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2004, 23 (19): 0-0 doi:

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UNIFIED ELASTOPLASTIC SOLUTION FOR SURROUNDING ROCKS OF OPENINGS WITH CONSIDERATION OF MATERIAL DILATANCY AND SOFTENING

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2004, 23 (19): 3213-3213 doi:

[PDF] 372 KB (1257)

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Based on the unified strength theory proposed by Yu Maohong and by considering the behaviors of strength reduction and volume dilatancy for some materials after yielding，that is plastic-softening，the analytical equations for calculating the radius of plastoesidual and plastic-softening zones as well as the displacements around openings are proposed according to the elastic-softening-residual plastic triple linear stress-strain model. At the same time，the equations of stress state for surrounding rocks are also given in the general form. The famous Kastner equation，the Airey equation and the other existing solutions may be taken as special cases of the proposed solution. In the mean time，the influences of shearing dilatancy，softening and different strength models on the results are also analyzed. The results of this paper have an important value in stability analysis of engineering practice and in reinforcement of surrounding rocks.

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COUPLED ELASTOPLASTIC-DAMAGE MODEL FOR
QUASI-BRITTLE SOLIDS

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2004, 23 (19): 3221-3221 doi:

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Based on the anisotropic damage model proposed by Dragon，et al for quasi-brittle solids under plane strain，a simple theory of friction induced plasticity is proposed by considering the effect of slide caused by friction in micro-cracks. The effect of friction on damage behavior of material is studied and the calculated results show that the stress decrement caused by friction can not be neglected in some loading paths.

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STUDY ON THE MODEL AND ITS MODIFYING METHOD FOR
ROCK SOFTENING AND DAMAGE BASED ON WEIBULL
RANDOM DISTRIBUTION

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2004, 23 (19): 3226-3226 doi:

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Based on the strength characteristics of rock micro-unit with Weibull distribution，a rock softening and damage constitutive model is established to reflect the full process of rock failure by using the stress-strain curve with parameter capable of rational description of micro-unit strength of rock. Moreover，the relationship between model parameters and confining pressure is discussed and the model parameters are modified in combination with the influence law of the model parameter on the model and the characteristics of rock stress-strain curve. Accordingly，the rock softening and damage model is proposed and shown to be rational with bright prospect of applications in engineering.

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SIMPLIFIED CONTINUUM DAMAGE MECHANICS MODEL FOR CONCRETE

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2004, 23 (19): 3232-3232 doi:

[PDF] 567 KB (1099)

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A simplified continuum damage mechanics model is proposed in this paper to describe the inelastic damage behavior of concrete. The constitutive damage behaviors of concrete usually involve anisotropic damage，unilateral effect，coupled volumetric and deviatoric inelastic deformation and other complicated failure mechanisms due to its heterogeneous morphology. In order to avoid analytical and numerical complexity，a scalar damage variable is introduced，while the anisotropy and unilateral effect of damage corresponding to different states of stress and stress histories are dipicted by introducing the Lode parameter m s . The responses of concrete subjected to complicated uniaxial and triaxial loading histories are analyzed，and the validity of the proposed model is demonstrated by the satisfactory agreement between the computed and experimental results.

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APPLICATION OF FSD COUPLING MODEL TO THE TEST OF
MULTIPLE HYDRAULIC FRACTURING

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2004, 23 (19): 3240-3240 doi:

[PDF] 338 KB (1068)

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By using the Rock Failure Process and Analysis code (RFPA)，which is based on the flow-stress-
damage (FSD) coupling model，the behavior of multiple hydraulic fractures in the homogeneous rocks is simulated and investigated. The simulation results reflect macroscopic failure evolution process induced by microscopic fracture subjected to hydraulic loading，which agrees well with the experimental results. Based on the simulation research，it is pointed out that the pore pressure magnitude on a local scale around crack tip and the distribution of pore pressure on a global scale may both affect the behaviors of cracks and fractured pressure. The fractures always propagate towards the regions with higher local pore pressure and the fracture pressure decreases with the increment of local pore pressure. The research provides valuable guidance to the designers of hydraulic fracturing engineering.

