A Calculation Method of Double Strength Reduction for Layered Slope Based on the Reduction of Water Content Intensity

The calculation of the factor of safety(FOS)is an important means of slope evaluation.This paper proposed an improved double strength reductionmethod(DRM)to analyze the safety of layered slopes.The physical properties of different soil layers of the slopes are different,so the single coefficient strength reduction method(SRM)is not enough to reflect the actual critical state of the slopes.Considering that the water content of the soil in the natural state is the main factor for the strength of the soil,the attenuation law of shear strength of clayey soil changing with water content is fitted.This paper also establishes the functional relationship between different reduction coefficients.Then,a USDFLD subroutine is programmed using the secondary development function of finite element software.Controlling the relationship between field variables and calculation time realizes double strength reduction applicable to the layered slope.Finally,by comparing the calculation results of different examples,it is proved that the stress and displacement distribution of the critical slope state obtained by the improved method is more realistic,and the calculated safety factor is more reliable.The newly proposedmethod considers the difference of intensity attenuation between different soil layers under natural conditions and avoids the disadvantage of the strength reduction method with uniform parameters,which provides a new idea and method for stability analysis of layered and complex slopes.

Borehole stability in naturally fractured rocks with drilling mud intrusion and associated fracture strength weakening:A coupled DFN-DEM approach

Borehole instability in naturally fractured rocks poses significant challenges to drilling.Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure(P w)and pore pressure(P p)during drilling,which may cause wellbore instability.However,the weakening of fracture strength due to mud intrusion is not considered in most existing borehole stability analyses,which may yield significant errors and misleading predictions.In addition,only limited factors were analyzed,and the fracture distribution was oversimplified.In this paper,the impacts of mud intrusion and associated fracture strength weakening on borehole stability in fractured rocks under both isotropic and anisotropic stress states are investigated using a coupled DEM(distinct element method)and DFN(discrete fracture network)method.It provides estimates of the effect of fracture strength weakening,wellbore pressure,in situ stresses,and sealing efficiency on borehole stability.The results show that mud intrusion and weakening of fracture strength can damage the borehole.This is demonstrated by the large displacement around the borehole,shear displacement on natural fractures,and the generation of fracture at shear limit.Mud intrusion reduces the shear strength of the fracture surface and leads to shear failure,which explains that the increase in mud weight may worsen borehole stability during overbalanced drilling in fractured formations.A higher in situ stress anisotropy exerts a significant influence on the mechanism of shear failure distribution around the wellbore.Moreover,the effect of sealing natural fractures on maintaining borehole stability is verified in this study,and the increase in sealing efficiency reduces the radial invasion distance of drilling mud.This study provides a directly quantitative prediction method of borehole instability in naturally fractured formations,which can consider the discrete fracture network,mud intrusion,and associated weakening of fracture strength.The information provided by the numerical approach(e.g.displacement around the borehole,shear displacement on fracture,and fracture at shear limit)is helpful for managing wellbore stability and designing wellbore-strengthening operations.

Discussion on the Core Strength Training Method for 100-Meter Event in Track and Field Sports

In track and field sports,the 100-meter race is an extremely intense sport that requires effective training of athletes’core strength.From the perspective of adolescents,in order to enhance core strength,it is necessary to effectively fix the pelvic position in the process of exercise,so that the core stability,balance,and coordination of athletes can be improved.The training process of the 100-meter event is mainly an anaerobic metabolic exercise,it is necessary to ensure that athletes maintain a high level of physical readiness during the exercises and concentrate highly on their core strength,so that they can achieve excellent results.This paper analyzes the core strength training for the 100-meter event in track and field sports,discusses its importance,and puts forward specific training methods,hoping to provide guidelines for relevant researchers.

Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model

The particulate discrete element method(DEM) can be employed to capture the response of rock,provided that appropriate bonding models are used to cement the particles to each other.Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors.Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional(2D) models.In situ rock formations are often heterogeneous,thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis.In situ stress states are basically three-dimensional(3D),and therefore it is important to develop 3D models for this purpose.This paper revisits an earlier experimental study on heterogeneous specimens,of which the relative proportions of weaker material(siltstone) and stronger,harder material(sandstone) were varied in a controlled manner.Using a 3D DEM model with the parallel bond model,virtual heterogeneous specimens were created.The overall responses in terms of variations in strength and stiffness with different percentages of weaker material(siltstone) were shown to agree with the experimental observations.There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations,suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.

Overhanging rock slope by design:An integrated approach using rock mass strength characterisation,large-scale numerical modelling and limit equilibrium methods

Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.

The Testing Strength Curves of Lightweight Aggregate Concrete by Rebound Method and Ultrasonic-rebound Combined Method

The strength curves of lightweight aggregate concrete （LWAC） were tested based on detecting LWAC with density of 1 400-1 900 kg/m3 and LWAC with strength grade of LC15-LC50 by rebound method and ultrasonic-rebound combined method.The results show that the common measured strength curves tested by above two methods can not satisfy the required accuracy of LWAC strength test.In addition,specified compressive strength curves of testing LWAC by rebound method and ultrasonic-rebound combined method are obtained,respectively.

Early Age Compressive Strength of Pastes by Electrical Resistivity Method and Maturity Method

The compressive strength development of Portland cement pastes was investigated by the electrical resistivity method and the maturity method.The experiments were carried out on the cement pastes with different water-cement ratios at different curing temperatures.The results show that the application of the maturity method has limitation to obtain the strength.It is found that both of the compressive strength and the electrical resistivity follow hyperbolic trend for all the mixes.The hyperbolic equation of each mix is obtained to estimate the ultimate resistivity value which can probably be reached.The relationship between electrical resistivity and compressive strength of the cement pastes is established based on the test results and interpreted by the empirical Archie equation and a strength-porosity equation.The relationship between the electrical resistivity after temperature correction and the compressive strength was linear and independent of curing temperature and water-cement ratio.

Application of strength reduction method to dynamic anti-sliding stability analysis of high gravity dam with complex dam foundation

Considering that there are some limitations in analyzing the anti-sliding seismic stability of dam-foundation systems with the traditional pseudo-static method and response spectrum method, the dynamic strength reduction method was used to study the deep anti-sliding stability of a high gravity dam with a complex dam foundation in response to strong earthquake-induced ground action. Based on static anti-sliding stability analysis of the dam foundation undertaken by decreasing the shear strength parameters of the rock mass in equal proportion, the seismic time history analysis was carried out. The proposed instability criterion for the dynamic strength reduction method was that the peak values of dynamic displacements and plastic strain energy change suddenly with the increase of the strength reduction factor. The elasto-plastic behavior of the dam foundation was idealized using the Drucker-Prager yield criterion based on the associated flow rule assumption. The result of elasto-plastic time history analysis of an overflow dam monolith based on the dynamic strength reduction method was compared with that of the dynamic linear elastic analysis, and the reliability of elasto-plastic time history analysis was confirmed. The results also show that the safety factors of the dam-foundation system in the static and dynamic cases are 3.25 and 3.0, respectively, and that the F2 fault has a significant influence on the anti-sliding stability of the high gravity dam. It is also concluded that the proposed instability criterion for the dynamic strength reduction method is feasible.

Mesomechanics Finite-element Method for Determining the Shear Strength of Mudded Intercalation Materials

A new method regarding mesomechanics finite-element research is proposed to predict the peak shear strength of mudded intercalation materials on a mesoscopic scale. Based on geometric and mechanical parameters, along with the strain failure criteria obtained by sample＇s deformation characteristics, uniaxial compression tests on the sample were simulated through a finite-element model, which yielded values consistent with the data from the laboratory uniaxial compression tests, implying that the method is reasonable. Based on this model, a shear test was performed to calculate the peak shear strength of the mudded intercalation, consistent with values reported in the literature, thereby providing a new approach for investigating the mechanical properties of mudded intercalation materials.

