름에 의한 추가 소류력으로 인해 랭킨토압의 사면붕괴각보다 크게 나타났다. 제방고(H)가 증가될수록 월류에 의한 제방의 월류 유속(<TEX>${\upsilon}$</TEX>)이 증가되었으며, 이로 인해 소류력이 추가로 작용되어 제방의 붕괴각(<TEX>${\theta}$</TEX>)과 붕괴면적(A)이 함께 증가되었다. 모형실험과 실물실험에 사용된 모래 시료가 동일한 입경크기로 한계세굴유속이 같아 월류 유속변화에 의해 세굴 특성이 지배되는 것으로 나타났다. This research conducted the two types of model tests to examine the failure parameters by levee overflow, those were the pilot-scale levee (model height 0.4~0.8 m) and real scale levee (model height 1.0 m). The procedure of levee failure by overflow was succeeded to the following three steps: At first step, the local scouring on levee slope was happened and the overflow velocity was increased slowly. At second step, the enlarged scouring surface and the rapid overflow velocity were succeeded. At last, the levee section was broken totally and the overflow velocity was decreased because of the wide failure surface of levee. The levee failure angle (<TEX>${\theta}$</TEX>) was appeared bigger than slope failure angle of Rankine earth pressure. The enlarged levee height (H) made the faster overflow velocity (<TEX>${\upsilon}$</TEX>) of the levees, therefore additional tractive force was applied to it, futhermore the failure angle (<TEX>${\theta}$</TEX>) and failure surface (A) were enlarged. Because the sand sample for pilot-scale and real scale tests had the same diameter, the critical scouring velocity of each type was also the same, and the scouring properties were governed by variation of overflow velocity.

Bearing capacity of strip foundations in horizontal-vertical reinforced soils

The formula for calculating the ultimate bearing capacity of horizontal-vertical reinforced soil is investigated based on the failure mode and the mechanism of sand beds reinforced with horizontal-vertical reinforcement. Two components of soils and reinforcement are calculated separately. The ultimate bearing capacity of a shallow, concentrically loaded strip footing on homogeneous soil is commonly determined using the Terzaghi superposition method. The contribution of horizontal-vertical reinforcement is calculated based on the bearing resistance of the soil against the transverse members. A vertical inclusion is treated as a retaining wall, the confinement being calculated using Rankine's earth pressure theory. An analytical solution is presented including the traditional factors of soil, unit soil weight, footing width, number of horizontal-vertical reinforcement layers, and reinforcement geometry. The results were validated against experimental results and the mean error of the theoretical model was about 10%, with a maximum error of about 20%.

Coefficient charts for active earth pressures under combined loadings

Rankine's theory of earth pressure cannot be directly employed to c-<TEX>${\phi}$</TEX> soils backfill with a sloping ground subjected to complex loadings. In this paper, an analytical solution for active earth pressures on retaining structures of cohesive backfill with an inclined surface subjected to surcharge, pore water pressure and seismic loadings, are derived on the basis of the lower-bound theorem of limit analysis combined with Rankine's earth pressure theory and the Mohr-Coulomb yield criterion. The generalized active earth pressure coefficients (dimensionless total active thrusts) are presented for use in comprehensive design charts which eliminate the need for tedious and cumbersome graphical diagram process. Charts are developed for rigid earth retaining structures under complex environmental loadings such as the surcharge, pore water pressure and seismic inertia force. An example is presented to illustrate the practical application for the proposed coefficient charts.

The performance of buildings adjacent to excavation supported by inclined struts

Limitations in the design method used for the support systems of urban buildings make them vulnerable to damage by adjacent excavations. This paper examines a traditional system used to support excavation sites and adjacent buildings in which inclined struts are connected to the wall or foundation of the adjacent building. This method can be considered to be a type of shoring or underpinning. The performance of buildings and the criteria for deformation control during excavation are introduced. Next, a 2D finite element analysis is presented in which an excavation is modeled considering the parameters from the adjacent building and the inclined struts. The numerical model is capable of simulating the overall excavation and installation of the support system. The soil is modeled using an elastic perfectly-plastic constitutive relation based on the Mohr-Coulomb criterion. The finite element model is validated using Rankine earth pressure and in situ data was measured during an excavation. The effect of different variables on performance and acceptable limits for the inclined strut are discussed. The model used for the parametric study shows the influence of the characteristics of the adjacent building, soil parameters, geometry of excavation, type of excavation and effect of strut installation. It was found that one type of strut arrangement produced the best possible result. The results can be used as a primary approximation of small-to-medium depth excavations in which struts are used to reduce the deflections.

Verification of Rankine Earth Pressure Theory Using Finite Element Analysis with Elastic-Plastic Material

To simulate the Rankine earth pressure theory in the finite element analysis, a frictionless rigid wall and backfill system supported by rollers can be used. Beginning from the initial at-rest pressure conditions, the wall is moved towards or away from the backfill in a series of increments, until the passive or active earth pressure condition is reached. To obtain numerical solutions, twenty-five finite isoparametric elements are used to simulate the backfill and six linear bar elements to represent the rigid retaining wall. In order to simulate the incremental displacements, bar elements with a very high stiffness are used. The effect of wall displacement can be accomplished by applying a load equal to the value of the bar stiffness times the displacement to the nodal points that connect bars and soil elements. The elastic-plastic Drucker-Prager soil model is used in this study. Two earth pressure study cases have been analyzed. The first case deals with a cohesionless soil, while the second one a cohesive soil. The obtained load-displacement curves and stress-displacement curves are presented. It is found that the earth pressures behind the retaining wall at different heights based on the numerical solutions are identical with the calculations obtained from the Rankine earth pressure theory.

Effect of seismic acceleration directions on dynamic earth pressures in retaining structures

In the conventional design of retaining structures in a seismic zone, seismic inertia forces are commonly assumed to act upwards and towards the wall facing to cause a maximum active thrust or act upwards and towards the backfill to cause a minimum passive resistance. However, under certain circumstances this design approach might underestimate the dynamic active thrust or overestimate the dynamic passive resistance acting on a rigid retaining structure. In this study, a new analytical method for dynamic active and passive forces in c-<TEX>${\phi}$</TEX> soils with an infinite slope was proposed based on the Rankine earth pressure theory and the Mohr-Coulomb yield criterion, to investigate the influence of seismic inertia force directions on the total active and passive forces. Four combinations of seismic acceleration with both vertical (upwards or downwards) and horizontal (towards the wall or backfill) directions, were considered. A series of dimensionless dynamic active and passive force charts were developed to evaluate the key influence factors, such as backfill inclination <TEX>${\beta}$</TEX>, dimensionless cohesion <TEX>$c/{\gamma}H$</TEX>, friction angle <TEX>${\phi}$</TEX>, horizontal and vertical seismic coefficients, <TEX>$k _h$</TEX> and <TEX>$k_v$</TEX>. A comparative study shows that a combination of downward and towards-the-wall seismic inertia forces causes a maximum active thrust while a combination of upward and towards-the-wall seismic inertia forces causes a minimum passive resistance. This finding is recommended for use in the design of retaining structures in a seismic zone.

Weak Form Quadrature Element Analysis of Diaphragm Walls

In combination with Rankine's earth pressure theory, a weak form quadrature element formulation is established for analysis of diaphragm walls. Results are compared with those of Paroi2, a finite element software package for diaphragm walls, to demonstrate the effectiveness and the advantages of the present formulation. Accurate results are obtained with only a few weak form quadrature beam elements, contrasting with dense finite element division that is needed for complex load distributions over the diaphragm wall.