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DISCUSSION ON INTERACTION BETWEEN DIFFERENT INTRINSIC LENGTH SCALE PARAMETERS FOR MATERIAL STRAIN LOCALIZATION ANALYSIS

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2004, 23 (19): 3245-3245 doi:

[PDF] 308 KB (995)

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Both gradient-dependent and rate-dependent constitutive models introduce intrinsic length scales in dynamic strain localization analysis of engineering materials. The intrinsic length scales in the two different constitutive models are discussed，respectively. The ways to predict the intrinsic length scales the two constitutive models are different and the expressions of the intrinsic length scale are also different from each other. To give a prediction of the intrinsic length scales for the general case with the two models，both the length curves corresponding to the damping effect and wave length versus wave number are computed. The internal length scales derived respectively from the damping effect，which is typical for the visco-plastic model，and the wave length is obtained from the critical wave number with unimaginary velocity. An intrinsic length scale domain with upper and lower bound values is obtained which includes the actual length scale. The proposed method can explain the results obtained with the two models. The way proposed here for prediction of the intrinsic length scale is more general than those commonly used to explain the phenomena observed in both the viscoplastic and gradient dependent models. Moreover，it has also been found that the sensitivity of the internal length scale for the visco-plastic parameter is higher than that for the gradient dependent parameter. Numerical example is given and the results are confirmed with those of theoretical analysis.

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2004, 23 (19): 3252-3252 doi:

[PDF] 326 KB (882)

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STUDY ON RELATIONSHIP BETWEEN SPLITTING BEHAVIOUR AND ELASTIC MODULUS OF THREE GORGES GRANITE

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2004, 23 (19): 3258-3258 doi:

[PDF] 389 KB (1180)

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By Brazilian tension tests of complete procedure for Three Gorges granite conducted by a servo-controlled testing machine，it is found that there exists obvious linear relationship between load and displacement of load point before breakage. It is believed that the relationship demonstrates the elastic character of rock and therefore the elastic modulus of rock can be estimated from the complete load-displacement curve. The splitting modulus in Brazilian tension test has been defined. Based on large quantity of Brazilian tension tests and uniaxial compression tests，the ratio of elastic modulus to splitting modulus of the Three Gorges granite is estimated as 19.2. Finally，the proportional relationship between load and displacement of load point is numerically simulated by 3D FEM. It is pointed out that the relationship is also affected by the elastic modulus and geometry of rock specimen.

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INTERPRETATION AND APPLICATION OF CPTU RESULTS BASED ON BLOCKY SOIL SAMPLES WITH HIGH QUALITY

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2004, 23 (19): 3262-3262 doi:

[PDF] 379 KB (805)

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The blocky soil samples with 250 mm diameter have been proved to be of superior quality compared even with the soil samples of thin-wall piston with 75 mm diameter. Therefore triaxial and oedometer tests on the blocky soil samples can give the best reference parameters for correlation to CPTU measurements. A new generation of correlation factors among CPTU parameters，undrained shear strength，pre-consolidation stress and over-consolidation ratios are developed for soft clays. It is the authors’ opinion that for important projects a combination of CPTU tests and blocky soil samples will give reliable design parameters leading to significant cost savings.

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ANALYSIS ON THE BOLT DEFORMATION AS RESULT OF JOINT SHEAR DISPLACEMENT

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2004, 23 (19): 3268-3268 doi:

[PDF] 285 KB (1253)

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When the bond between bolt and grout is intact the shear stress distribution of the bolt side is described by exponent curve. When the bond is destroyed the shear stress distribution on the bolt side can be expressed by parabolic curve. The relationships between axial stress and axial displacement with or without bond failure are presented. Some parameters can be back-analyzed from experimental data of axial tensile stress of bolt. Some parameters can be estimated by empirical equations. The relationships between transverse displacement and shear stress of bolt are also given for the cases with or without compressive failure of rock. Based on the derived analytical equations the relationships between shear stress and shear displacement of bolted joint are also presented and some parameters with significant influence on stiffness of bolted joint are analyzed. All the relevant analysis shows that higher axial compressive strength of rock and greater ratio of bolt section to bolted joint area can lead to higher shear resistance of bolted joint. The analysis also shows that joint anchored by inclined bolt has greater shear stiffness than that anchored by bolt perpendicular to joint. The joint anchored by inclined bolt has higher shear resistance with less shear displacement than the joint anchored by perpendicular bolt. The shear resistance of bolted joint can be obviously improved by higher ratio of bolt section to bolted joint area and inclined bolt.

