Application of Two Dimensional RQD in Stability Analysis for Rock Slopes

Rock slope RQD (Rock Quality Designation) provides engineering geologists with an orientation RQD technique. The probability patterns of rock masses of slope are calculated and simulated with the aid of the Monto Carlo method on the basis of survey data of discontinuity. Consequently, the two dimentional RQD in the range of 360° of rock slope is estimated and the concept of orientation RQD is proposed. Finally, the method of orientation RQD is applied into a research to find out the relationship between railway slope engineering activities and geological environments.

A method to interpret fracture aperture of rock slope using adaptive shape and unmanned aerial vehicle multi-angle nap-of-the-object photogrammetry

The aperture of natural rock fractures significantly affects the deformation and strength properties of rock masses,as well as the hydrodynamic properties of fractured rock masses.The conventional measurement methods are inadequate for collecting data on high-steep rock slopes in complex mountainous regions.This study establishes a high-resolution three-dimensional model of a rock slope using unmanned aerial vehicle(UAV)multi-angle nap-of-the-object photogrammetry to obtain edge feature points of fractures.Fracture opening morphology is characterized using coordinate projection and transformation.Fracture central axis is determined using vertical measuring lines,allowing for the interpretation of aperture of adaptive fracture shape.The feasibility and reliability of the new method are verified at a construction site of a railway in southeast Tibet,China.The study shows that the fracture aperture has a significant interval effect and size effect.The optimal sampling length for fractures is approximately 0.5e1 m,and the optimal aperture interpretation results can be achieved when the measuring line spacing is 1%of the sampling length.Tensile fractures in the study area generally have larger apertures than shear fractures,and their tendency to increase with slope height is also greater than that of shear fractures.The aperture of tensile fractures is generally positively correlated with their trace length,while the correlation between the aperture of shear fractures and their trace length appears to be weak.Fractures of different orientations exhibit certain differences in their distribution of aperture,but generally follow the forms of normal,log-normal,and gamma distributions.This study provides essential data support for rock and slope stability evaluation,which is of significant practical importance.

A semi-infinite beam theoretical model on predicting rock slope subsidence induced by underground mining

When the mining goaf is close to the cliff,rock slope subsidence induced by underground mining is significantly affected by its boundary conditions.In this study,an analytical method is proposed by considering the key strata as a semi-infinite Euler-Bernoulli beam rested on a Winkler foundation with a local subsidence area.The analytical solutions of deflection are derived by analyzing the boundary and continuity conditions of the cliff.Then,the analytical solutions are verified by the results from experimental tests,FEM and InSAR,respectively.After that,the influence of changing parameters on deflections is studied with sensitivity analysis.The results show that the distance between goaf and cliff significantly affects the deflection of semi-infinite beam.The response of semi-infinite beam is obviously determined by the length of goaf and the bending stiffness of beam.The comparisons between semi-infinite beam and infinite beam illustrate the ascendancy of the improved model in such problems.

Dynamic response and failure process of horizontal-layered fractured structure rock slope under strong earthquake

Rock slope with horizontal-layered fractured structure(HLFS)has high stability in its natural state.However,a strong earthquake can induce rock fissure expansion,ultimately leading to slope failure.In this study,the dynamic response,failure mode,and spectral characteristics of rock slope with HLFS under strong earthquake conditions were investigated based on the large-scale shaking table model test.On this basis,multiple sets of numerical calculation models were further established by UDEC discrete element program.Five influencing factors were considered in the parametric study of numerical simulations,including slope height,slope angle,bedding-plane spacing and secondary joint spacing as well as bedrock dip angle.The results showed that the failure process of rock slope with HLFS under earthquake action is mainly divided into four phases,i.e.,the tensile crack of the slope shoulder joints and shear dislocation at the top bedding plane,the extension of vertical joint cracks and increase of shear displacement,the formation of step-through sliding surfaces and the instability,and finally collapse of fractured rock mass.The acceleration response of slopes exhibits elevation amplification effect and surface effect.Numerical simulations indicate that the seismic stability of slopes with HLFS exhibits a negative correlation with slope height and angle,but a positive correlation with bedding-plane spacing,joint spacing,and bedrock dip angle.The results of this study can provide a reference for seismic stability evaluation of weathered rock slopes.

