Rankine Earth Pressure Theory 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.

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.

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.

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.

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.

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.

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.

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.

Influence Analysis of Ground Asymmetric Load to the Surrounding Rock Pressure of Existing Open Trench Tunnel

Based on the Protojiakonov's theory and Rankine's earth pressure theory, the existing open trench tunnel under ground asymmetric load, the failure mode of the surrounding rock and the calculation of the surrounding rock pressure will be analysed in this paper. According to the buried depth, the analysis shows that the surrounding rock pressure calculation can be divided into three situations: when the tunnel is deep buried, the Protojiakonov's theory is used to calculate the surrounding rock pressure; when the tunnel is shallow buried and the side wall generate soil arching effect, the surrounding rock pressure calculation of the side wall will consider the soil arching effect and use the Protojiakonov's theory. However, another side wall will use the Rankine's earth pressure theory; when the tunnel is shallow buried and the side wall can't generate soil arching effect, regarding the two side walls as retaining walls according to the Rankine's earth pressure theory.

Analytical Solution for Rankine’s Seismic Active Earth Pressure in c-ϕ Soil with Infinite Slope

AbstractThis paper presents an analytical solution to determine seismic active earth pressure on a rigid frictionless retaining wall of c-ϕ soil backfill with an infinite slope, considering horizontal and vertical seismic coefficients. This solution is a generalized explicit expression and was derived based on the Rankine earth pressure theory and the Mohr-Coulomb yield criterion. To verify the derived solution, a special case was analyzed, and its result is identical to that obtained by earlier researchers. By analyzing the distribution of the seismic active earth pressures along the wall depth, a tension crack zone behind the wall was identified, and the seismic active earth pressure coefficient considering the tension crack was obtained. This study also investigated the effects of wall friction, soil friction angle and dimensionless cohesion, backfill slope, and horizontal and vertical seismic coefficients on the seismic active earth pressure coefficients. Design charts for seismic active earth pressur...

Analysis Again for Earth Pressure Calculation Theory Considering Displacement Effects

According to Moore-Coulomb strength theory, combined with the shear strength reduction method, assumed that the exerted value of the soil’s internal friction Angle and displacement were in nonlinear, and the exerted value of the soil’s cohesion and displacement were in linear, and then put forward a unified, continuous with displacement earth pressure calculation model, and this model could be used to calculate the active and passive earth pressure for cohesive soils and cohesionless soils in any nonlimited state and any movement mode. Through the analysis of the calculation model showed that: (1) The above assumptions were all reasonable from the two perspectives of the theoretical and the measuring; (2) The variation process of earth pressure acted on the retaining wall with displacement, could regard as the process of the soil’s shear strength parameters exerting gradually; (3) Given the physical meanings to the calculated parameters; (4) Analyzed the characteristics of the calculation model, and pointed out that there were calculation errors when the displacement of retaining wall was in (0, x0H) for the Rankine earth pressure theory.

Behaviour of geogrid reinforced soil retaining wall with concrete-rigid facing

Monitoring was carried out during construction of a cast-in-situ concrete-rigid facing geogrid reinforced soil retaining wall in the Gan (Zhou)-Long (Yan) railway main line of China. The monitoring included the vertical foundation pressure and lateral earth pressure of the reinforced soil wall facing, the tensile strain in the reinforcement and the horizontal deformation of the facing. The vertical foundation pressure of reinforced soil retaining wall is non-linear along the reinforcement length, and the maximum value is at the middle of the reinforcement length, moreover the value reduces gradually at top and bottom. The measured lateral earth pressure within the reinforced soil wall is non-linear along the height and the value is less than the active lateral earth pressure. The distribution of tensile strain in the geogrid reinforcements within the upper portion of the wall is single-peak value, but the distribution of tensile strain in the reinforcements within the lower portion of the wall has double-peak values. The potential failure plane within the upper portion of the wall is similar to “ 0.3H method”, whereas the potential failure plane within portion of the lower wall is closer to the active Rankine earth pressure theory. The position of the maximum lateral displacement of the wall face during construction is within portion of the lower wall, moreover the position of the maximum lateral displacement of the wall face post-construction is within the portion of the top wall. These monitoring results of the behaviour of the wall can be used as a reference for future study and design of geogrid reinforced soil retaining wall systems.