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RUPTURE STRESS OF SHAFT WALL IN MINE DUE TO GROUND SUBSIDENCE

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2004, 23 (19): 3274-3274 doi:

[PDF] 327 KB (996)

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This paper is aimed at finding out the important effect of temperature on shaft rupture accident. Based on the theories of the thermal expansion and thermal transmission in physics and thermoelastic theory and the solution of statically indeterminate system in solid mechanics，the formation cause of temperature stress in shaft wall is analyzed and the corresponding formulae are obtained. At the same time，the coincidence function between temperature and underground water level is investigated. The dangerous rupture section in shaft wall is found by the research of distribution laws of negative skin friction induced by the longitudinal thermal expansion. All stress components at the dangerous point of the dangerous rupture section，including gravity stress，ground pressure stress as well as temperature stress，are analyzed. The analytical result shows that the vertical and hoop temperature stresses are about 80% and 70% of the total stress，respectively，at the dangerous point. Therefore，the temperature stress is the most important factor causing the fracture of shaft. The obtained results can be applied to the design of shaft in mine and the identification of fracture accident of shaft wall.

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EXCAVATION AND OPTIMIZATION THEORY FOR GIANT UNDERGROUND CAVERNS CONSTRUCTED IN HIGH DIPPING LAMINAR STRATA

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2004, 23 (19): 3281-3281 doi:

[PDF] 494 KB (985)

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Construction sequences and support parameters have strong influence on stability of giant underground caverns. Based on 3D fracture and damage FEM and fundamental principles of dynamic construction mechanics，numerical simulations are conducted to obtain the optimal construction sequences for the caverns constructed in high dipping laminar strata of Longtan hydropower station，China. The size of the powerhouse caverns is the largest in the world. The optimal construction sequences of the caverns are obtained by comparing the damaged zone of surrounding rock mass with displacements of key points around the caverns. The numerical methods and some conclusions from the research work are useful for the design and construction of analogous rock engineering.

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RELATION BETWEEN ABUTMENT PRESSURE AND RELIEVED GAS DELIVERY FOR FULLY-MECHANIZED TOP COAL CAVING

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2004, 23 (19): 3288-3288 doi:

[PDF] 226 KB (1040)

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After mining in methane-rich thick seams，the law of relieved gas delivery in coal and rock mass is closely related to its permeability，which is influenced by the change of abutment pressure. In other words，the law of relieved gas delivery of coal caving is influenced obviously by the abutment pressure. The flow characteristics of relieved gas in coal and rock mass influenced by mining are analyzed. Based on the analysis results of ground pressure measuring and gas monitoring in 110# fully-mechanized top coal caving face in Weijiadi Coal Mine，Jingyuan Mining Company，the variation curve of abutment pressure and permeability coefficient with distance from the working face is obtained，and the theoretical foundation for effective prevention of gas accidents in working face of fully-mechanized top coal caving and reasonable drainage and usage of gas resource are provided.

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2004, 23 (19): 3292-3292 doi:

[PDF] 314 KB (1065)

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The evolution law of the crack generation-extension-connection-failure in the surrounding rocks of roadway caused by mining is investigated in the paper by using similar simulation and fractal geometry theory. Cracks in the two roadway walls are extending to the depth in arc shape and diminish in a power function law. Cracks at the top of the two sides abide by the conic evolution law. The cracks of the roadway top mostly concentrate at the top of the roadway walls. The crack distribution and evolution of the surrounding rocks of roadway can be quantitatively depicted by the fractal dimension of crack density. The research results are useful for understanding the occurrence and development law inside the surrounding rocks，and applied
as the basis of selection of bolting scheme of roadway and optimization of bolting parameters.

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STUDY ON SURROUNDING ROCK STABILITY OF WORKING FACE SUPPORTED BY BOLT-MESH-ANCHOR IN SOFT AND THICK
COAL SEAM

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2004, 23 (19): 3298-3298 doi:

[PDF] 516 KB (993)

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In order to study the stability of surrounding rocks of working face supported by the bolt-mesh-anchor technology in soft and thick coal seam excavated by fully-mechanized sublevel caving system，the deformation-failure of the pseudo-continuous roof and side coal is analyzed，respectively，by the theories of Timoshenko beam and rock mechanics. Various factors influencing the stability of rocks around working face are therefore identified. Based on the studies，all kinds of bolt-mesh-anchor supporting schemes are proposed and simulated by program UDEC3.0 with emphasis on the deformation states of surrounding rocks under various supporting intensity. At the same time the mutual effect-relation between the roof and side coal is discussed，and the supporting scheme is proposed with optimized supporting parameters. The in-situ test results show that supporting scheme No. 6 can meet the requirements of engineering with better economical and social benefits.

