• Geomechanics and Engineering
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• v.8 no.3
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• pp.461-476
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• 2015

Rankine's theory of earth pressure cannot be directly employed to c-${\phi}$ 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.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.543-559
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• 2002

In this paper we formulate the linear theory for compressible fluids in cylindrical geometry with small perturbation at the material interface. We derive the first order equations in the smooth regions, boundary conditions at the shock fronts and the contact interface by linearizing the Euler equations and Rankine-Hugoniot conditions. The small amplitude solution formulated in this paper will be important for calibration of results from full numerical simulation of compressible fluids in cylindrical geometry.

• Journal of the Korean Geotechnical Society
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• v.34 no.10
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• pp.17-28
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• 2018

Important parameters for the stability checks of cantilever wall are the active earth pressure and the weight of soil above the heel of the base slab. If the heel length is so long enough that the shear zone bounded by the failure plane is not obstructed by the stem of the wall, the Rankine active condition is assumed to exist along the vertical plane which is located at the edge of the heel of the base slab. Then the Rankine active earth pressure equations may be theoretically used to calculate the lateral pressure on the vertical plane. However, in case of the cantilever wall with a short heel, the application of Rankine theory is not only theoretically incorrect but also makes the lateral earth pressure larger than the actual pressure and results in uneconomical design. In this study, for the cantilever wall with a short heel the limit analysis method is used to investigate the mechanism of development of the active earth pressure and then the magnitude and location of the resultants of the pressure and the weight of the soil above the heel are determined. The calculated results are compared with the existing methods for the stability check. In case of the cantilever wall with a short heel, the results by the Mohr circle method and Teng's method show max. 3.7% and 32% larger than those of the limit analysis method respectively.

• Geotechnical Engineering
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• v.4 no.1
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• pp.7-16
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• 1988

The safety factor has been used widely and uniquely at present to check the safety of the structure . However, probability of failure would be logically attempted to check the reliability of the structure in future Coulomb's theory or Rankine's theory has been applied in practice to retaining earth structure in spite of the fact that the lateral earth pressure, which is the primary factor in the determination of wall structure, depends on the modes of wall movement . This study is concentrated on the two modes of , wall movement (active case rotation about bottom(AB) , active case rotation about top(AT)) of the overturning'failure of vertical wall with horizontal sand backfill . The static active earth pressure is determined by applying each of Coulomb's theory, Dubrova's redistribution theory and Chang's method The earthquake active earth pressure is determined by adding Seed and Whitman's earthquake pressure to the static earth pressure , On the condition that design variables are fixed with each of the above earth pressure, reliability is analyzed using the recently developed method of AFOSM (Advanced First Order Second Moment)

• Geotechnical Engineering
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• v.13 no.4
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• pp.135-148
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• 1997

Coulomb's theory has been usually used in practice to obtain lateral earth pressure against retaining wall. Such theory is based in the assumption that the lateral pressure is a tai angular distribution, since the point of applying the lateral thrust cannot be obtained by using it. However, the results of laboratory and field tests showed that the lateral pressure was not a triangular but a nonlinear distribution. To overcome the drawback of the Coulomb's theory, the different theoretical approaches(Handy, 1985. Kingsley, 1989 : Kellogg, 1993, Chung et at,1993, 1996a) were performed for gravity wall backfilled by cohesionless soil. On the other hand, for retaining wall backfilled by ,cohesive soil, theoretical analyses were carried out only on the basis of the Rankine's or Coulomb's concepts, but the equations showed different results. Here was newly derived the equations of lateral pressures under undrained condition against gravity wall backfilled by cohesive soil. They were based on the Coulomb's wedge, adopted the arching concept. Some of the equations were derived by neglecting tension crack, while the others by considering it. Comparative results for applying different examples showed that the equation considering tension crack might be reasonable.