An approach for determination of lateral limit angle in kinematic planar sliding analysis for rock slopes

Planar sliding is one of the frequently observed types of failure in rock slopes.Kinematic analysis is a classic and widely used method to examine the potential failure modes in rock masses.The accuracy of planar sliding kinematic analysis is significantly influenced by the value assigned to the lateral limit angleγlim.However,the assignment ofγlim is currently used generally based on an empirical criterion.This study aims to propose an approach for determining the value ofγlim in deterministic and probabilistic kinematic planar sliding analysis.A new perspective is presented to reveal thatγlim essentially influences the probability of forming a potential planar sliding block.The procedure to calculate this probability is introduced using the block theory method.It is found that the probability is correlated with the number of discontinuity sets presented in rock masses.Thus,different values ofγlim for rock masses with different sets of discontinuities are recommended in both probabilistic and deterministic planar sliding kinematic analyses;whereas a fixed value ofγlim is commonly assigned to different types of rock masses in traditional method.Finally,an engineering case was used to compare the proposed and traditional kinematic analysis methods.The error rates of the traditional method vary from 45%to 119%,while that of the proposed method ranges between 1%and 17%.Therefore,it is likely that the proposed method is superior to the traditional one.

Limit load and failure mechanisms of a vertical Hoek-Brown rock slope

The problem considered in this short note is the limit load determination of a vertical rock slope.The classical limit theorem is employed with the use of adaptive finite elements and nonlinear programming to determine upper and lower bound limit loads of a Hoek-Brown vertical rock slope.The objective function of the mathematical programming problem is such as to optimize a boundary load,which is known as the limit load,resembling the ultimate bearing capacity of a strip footing.While focusing on the vertical slope,parametric studies are carried out for several dimensionless ratios such as the dimensionless footing distance ratio,the dimensionless height ratio,and the dimensionless rock strength ratio.A comprehensive set of design charts is presented,and failure envelopes shown with the results explained in terms of three identified failure mechanisms,i.e.the face,the toe,and the Prandtl-type failures.These novel results can be used with great confidence in design practice,in particularly noting that the current industry-based design procedures for the presented problem are rarely found.

Stability of bedded rock slopes subjected to hydro-fluctuation and associated strength deterioration

Reservoir-induced earthquakes(RIEs)occur frequently in the Three Gorges Reservoir Area(TGRA)and the rock mass strength of the hydro-fluctuation belt(HFB)deteriorates severely due to the reservoirinduced seismic loads.Three models of typical bedded rock slopes(BRSs),i.e.gently(GIS),moderately(MIS),and steeply(SIS)inclined slopes,were proposed according to field investigations.The dynamic response mechanism and stability of the BRSs,affected by the rock mass deterioration of the HFB,were investigated by the shaking table test and the universal distinct element code(UDEC)simulation.Specifically,the amplification coefficient of the peak ground acceleration(PGA)of the slope was gradually attenuated under multiple seismic loads,and the acceleration response showed obvious“surface effect”and“elevation effect”in the horizontal and vertical directions,respectively.The“S-type”cubic function and“steep-rise type”exponential function were used to characterize the cumulative damage evolution of the slope caused by microseismic waves(low seismic waves)and high seismic waves,respectively.According to the dynamic responses of the acceleration,cumulative displacement,rock pressure,pore water pressure,damping ratio,natural frequency,stability coefficient,and sliding velocity of the slope,the typical evolution processes of the dynamic cumulative damage and instability failure of the slope were generalized,and the numerical and experimental results were compared.Considering the dynamic effects of the slope height(SH),slope angle(SA),bedding plane thickness(BPT),dip angle of the bedding plane(DABP),dynamic load amplitude(DLA),dynamic load frequency(DLF),height of water level of the hydro-fluctuation belt(HWLHFB),degradation range of the hydro-fluctuation belt(DRHFB),and degradation shape of the hydro-fluctuation belt(DSHFB),the sensitivity of factors influencing the slope dynamic stability using the orthogonal analysis method(OAM)was DLA>DRHFB>SA>SH>DLF>HWLHFB>DSHFB>DABP>BPT.