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STUDY ON REGULARITY OF STRUCTURAL BEHAVIOURS
AROUND COAL FACE UNDER THE SHALLOW-BURIED LOOSE ROOF

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2004, 23 (19): 3305-3305 doi:

[PDF] 199 KB (1256)

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The regularity of strata pressure around coal face in Queen seam of PVK colliery in India is analyzed. It has shown that the pressure arch，rather than the beam or plate，can be formed under the shallow-buried and very loose roof. When coal face reaches a certain distance，the pressure arch is destroyed and the initial weighting occurs. When the arch vault is close to ground surface，the rock mass of the key structure inside pressure arch is destroyed and more fierce pressure occurs. Subsequently，the rock mass of the subordinate structure outside the pressure arch is destroyed followed by surface subsidence. The periodic destruction and advancement of arch structure cause the occurrence of periodic pressure. The result reasonably explains the phenomenon that the behavior of ground pressure is very strong even under the very loose roof and can be referred for further studies in similar conditions.

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INFLUENCE OF SHALLOW TUNNEL EXCAVATION ON GROUND SURFACE BUILDINGS

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2004, 23 (19): 3310-3310 doi:

[PDF] 390 KB (1311)

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By using stochastic medium theory，the excavation induced ground surface movement and deformation in the transverse and longitudinal direction of Tongyoushan double-arch tunnel are analyzed. And the simplified formulas for complex tunnel cross-section are derived. The fundamental surface moving parameters are obtained by using back-analysis method based on ground surface measurement data of middle cave. Furthermore，by using the scaling method，the surface moving parameters of the main tunnel can be obtained，and eventually the ground surface movement and deformation of the main tunnel due to the excavation can be predicted. According to the results，the influence of excavation on ground surface buildings is estimated. The conclusion obtained in this paper has some significance in guiding the tunnel construction.

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CONSTRAINT EFFECT OF PILOT-DRIFT AND
SEPARATION-PILE STRUCTURE ON GROUND MOVEMENTS
INDUCED BY SHALLOW TUNNELING

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2004, 23 (19): 3317-3317 doi:

[PDF] 292 KB (926)

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Based on the construction of a shallow-buried tunnel in Beijing metro，the constraint effect of pilot-drift and separation-pile structure on ground movements induced by shallow tunneling is analysed. Restricted by the surface environment of construction area，two pilot-drifts with small cross-section and shotcrete linings were constructed above each side of the subway running tunnel，and reinforced concrete piles were installed in the ground below the drifts to separate the negative effects of tunnel construction on the two high-rise buildings located nearby at each side of the tunnel，respectively. Based on the mechanisms of the pilot-drift and separation-pile structure，a simplified analytical model is formulated to estimate the deformation of structure and ground，and a three-dimensional elasto-plastic finite element model is constructed to simulate the tunneling sequence and its effects on surrounding environment. The comparison between the modeling results and in-situ monitoring data is conducted，and the key factors affecting the performance of the pilot-drift and separation-pile structure are summarized.

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LIQUEFACTION AND DISPLACEMENT OF SATURATED SAND
UNDER WATER PRESSURE OSCILLATION

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2004, 23 (19): 3324-3324 doi:

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In order to investigate the influence of vertical water pressure oscillation on the liquefaction of saturated sand，one dimensional side-constrained model of saturated sand is presented based on biphase continuous media theory. The development of liquefaction and the liquefaction thickness are analyzed. It is shown that the developing rate of liquefaction increases with the increment of load and the decrement of sand strength or the permeability，but the deformation of sand increases with the decrement of sand strength and increment of permeability and load. If the permeability of sand is homogeneous，the pore pressure and the strain rise sharply near the place with the smallest permeability. This solution may explain why the fracture occurs in the sand column in some conditions. With the development of liquefaction，the strength of the soil foundation becomes smaller and smaller. The foundation will slide or flow when the limited state arrives. That means，landslides or debris flow will occur.