• Journal of the Korean Geotechnical Society
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• v.22 no.2
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• pp.29-39
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• 2006

In the companion paper (Paik 2006), a new formulation for calculating the nonlinearly distributed active earth pressure acting on a caisson backfilled with crushed rock and sand is proposed, and it takes into account arching effects as well as difference in internal friction angles and unit weights between sand and crushed rock. In this study, in order to partially check the accuracy of the proposed equation, the results of the proposed equation are compared with the equation proposed by Paik (2003a) for caissons with rough surface and homogeneous backfill, and are compared with results of Rankine's theory for caissons with smooth surface and homogeneous backfill. In addition, a parametric study is performed to investigate the effect of $phi_{r}$, $phi_{s}$, $\delta_{r}$, $\gamma_{r}$, $\gamma_{s}$ and $\beta$ on the magnitude of active earth pressure acting on the caisson, and construction methods for minimizing active earth pressure on the caisson are also provided based on the results of a parametric study.

• Geomechanics and Engineering
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• v.20 no.6
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• pp.527-536
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• 2020

The paper represents an optimization algorithm for reinforced concrete retaining wall design. The proposed method, called Rao-3 optimization algorithm, is a recently developed algorithm. The total weight of the steel and concrete, which are used for constructing the retaining wall, were chosen as the objective function. Building Code Requirements for Structural Concrete (ACI 318-05) and Rankine's theory for lateral earth pressure were considered for structural and geotechnical design, respectively. Number of the design variables are 12. Eight of those express the geometrical dimensions of the wall and four of those express the steel reinforcement of the wall. The safety against overturning, sliding and bearing capacity failure were regarded as the geotechnical constraints. The safety against bending and shear failure, minimum and maximum areas of reinforcement, development lengths of steel reinforcement were regarded as structural constraints. The performance of proposed algorithm was evaluated with two design examples.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.2
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• pp.8-19
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• 1998

Nonlinear flow characteristics of a hydrofoil running under the free surface are investigated based on potential flow theory using singularity distribution techniques. Following Hess & Smith's method[12], sources and vortices are distributed on the surface of the foil and Rankine sources are distributed at a distance above the undisturbed free surface to solve the nonlinear free surface waves(so called Raised Panel Method). Using the linearized Neumann-Kelvin solution, the conversed solutions which rigidly satisfy the nonlinear free surface condition is obtained through an iterative technique. It is validated that the nonlinear solutions are compared with Duncan's experimental results(NACA 0012, $\alpha=5^{\circ}$), showing good correlations with each other. At a very shallow submergence and a very high speed the converged solutions are obtained. As the speed increases higher, it is shown that the difference between the nonlinear and linear solutions are trivial. Finally, the effects of the camber and thickness on the nonlinear flow characteristics of the foil are investigated.

• Journal of the Korean Society of Safety
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• v.12 no.3
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• pp.139-146
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• 1997

In this study, centrifugal model tests were performed to investigate the behavior of excavated earth retaining wall with the depth of excavation and different types of wall(aluminum, steel panel). Jumunjin standard sand was used for foundation soil. The raining method was adopted to form the required relative density of the model ground. The lateral earth pressure measured from tests were compared with estimated active earth pressure by Rankine's theory. The test results have shown that the earth pressure acting on the retaining wall and the rotation displacement of the wall are influenced by the depth of excavation and the type of wall. It was found from the test results that the deformation of the wall increases with the depth of excavation.

• Journal of the Korean Geotechnical Society
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• v.39 no.7
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• pp.5-15
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• 2023

The evaluation of passive earth pressure plays a crucial role in the design of earth-retaining structures such as retaining walls and temporary earth-retaining walls to withstand horizontal earth pressure. In the earth pressure theory, active and passive earth pressures represent the earth pressures at the limit state, where the wall displacement reaches the maximum allowed displacement. In the design of earth-retaining structures, the passive earth pressure is considered as the resisting force. In this context, the limit displacement at which passive earth pressure occurs is significantly greater than that associated with the active earth pressure. Therefore, it is irrational to apply this displacement directly to the calculation of passive earth pressure. Instead, it is necessary to consider the mobilized passive earth pressure exerted at the allowable horizontal displacement to evaluate the structural stability. This study proposes an allowable wall displacement, denoted as 0.002 H (where H represents the excavation depth), based on a literature review that focuses on sandy soils. To calculate the mobilized passive earth pressure from the wall displacement, a semi-empirical equation is proposed. By analyzing the obtained data on mobilized passive earth pressure, a reduction factor applicable to Rankine's passive earth pressure is proposed for practical application in sandy soils under different wall movement types.