Influence of joint spacing and rock characteristics on the toppling stability of cut rock slope through a simplified limit equilibrium method

Toppling failure of rock mass/soil slope is an important geological and environmental problem.Clarifying its failure mechanism under different conditions has great significance in engineering.The toppling failure of a cutting slope occurred in a hydropower station in Kyushu,Japan illustrates that the joint characteristic played a significant role in the occurrence of rock slope tipping failure.Thus,in order to consider the mechanical properties of jointed rock mass and the influence of geometric conditions,a simplified analytical approach based on the limit equilibrium method for modeling the flexural toppling of cut rock slopes is proposed to consider the influence of the mechanical properties and geometry condition of jointed rock mass.The theoretical solution is compared with the numerical solution taking Kyushu Hydropower Station in Japan as one case,and it is found that the theoretical solution obtained by the simplified analysis method is consistent with the numerical analytical solution,thus verifying the accuracy of the simplified method.Meanwhile,the Goodman-Bray approach conventionally used in engineering practice is improved according to the analytical results.The results show that the allowable slope angle may be obtained by the improved Goodman-Bray approach considering the joint spacing,the joint frictional angle and the tensile strength of rock mass together.

Stability analysis of intermittently jointed rock slopes based on the stepped failure mode

In practical engineering,due to the noncontinuity characteristics of joints in rock slopes,in addition to plane failure,stepped sliding failure may occur for intermittently jointed rock slopes.Especially for intermittently bedding jointed rock slopes,the correlation and difference in strength parameters between joints and rock bridges,along with the various failure modes and intermittency of rock bridges,contribute to the complexity of stepped failure modes and the unpredictability of failure regions.Based on the upper-bound limit analysis method and multi-sliders step-path failure mode,considering the shear and tensile failure of rock bridges and the weakened relationship between the strength parameters of rock bridges and jointed surfaces,by introducing the modified M-C failure criterion and the formula for calculating the energy consumption of tensile failure of rock bridges,two failure mechanisms are constructed to obtain the safety factor(F_(s))of intermittently jointed rock slopes.The sequential quadratic programming method is used to obtain the optimal upper-bound solution for F_(s).The influence of multiple key parameters(slope height H,horizontal distance L,Slope angleβ,shear strength parameters of the rock bridgeφr and cr,Dimensionless parameter u,weakening coefficients of the internal friction angle and cohesion between the rock bridges and joint surfaces Kφand Kc)on the stability analysis of intermittently jointed rock slopes under the shear failure mode of rock bridges as well as under the tensile failure mode is also explored.The reliability of the failure mechanisms is verified by comparative analysis with theoretical results,numerical results,and landslide cases,and the variation rules of F_(s)with each key parameter are obtained.The results show that F_(s) varies linearly withφr and cr of the rock bridge and with K_(φ)and K_(c),whereas F_(s)changes nonlinearly with H and L.In particular,with the increase in Kφand Kc,Fs increases by approximately 52.78%and 171.02%on average,respectively.For rock bridge tensile failure,F_(s) shows a nonlinearly positive correlation withφr,cr,Kφand Kc.In particular,with the increase in Kφand Kc,Fs increases by approximately 13%and 61.69%on average,respectively.Fs decreases rapidly with increasing slope gradientβand decreasing dimensionless parameterμ.When Kφand Kc are both less than 1.0,the stepped sliding surface occurs more easily than the plane failure surface,especially in the case of tensile failure of the rock bridge.In addition,rock slopes with higher strength parameters,taller heights,and greater weakening coefficients are prone to rock bridge tension failure with lower Fs,and more attention should be given to the occurrence of such accidents in actual engineering.