Reliability of passive earth pressure

Passive earth pressure calculations in geotechnical analysis are usually performed with the aid of the Rankine or Coulomb theories of earth pressure based on uniform soil properties. These traditional earth pressure theories assume that the soil is uniform. The fact that soils are spatially variable leads to two potential problems in design: do sampled soil properties adequately reflect the effective properties of the entire soil mass and does spatial variability in soil properties lead to passive earth pressures that are significantly different from those predicted using traditional theories? This paper combines non-linear finite element analysis with random field simulation to investigate these two questions. The specific case investigated is a two-dimensional frictionless passive wall with a cohesionless drained soil mass. The wall is designed against sliding using Rankine's earth pressure theory. The unit weight is assumed to be constant throughout the soil mass and the design friction angle is obtained by sampling the simulated random soil field. For a single sample, the friction angle is used as an effective soil property in the Rankine model. For two samples, an average of the sampled friction angles is used. Failure is defined as occurring when the Rankine predicted passive resistance acting on the wall, modified by a factor of safety, is greater than that computed by the random finite element method. Using Monte Carlo simulation, the probability of failure of the traditional design approach is assessed as a function of the factor of safety using and the spatial variability of the soil.

Characterization of the angle of repose of binary granular materials

When a heap or pile of granular material accumulates at the toe of a failed slope, the pile rests at its angle of repose. The gradual build up of a heap of soil in the laboratory simulates the formation of the heap at the toe of a slope. In this study, the angle of repose developed by binary granular mixtures of coarse sand (1.16 mm in average diameter) and fine sand (0.10 mm in average diameter) was measured in the laboratory. The influence on the angle of repose by the roughness of the base on which the mixtures were placed was also investigated. When the mixtures were placed on a rough surface, the heap developed its angle of repose by two different modes of failure. When the mixtures were controlled by the coarse sand fraction, failure took place on a layer located at the free surface of the heap. When the fine sand fraction controlled the composition of the mixture, the heap developed its angle of repose after the material failed by lateral spreading. When the mixture was placed on a smooth surface, the heap developed its angle of repose by a single mode of failure, namely lateral spreading at the interface of the mixture and the smooth base. A theoretical analysis relating the angle of repose, the internal angle friction of the mixtures, and the interface basal friction angle is also presented.Key words: angle of repose, binary granular material, quartz sand, angle of internal friction, interface friction angle, Rankine earth pressure theory.

Reliability of traditional retaining wall design

Retaining wall design has long been carried out with the aid of either the Rankine or Coulomb theories of earth pressure. To obtain a closed-form solution, these traditional earth pressure theories assume that the soil is uniform. The fact that soils are actually spatially variable leads, however, to two potential problems in design: do sampled soil properties adequately reflect the effective properties of the entire retained soil mass, and does spatial variability of soil properties lead to active earth pressure effects that are significantly different from those predicted using traditional models? This paper combines non-linear finite element analysis with random field simulation to investigate these two questions and assess just how safe current design practice is. The specific case investigated is a two-dimensional frictionless wall retaining a cohesionless drained backfill. The wall is designed against sliding using Rankine's earth pressure theory. The design friction angle and unit weight values are obtained by sampling the simulated random soil field at one location, and these sampled soil properties are then used as the effective soil properties in the Rankine model. Failure is defined as occurring when the Rankine predicted force acting on the retaining wall, modified by an appropriate factor of safety, is less than that computed by the random finite element method employing the actual soil property (random) fields. Using Monte Carlo simulation, the probability of failure of the traditional design approach is assessed as a function of the factor of safety used and the spatial variability of the soil.

Reliability of traditional retaining wall design

Retaining wall design has long been carried out with the aid of either the Rankine or Coulomb theories of earth pressure. To obtain a closed-form solution, these traditional earth pressure theories assume that the soil is uniform. The fact that soils are actually spatially variable leads, however, to two potential problems in design: do sampled soil properties adequately reflect the effective properties of the entire retained soil mass, and does spatial variability of soil properties lead to active earth pressure effects that are significantly different from those predicted using traditional models? This paper combines non-linear finite element analysis with random field simulation to investigate these two questions and assess just how safe current design practice is. The specific case investigated is a two-dimensional frictionless wall retaining a cohesionless drained backfill. The wall is designed against sliding using Rankine's earth pressure theory. The design friction angle and unit weight values are obtained by sampling the simulated random soil field at one location, and these sampled soil properties are then used as the effective soil properties in the Rankine model. Failure is defined as occurring when the Rankine predicted force acting on the retaining wall, modified by an appropriate factor of safety, is less than that computed by the random finite element method employing the actual soil property (random) fields. Using Monte Carlo simulation, the probability of failure of the traditional design approach is assessed as a function of the factor of safety used and the spatial variability of the soil.