Tensile strength of sea ice using splitting tests based on the digital image correlation method

The splitting test is a competitive alternative method to study the tensile strength of sea ice owing to its suitability for sampling.However,the approach was questioned to the neglect of local plastic deformation during the tests.In this study,splitting tests were performed on sea ice,with 32 samples subjected to the regular procedure and 8 samples subjected to the digital image correlation method.The salinity,density,and temperature were measured to determine the total porosity.With the advantage of the digital image correlation method,the full-field deformation of the ice samples could be determined.In the loading direction,the samples mainly deformed at the ice-platen contact area.In the direction vertical to the loading,deformation appears along the central line where the splitting crack occurs.Based on the distribution of the sample deformation,a modified solution was derived to calculate the tensile strength with the maximum load.Based on the modified solution,the tensile strength was further calculated together with the splitting test results.The results show that the tensile strength has a negative correlation with the total porosity,which agrees with previous studies based on uniaxial tension tests.

A strength reduction method based on double reduction parameters and its application

In the traditional strength reduction method,the cohesion and the friction angle adopt the same reduction parameter,resulting in equivalent proportional reduction.This method does not consider the different effects of the cohesion and friction angle on the stability of the same slope and is defective to some extent.Regarding this defect,a strength reduction method based on double reduction parameters,which adopts different reduction parameters,is proposed.The core of the double-parameter reduction method is the matching reduction principle of the slope with different angles.This principle is represented by the ratio of the reduction parameter of the cohesion to that of the friction angle,described asη.With the increase in the slope angle,ηincreases;in particular,when the slope angle is 45°,ηis 1.0.Through the matching reduction principle,different safety margin factors can be calculated for the cohesion and friction angle.In combination with these two safety margin factors,a formula for calculating the overall safety factor of the slope is proposed,reflecting the different contributions of the cohesion and friction angle to the slope stability.Finally,it is shown that the strength reduction method based on double reduction parameters acquires a larger safety factor than the classic limit equilibrium method,but the calculation results are very close to those obtained by the limit equilibrium method.

Correlations between direct and indirect strength test methods

The difficulties associated with performing direct compression strength tests on rocks lead to the development of indirect test methods for the rock strength assessment. Indirect test methods are simple, more economical, less time-consuming, and easily adaptable to the field. The main aim of this study was to derive correlations between direct and indirect test methods for basalt and rhyolite rock types from Carlin trend deposits in Nevada. In the destructive methods, point load index, block punch index, and splitting tensile strength tests are performed. In the non-destructive methods, Schmidt hammer and ultrasonic pulse velocity tests are performed. Correlations between the direct and indirect compression strength tests are developed using linear and nonlinear regression analysis methods. The results show that the splitting tensile strength has the best correlation with the uniaxial compression strength.Furthermore, the Poisson's ratio has no correlation with any of the direct and indirect test results.

Strength reduction method for slope based on a ubiquitous-joint criterion and its application

In order to expand the application of strength reduction methods with the ubiquitous-joint criterion,the corresponding program is compiled using FLAC3D software.A procedure for strength reduction in the ubiquitous-joint criterion is proposed to study the safety factor of slopes as well as the relationships of the bedding plane inclination angle β and the safety factor F.The results show that:1) for the bedding rock slope,the various failure modes cause different variations of the safety factor F;2) a bedding rock slope can be divided into two types by the angle between the bedding plane inclination and slope surface inclination α;when α≤45°,the bedding slope can be strictly defined as the subsequent bedding rock slope;when 45°<α<90°,the bedding slope is defined as an oblique bedding slope;3) for bedding rock slopes,the safety factor increases with an increase in α;for inverse bedding slopes,when the bedding plane inclination angle β is small,the safety factor F of the slope increases at first,then decreases with an increase in α;when β is large,the safety factor F increases with an increase in α.