Experimental study on instability mechanism and critical intensity of rainfall of high-steep rock slopes under unsaturated conditions

Two critical factors,namely intense precipitation and intricate excavation,can trigger rock mass disasters in mining operations.In this study,an indoor rainfall system was developed to precisely regulate the flow and intensity of precipitation.A large-scale model experiment was conducted on a self-designed physical simulation experiment platform to investigate the failure and instability of high-steep rock slopes under unsaturated conditions.The real-time reproduction of the progressive failure process in high-steep rock slopes enabled the determination of the critical rainfall intensity and revealed the mechanism underlying slope instability.Experiment results indicated that rainfall may be the primary factor contributing to rock mass instability,while continuous pillar mining exacerbates the extent of rock mass failure.The critical failure stage of high-steep rock slopes occurs at a rainfall intensity of 40 mm/h,whereas a rainfall exceeding 50 mm can induce critical instability and precipitation reaching up to 60 mm will result in slope failure.The improved region growing segmentation method(IRGSM)was subsequently employed for image recognition of rock mass deformation in underground mines.Herein an error comparison with the simple linear iterative cluster(SLIC)superpixel method and the original region growing segmentation method(ORGSM)showed that the average identification error in the X and Y directions by the method was reduced significantly(1.82%and 1.80%in IRGSM;4.70%and 6.26%in SLIC;9.45%and 12.40%in ORGSM).Ultimately,the relationship between rainfall intensity and failure probability was analyzed using the Monte Carlo method.Moreover,the stability assessment criteria of rock slope under unsaturated condition were quantitatively and accurately evaluated.

Evaluation of toppling rock slopes using a composite cloud model with DEMATEL–CRITIC method

Safety evaluation of toppling rock slopes developing in reservoir areas is crucial. To reduce the uncertainty of safety evaluation, this study developed a composite cloud model, which improved the combination weights of the decision-making trial and evaluation laboratory (DEMATEL) and criteria importance through intercriteria correlation (CRITIC) methods. A safety evaluation system was developed according to in situ monitoring data. The backward cloud generator was used to calculate the numerical characteristics of a cloud model of quantitative indices, and different virtual clouds were used to synthesize some clouds into a generalized one. The synthesized numerical characteristics were calculated to comprehensively evaluate the safety of toppling rock slopes. A case study of a toppling rock slope near the Huangdeng Hydropower Station in China was conducted using monitoring data collected since operation of the hydropower project began. The results indicated that the toppling rock slope was moderately safe with a low safety margin. The composite cloud model considers the fuzziness and randomness of safety evaluation and enables interchange between qualitative and quantitative knowledge. This study provides a new theoretical method for evaluating the safety of toppling rock slopes. It can aid in the predication, control, and even prevention of disasters.

Deformation and failure mechanism of Yanjiao rock slope influenced by rainfall and water level fluctuation of the Xiluodu hydropower station reservoir

With the construction of the Xiluodu hydropower station on the Jinsha River,the reservoir impoundment began in 2013 and the water level fluctuates annually between 540 m and 600 m above sea level.The Yanjiao rock slope which is located on the left bank of the Jinsha River 75 km upstream of the Xiluodu dam site,began to deform in 2014.The potential failure of the slope not only threatens Yanjiao town but also affects the safe operation of the Xiluodu reservoir.This paper is to find the factors influencing the Yanjiao slope deformation through field investigation,geotechnical reconnaissance,and monitoring.Results show that the Yanjiao slope can be divided into a bank collapse area(BCA)and a strong deformation area(SDA)based on the crack distribution characteristics of the slope.The rear area of the slope has been experiencing persistent deformation with a maximum cumulative displacement(GPS monitoring point G4)of 505 mm and 399 mm in the horizontal and vertical directions,respectively.The potential failure surface of the slope is formed 36 m below the surface based on the borehole inclinometer.The bank collapses of the Yanjiao slope are directly caused by the reservoir impoundment while the deformation area of the slope is affected by the combination of the rainfall and reservoir water level fluctuation.Based on mechanism of the Yanjiao slope,prestressed anchor combined with the surface drainage and slope unloading are recommended to prevent potential deformation.