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ALGORITHM RESEARCH ON REFINED SUB-REGIONAL
RECIPROCAL METHOD IN TIME DOMAIN FOR WAVE
SCATTERING PROBLEM IN UNBOUNDED MEDIUM

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2004, 23 (19): 3330-3330 doi:

[PDF] 372 KB (863)

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A refined sub-regional time domain reciprocal procedure in precise step-by-step integration scheme dealing with the problem of wave scattering in unbounded space with inhomogeneous geology or irregular geography is proposed based on the damping solvent extraction method (DSEM)，where the radiation condition of the unbounded domain is automatically satisfied，and the frequency-dependence or convolution integral，as required in the other algorithms in time domain，are synchronously avoided. The numerical implementation of the method is given in detail and is suitable for the case of complicated cavity geometry. The wave scattering at the boundary of cylindrical cavity in 2D infinite space with the horizontally incident SV-wave conditions is simulated to validate the proposed method. The numerical results are compared with the solutions obtained by Cloning element method and analytical formula. It has been shown that the proposed procedure is of good accuracy and feasibility，especially for middle and low frequency ranges in seismic analysis.

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ON FRACTURE STRENGTH OF ROCKS WITH CRACKS
UNDER WATER ACTION

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2004, 23 (19): 3337-3337 doi:

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The effects of water pressure and chemical damage on the stress intensity factor of crack in rocks are analyzed，and a new fracture strength criterion of rocks with cracks under water pressure and chemical damage is put forward. This new criterion can quantitatively reflect the effects of static water pressure，dynamic water pressure or hydraulic gradient，and water-chemical damage. The effects of water on the fracture strength of rocks with cracks stem not only from static or dynamic water pressure of crack in rocks，but also from chemical damage of water on the internal friction and coherence of crack in rocks. The formula of the new fracture strength criterion of rocks with cracks is different for the two cases of close and open cracks in rocks.

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OPTIMUM DESIGN OF PARAMETERS FOR COMPOSITE SOIL
NAIL WALL IN SOFT SOIL FOUNDATION

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2004, 23 (19): 3342-3342 doi:

[PDF] 237 KB (938)

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Based on more than ten examples of deep pit foundation engineering in Zhengdong New District，the model for global safety factor is established by simplified Bishop¢s circular slice method and complex method. The model for sensitivity is also founded by the global finite-difference method. The relationship among design parameters，safety factor，design parameters and the sensitivity is analyzed. The range of preliminary values of optimum design are given for guiding optimum design of composite soil nail wall and the similar engineering construction in soft soil foundation.

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NEW APPROACH OF DEVELOPMENT OF SOIL MECHANICS
FROM SCIENTIFIC EXPERIMENTS METHODOLOGY

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2004, 23 (19): 3348-3348 doi:

[PDF] 180 KB (1225)

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Soil is assembly of many minerals with multiphases. Soil is easy to change and has many shapes. It is from experiments that people began to learn the knowledge about soil mechanics. In other words，the formation and development of the soil mechanics theory is linked closely to the methodology of experiments. Some modern techniques，such as SEM and CT，have emerged in recent years and have greatly improved the study of soil microstructure，which are hot tropics today. In this paper，the characteristics of the experiments approach for soil mechanics is analyzed. Based on the analysis of characteristics of experiments methods，the modern physical simulation experiments，such as SEM and CT，can also be used in description of constitutive model of soil. And a new scientific method——virtual technology，which can show the transfer and the reaction of influential factors under additional stress in complex condition，is discussed in the paper. This is a new approach for establishing constitutive model of soil，and interests more and more scientists and engineers.

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ONE-DIMENSIONAL NONLINEAR CONSOLIDATION OF SATURATED SOFT CLAY UNDER CYCLIC LOAD

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2004, 23 (19): 3353-3353 doi:

[PDF] 339 KB (1013)

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Analysis of nonlinear consolidation for saturated soft soil under cyclic loading is of importance in engineering practice. This paper deals with the behavior of one-dimensional nonlinear consolidation of one layer soil under cyclic loading by applying the method of Laplace transform to the nonlinear consolidation of saturated soil model. Solution is presented in inverse Laplace transform. Some characters of one dimensional nonlinear consolidation of saturated soft clay under cyclic loads are explored. Some useful results obtained from several kinds of commonly encountered loadings are illustrated in the paper，which are meaningful to engineering practice.

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CALCULATION THEORY OF INTEGRATED AND ARBITRARILY
ARRANGED INTERFERENTIAL WELLS BEARING
PRESSURE UNDER WATER AND ITS APPLICATION

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2004, 23 (19): 3359-3359 doi:

[PDF] 325 KB (1279)

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Well-point dewater is a commonly used method to reduce underground water level in construction of deep-pit and underground structures. The steady flow theory，being a special example of unsteady flow theory，is widely used in the calculation of interferential wells. Under certain hydrogeological conditions，the interferential wells are often generalized as a hydrogeological model further to build the corresponding numerical model. Based on the steady flow theory，the model of underground hydrodynamics is proposed by using potential function and superposition theorem. The influence of all the arbitrarily arranged wells on water dropping depth and different parameters in different water-bearing layers are considered. And the corresponding theoretical formula is derived for the integrated and arbitrarily arranged interferential wells bearing pressure under water. The calculated results of practical engineering examples are in good agreement with the measured ones.