Limit analysis of vertical anti-pulling screw pile group under inclined loading on 3D elastic-plastic finite element strength reduction method

Based on the functional theory, catastrophe theory, simultaneity principle and the idea of strength reduction method(SRM), the bearing capacity functional and SRM of pile group foundation were established, and the criteria of ultimate load and the concept of safety storage coefficient(CSS) were advanced. The inclined ultimate loads by the static loading test, load increment method(LIM) and SRM are compared. Theoretically, the ultimate load of piles does not change with the loading levels when it is calculated by SRM. When the one strength reduction parameter is applied in the calculation boundary, there are calculating errors because the bearing capacity action of soils happened in the finite zone. The inclined loadings are 108, 132 and 144 kN, and SSC are 1.07, 0.94 and 0.79, respectively, so the calculation values of ultimate loads are about 115.56, 124.08 and 113.76 kN, respectively. The error between calculations and observation values is less than 6%. But the error between calculations of LIM and observations is 20%. Because of the effect of inclined loading, the push-rotation phenomenon of screw pile group appears. Under this testing, the ultimate bearing capacity of piles is mostly determined by the horizontal ultimate bearing capacity, and the effect of the vertical component of inclined load should also be considered.

A Novel Method for Measuring Flexure Strength of Brittle Materials

A novel test method to measure flexure strength for silicon slices and other brittle materials was suggested by using simple supported circular slice samples and steel ball impact loading. The maximal tensile stress expression under concentrating impact load for center of simple supported circular plate was derived based on kinetic energy theorem and small deflection theory of thin plate. The instrument used in the method is simple, the test results are accurate, and the test does not need large scale loading apparatus. An experimental correct method was presented for test results deviated from small deflection limit when the slices were thinner or the strength of slice was higher.

Various admixtures to mitigate the long-term strength retrogression of Portland cement cured under high pressure and high temperature conditions

In order to investigate the problem of long-term strength retrogression in oil well cement systems exposed to high pressure and high temperature(HPHT)curing conditions,various influencing factors,including cement sources,particle sizes of silica flour,and additions of silica fume,alumina,colloidal iron oxide and nano-graphene,were investigated.To simulate the environment of cementing geothermal wells and deep wells,cement slurries were directly cured at 50 MPa and 200?C.Mineral compositions(as determined by X-ray diffraction Rietveld refinement),water permeability,compressive strength and Young’s modulus were used to evaluate the qualities of the set cement.Short-term curing(2e30 d)test results indicated that the adoption of 6 m m ultrafine crystalline silica played the most important role in stabilizing the mechanical properties of oil well cement systems,while the addition of silica fume had a detrimental effect on strength stability.Long-term curing(2e180 d)test results indicated that nano-graphene could stabilize the Young’s modulus of oil well cement systems.However,none of the ad-mixtures studied here can completely prevent the strength retrogression phenomenon due to their inability to stop the conversion of amorphous to crystalline phases.

An Integrated Structural Strength Analysis Method for Spar Type Floating Wind Turbine

An integrated structural strength analysis method for a Spar type floating wind turbine is proposed in this paper,and technical issues related to turbine structure modeling and stress combination are also addressed.The NREL-5MW ＂Hywind＂ Spar type wind turbine is adopted as study object.Time-domain dynamic coupled simulations are performed by a fully-coupled aero-hydro-servo-elastic tool,FAST,on the purpose of obtaining the dynamic characteristics of the floating wind turbine,and determining parameters for design load cases of finite element calculation.Then design load cases are identified,and finite element analyses are performed for these design load cases.The structural stresses due to wave-induced loads and wind-induced loads are calculated,and then combined to assess the structural strength of the floating wind turbine.The feasibility of the proposed structural strength analysis method for floating wind turbines is then validated.