Smart and fast reinforcement design for anti-dip bedding rock slopes

Rock slopes are usually reinforced by a number of rock bolts due to the high efficiency and low price.However,where should the rock bolts be installed is still a troublesome issue.For anti-dip bedding rock slopes(ABRSs),the installation position of rock bolts is a controlling factor that determines the reinforcement effect.In this work,a theoretical method is firstly proposed for assessing the stability of ABRSs reinforced by rock bolts using a limit equilibrium model.A comparison of theoretical calculations and numerical results was conducted to test the correctness of the theoretical method.Based on the stability assessment of ABRSs,we introduce adaptive moment estimation method(Adam)to optimize the installation location of rock bolts.Using Adam optimizer,the optimal layout of rock bolts with the maximum factor of safety can be determined,and the factor of safety of the slope increases by about 25%using the same amount of rock bolts but with different installation locations.The proposed method enables the fast stability analysis and supporting design for reinforced ABRSs,which paves the way to smart supporting design of slopes.

Dynamic damage evolution of bank slopes with serrated structural planes considering the deteriorated rock mass and frequent reservoirinduced earthquakes

To investigate the dynamic damage evolution characteristics of bank slopes with serrated structural planes,the shaking table model test and the numerical simulation were utilized.The main findings indicate that under continuous seismic loads,the deformation of the bank slope increased,particularly around the hydro-fluctuation belt,accompanying by the pore water pressure rising.The soil pressure increased and then decreased showed dynamic variation characteristics.As the undulation angle of the serrated structural planes increased(30°, 45°, and 60°),the failure modes were climbing,climbinggnawing,and gnawing respectively.The first-order natural frequency was used to calculate the damage degree(Dd)of the bank slope.During microseisms and small earthquakes,it was discovered that the evolution of Dd followed the“S”shape,which was fitted by a logic function.Additionally,the quadratic function was used to fit the Dd during moderately strong earthquakes.Through the numerical simulation,the variation characteristics of safety factors(Sf)for slopes with serrated structural planes and slopes with straight structural planes were compared.Under continuous seismic loads,the Sf of slopes with straight structural planes reduce stalely,whereas the Sf for slopes with serrated structural planes was greater than the former and the reduction rate was increasing.

Preliminary results on a near-real-time rock slope damage monitoring system based on relative velocity changes following the September 5,2022 M_(S) 6.8 Luding,China earthquake

Relative seismic velocity change(dv/v)is important for monitoring changes in subsurface material properties and evaluating earthquake-induced rock slope damage in a geological disaster-prone region.In this paper,we present a rapid damage assessment on three slow-moving rock slopes by measuring dv/v decrease caused by the 2022 M_(S) 6.8 Luding earthquake in Southwest China.By applying the stretching method to the cross-correlated seismic wavefields between sensors installed on each slope,we obtain earthquake-induced dv/v decreases of~2.1%,~0.5%,and~0.2%on three slopes at distances ranging from~86 to~370 km to the epicenter,respectively.Moreover,based on seismic data recorded by 16 sensors deployed on the rock slope at a distance of~370 km away from the epicenter,a localized dv/v decease region was observed at the crest of the slope by calculating the spatial dv/v images before and after the earthquake.We also derive an empirical in situ stress sensitivity of -7.29×10^(-8)/Pa by relating the dv/v change to the measured peak dynamic stresses.Our results indicate that a rapid dv/v assessment not only can help facilitate on-site emergency response to earthquakeinduced secondary geological disasters but also can provide a better understanding of the subsurface geological risks under diverse seismic loadings.

Influence of surface roughness on the development of moss-dominated biocrusts on mountainous rock-cut slopes in West Sichuan, China

Since natural restoration combined with artificial auxiliary measures may achieve a relatively rapid restoration effect at a lower cost, it has become an essential measure for the ecological restoration of rock slopes. Previous studies have focused heavily on the relationship between substrate nutrients and water conditions and the development of mosses on the rock surface, but quantitative characterization of substantial effect of rock surface texture(e.g., microrelief) on moss growth is absent. The undulating microrelief on the rock surface can increase the heterogeneity of the microhabitat, which may be an important factor affecting the development of mossdominated biocrusts. In this study, the roughness of rock surfaces, moss coverage and biomass, weight and major nutrient contents of soils within the biocrusts were measured in the western mountainous area of Sichuan Province, Southwest China to further examine the role of rock surface microrelief in the biocrusts. The results showed that three main factors affecting the development of the biocrusts were bryophyte emergence, soil accumulation, and lithology. The presence of moss accelerates soil formation on rock surfaces and lead to the accumulation of nutrients so that all parts of the moss-dominated biocrusts system can develop synergistically. It was found that a microrelief structure with a roughness between 1.5 and 2.5 could gather soil and bryophyte propagules effectively, which may have a strong relationship with the angle of repose. When the roughness is 1.5, the corresponding undulation angle is very close to the theoretical minimum value of the undulation angle calculated according to the relationships between the undulation angle of the protrusion, slope and angle of repose.