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TIME-DEPENDENCY ANALYSIS OF SOIL COMPACTION PILE IN SOFT CLAY GROUND

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2004, 23 (19): 3365-3365 doi:

[PDF] 307 KB (1034)

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Because of soil squeezing effect and excess pore water pressur，reconsolidation settlement will occur around soil compaction piles in saturated soft clay during pile driving. The issue of reconsolidation settlement is analyzed in this paper with respect to the excess pore water pressure formation and dispersing scatter discipline. In addition，calculation methods of pile settlement due to soil reconsolidation settlement is studied by using the interaction effect principle. The research indicates that the pile settlement due to soil reconsolidation settlement is far more than that due to vertical load，and this kind of settlement will go up with time. Therefore，the time-dependency of pile settlement is theoretically studied.

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ANALYSIS ON BEARING BEHAVIOUR OF 1-STAGE SUPER
LONG-LARGE DIAMETER TESTING PILES IN SUTONG BRIDGE

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2004, 23 (19): 3370-3370 doi:

[PDF] 227 KB (1323)

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The self-balanced testing method associated with stress gauges buried in shafts was applied to study the bearing behavior of 5 super long-large diameter piles for the 1-stage test project of Sutong bridge. The effects of grouting are (1) to eliminate the influence of technological defects，and recover the bearing capacities of strata，and (2) to improve the bearing capacities of piles. According to test results，the calculation values of ultimate bearing capacity of pile without sedimentation is increased for 34%～74%，and that of pile base is increased for 2%～153%. Compared with test results before grouting，the ultimate bearing capacity of pile is increased for 56%～100% after grouting，the total frictional resistance is increased for 12.39%～52.87% and the total base bearing capacity is increased for 4.91～25.67 times. After grouting，the ratio of base bearing capacity is increased from 1.88%～11.68% to 22.14%～34.67%，so that the bearing behavior of pile is improved greatly.

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EXPERIMENT ON BEHAVIOUR OF POLYPROPYLENE-FIBER-NET SHOTCRETE AND LINING

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2004, 23 (19): 3376-3376 doi:

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In comparison with the traditional plain shotcrete，the tensile，flexural and permeability strength of polyropylene-fiber-net shotcrete are improved for 56.2%，92.9% and 100%，respectively. The density and quality stability of concrete are improved，the resilience loss is reduced for 10%～20%，and dust is reduced for more than 100% in the spraying. In railway and highway tunnels，polyropylene-fiber-net shotcrete has been used as primary support and permanent lining successfully. A comprehensive construction technology has been formed，and the structural strength and quality have been improved in recent years.

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APPLICATION OF STRENGTH REDUCTION FEM
IN SOIL AND ROCK SLOPE

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2004, 23 (19): 3381-3381 doi:

[PDF] 714 KB (7750)

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With the c-tanj reduction，the FEM model of slope reaches instability，and the value of the nodal displacement just after slope failure has a big jump compared with that before failure. This actually means that no stress distribution can be achieved to satisfy both the yield criterion and global equilibrium. Slope failure and numerical non-convergence take place at the same time. So non-convergence in finite element program can be taken as a suitable evaluation criterion of slope failure. The influence on safety factor precision of different yield criterions，flow rule，FEM itself is thoroughly analyzed. At the same time some measures to improve the precision are put forward. A cone characterizes the Mohr-Coulomb surface in three-dimensional stress space with the vertices in deviatoric cross section. It brings difficulty to numerical analysis. For convenience this surface can be replaced by a smooth surface yield criterion，Mohr-Coulomb equivalent area circle DP yield criterion，which was proposed by professor Xu Gancheng and Zheng Yingren in 1990. The results show that the average error of safety factors obtained by FEM with Mohr-Coulomb equivalent area circle DP yield criterion and by Spencer method is about 5%. The average error of safety factor obtained by FEM with the plane strain Mohr-Coulomb matching DP yield criterion and by Spencer method is about 2%. The strength reduction FEM can also be used in the jointed rock slope. Through a series of case studies，the applicability of the proposed method is clearly exhibited.