A New Criterion for Defining Inhomogeneous Slope Failure Using the Strength Reduction Method

A new variational method treating the system as a whole with rigorous mathematical and physical derivation was presented in this paper.Combined with classical and engineering examples,variational energy expressions of slopes were derived.In addition,the calculation programs were written in the FISH language set in FLAC3D(fast Lagrangian analysis of continua in three dimensions)software.Factors of safety(FOSs)of the models were determined by the variational method based on the strength reduction method(SRM)and then compared with other criteria or methods.The result showed that the variational method reflected the process of slope plasticity and failure uniformly and was feasible to analyze the stability of inhomogeneous slopes.The method was applicable to both two-dimensional and three-dimensional heterogeneous slopes.The small error with other criteria or methods also showed the accuracy of this method.This method unified other criteria,avoided the artificial error of other criteria,and provided a logical derivation for the instability of heterogeneous slope.This method considered the system as a whole and avoided the shortcomings of the general method of one-sided instability analysis.The proposed method is of great significance as it considers the coupling effect of stress and strain of materials and gives the mechanical basis for the instability of complex slopes.

Two-dimensional face stability analysis in rock masses governed by the Hoek-Brown strength criterion with a new multi-horn mechanism

The face stability problem is a major concern for tunnels excavated in rock masses governed by the Hoek-Brown strength criterion.To provide an accurate prediction for the theoretical solution of the critical face pressure,this study adopts the piecewise linear method(PLM)to account for the nonlinearity of the strength envelope and proposes a new multi-horn rotational mechanism based on the Hoek-Brown strength criterion and the associative flow rule.The analytical solution of critical support pressure is derived from the energy-work balance equation in the framework of the plastic limit theorem;it is formulated as a multivariable nonlinear optimization problem relying on 2m dependent variables(m is the number of segments).Meanwhile,two classic linearized measures,the generalized tangential technique(GTT)and equivalent Mohr-Coulomb parameters method(EMM),are incorporated into the analysis for comparison.Surprisingly,the parametric study indicates a significant improvement in support pressure by up to 13%compared with the GTT,and as expected,the stability of the tunnel face is greatly influenced by the rock strength parameters.The stress distribution on the rupture surface is calculated to gain an intuitive understanding of the failure at the limit state.Although the limit analysis is incapable of calculating the true stress distribution in rock masses,a rough approximation of the stress vector on the rupture surface is permitted.In the end,sets of normalized face pressure are provided in the form of charts for a quick assessment of face stability in rock masses.

Slope analysis based on local strength reduction method and variable-modulus elasto-plastic model

Employing an ideal elasto-plastic model,the typically used strength reduction method reduced the strength of all soil elements of a slope.Therefore,this method was called the global strength reduction method(GSRM).However,the deformation field obtained by GSRM could not reflect the real deformation of a slope when the slope became unstable.For most slopes,failure occurs once the strength of some regional soil is sufficiently weakened; thus,the local strength reduction method(LSRM)was proposed to analyze slope stability.In contrast with GSRM,LSRM only reduces the strength of local soil,while the strength of other soil remains unchanged.Therefore,deformation by LSRM is more reasonable than that by GSRM.In addition,the accuracy of the slope's deformation depends on the constitutive model to a large degree,and the variable-modulus elasto-plastic model was thus adopted.This constitutive model was an improvement of the Duncan–Chang model,which modified soil's deformation modulus according to stress level,and it thus better reflected the plastic feature of soil.Most importantly,the parameters of the variable-modulus elasto-plastic model could be determined through in-situ tests,and parameters determination by plate loading test and pressuremeter test were introduced.Therefore,it is easy to put this model into practice.Finally,LSRM and the variable-modulus elasto-plastic model were used to analyze Egongdai ancient landslide.Safety factor,deformation field,and optimal reinforcement measures for Egongdai ancient landslide were obtained based on the proposed method.