Seismic dynamic stability of double-slider rock slopes containing tension cracks

Earthquakes have significant impact on rock slopes,thus studying the seismic stability of double-slider rock slopes containing tension cracks is crucial.We proposed an analysis method on the seismic dynamic slope stability.This method utilizes discrete Fourier transform to decompose real earthquake waves into a combination of harmonic waves.These waves are then used in conjunction with the pseudo-dynamic method and safety factor calculation formula to compute the safety factor.This approach accurately captures the influence of seismic time history characteristics on the dynamic stability of double-slider rock slopes containing tension cracks.The minimum safety factor in the obtained time history curves of the safety factor reflects the most unfavorable state of the slopes under seismic effects.Quantitative analysis is conducted using six sets of actual earthquake ground motion data obtained from the Pacific Earthquake Engineering Research Center’s NGAWest2 ground-shaking record database.The conclusions are as follows:(1)There is an inverse correlation between the average seismic acceleration amplitude and the minimum safety factor.Conversely,the seismic acceleration amplitude standard deviation shows a positive correlation with the minimum safety factor.The global sensitivity of geometric parameters in the slope model is higher than other influencing factors.(2)The proposed dynamic stability analysis method can capture the dynamic characteristics of earthquakes,emphasizing the minimum safety factor of the slope in the seismic time history as a stability indicator.In contrast,the pseudo-static method may yield unsafe results.(3)A safety factor expression considering hydrostatic pressure is proposed.A negative correlation was observed between the height of the water level line and the minimum safety factor.

3D limit analysis of rock slopes based on equivalent linear failure criterion with tension cut-off

Hoek-Brown (HB) failure criterion is widely used to predict the strength of intact or heavily jointed rock mass. For stability analysis of rock slopes governed by the HB failure criterion, the equivalent linearity to Mohr-Coulomb (MC) criterion is often adopted, leading to the well-known equivalent Mohr-Coulomb method (EMCM). Existing studies on EMCM analysis mainly consider the shear strength of rock material, while consideration of the tensile strength is rare. This contradicts the fact that the underlying tensile strength of rock mass has considerable impact on the rock slope stability in real world. In this regard, this paper proposes a limit analysis-based approach that can account for tension in the three-dimensional (3D) stability analysis of HB rock slope. This approach is established on the equivalent linearity of the HB criterion with consideration of tensile strength, known as the equivalent tension cut-off MC method (ETMCM), and using a horn-like 3D mechanism of limit analysis. The safety factor solutions given by the proposed approach are validated by previous studies and numerical results. Parametric studies are conducted to investigate the effect of rock tensile strength on slope stability. Results show that the consideration of tension leads to a more conservative safety factor and a sharper curvature of the failure surface, and these impacts tend to be more obvious with the increases in slope inclination and slope width. Finally, the stability of the HB rock slope under seepage conditions is studied using the proposed approach. The results indicate that the effect of tensile strength is highly remarkable in seepage circumstances.

RockFall软件在铁路边坡危岩失稳运动路径分析中的应用

山区铁路岩质边坡坡体失稳和危岩崩塌等灾害,对线路运营安全有潜在风险。危岩体发生破坏时的运动方式受下部斜坡的物质组成、边坡坡角、危岩体几何形状、岩体性质等的影响,运动距离、运动方式及冲击能量各不相同。采用RockFall软件模拟了丰沙铁路北侧山体危岩体破坏后的运动规律,得出危岩体破坏后沿坡面的运动路径、运动速度、冲击能量等信息,可为崩塌落石防治措施选择提供合理依据。

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.