Low Safety Factor Research Articles

Numerical investigations of rock bridge effect on open pit slope stability

Abstract In this study, the effect of rock bridges on rock slope stability was investigated by incorporating non-persistent joint networks in numerical models, and the critical profiles of an open pit mine were analysed. Parallel deterministic networks of infinite and finite lengths, ubiquitous joint network model and Veneziano joint network model were used in order to simulate the rock fractures. Materials were modelled based on the generalised Hoek―Brown and equivalent Mohr–Coulomb failure criteria. The parallel deterministic infinite and the ubiquitous joint network models produced lower safety factors. The introduction of rock bridges along discontinuity planes in the parallel deterministic network and Veneziano joint network models significantly contributed to the stability and strain distribution, which should be considered in stability analysis of rock mass in open pit by rock slope practitioners. The results show the significance of joints in hard rock behaviour and the joints should be included in order to attain practical and realistic simulations.

Concomitant synaptic impairment of neuromuscular junction and axonal polyneuropathies

Peripheral axonal neuropathy (PAN) is a progressive axonopathy marked by loss of motor, sensory and autonomic fibers with reduced stability of neuromuscular transmission. In a previous work in demyelinating neuropathies, we showed that repetitive nerve stimulation (RNS) induced significant decremental responses in amplitude and area of muscle action potentials (CMAPs). In this work we studied prospectively, 111 diagnosed patients (clinically and electrophysiologically) with PAN, by performing RNS to assess the degree of weakened synaptic transmission at the NMJ and find out whether it is one of the aspects of PAN. Males constituted 61 patients while females are 50 with a mean age of 56 years. Nerve conduction study (NCS) and Electromyogram (EMG) revealed that patients with sensorimotor axonal neuropathy (n75), motor (n28) and the least (n8) were those with pure axonal sensory neuropathy. RNS of both axillary, musculocutaneous and Left Ulnar nerves, showed 87%, 80% and 28% decrements in amplitude and 91%, 84% and 43% in area for axillary, musculocutaneous and Left Ulnar nerves, respectively in 85 patients. This would suggest lower safety factors in neuromuscular transmission. The proximal nerves were significantly more sensitive in revealing the deficit than the distal ulnar nerve. The highly significant decrements of CMAPs in this study, could be attributed to disorders of peripheral nerves at the presynaptic level, induced by axonal loss. This leads to deficient exocytosis of Acetylcholine at the NMJ. Hence, this lack of availability of neurotransmitter would not be secure enough to stimulate the nicotinic postsynaptic receptors.

Mapping of power deposition zone of electron Bernstein waves externally excited in tokamak plasmas

In toroidal plasmas, electron Bernstein (EB) waves mode-converted from X waves at the upper hybrid resonance (UHR) layer propagate toward the higher field side and are cyclotron-damped away at Doppler shifted frequency before arriving at the electron cyclotron resonance (ECR) layer. Resulting power deposition profile depends on local density, temperature and field profiles and is usually analyzed using the ray tracing technique for EB wave propagation and absorption in inhomogeneous magnetized plasmas. In axisymmetric tokamak plasmas, the ray tracing equation of EB waves can be cast into the form of equation of particle motion in a potential field. The particle trajectory and its momentum correspond to the wave trajectory and the refractive index, respectively. The potential field reflects the dispersion characteristics of EB waves, that is, the perpendicular refractive index strongly increases as the waves approach to the ECR layer from the lower field side, making a deep trench of potential along the ECR layer. Therefore the EB waves perpendicularly approach the ECR layer, which enable us to estimate the parallel refractive index and the parallel velocity of resonance electrons near the ECR layer. Thus, possible power deposition zone can be mapped and the associated current drive efficiency is roughly estimated directly from the information on wave frequency and plasma profiles without ray tracing calculations (direct mapping). The mapped zone, in the case of a moderately over dense plasma, is shown to be coincident with the ray tracing results for both XB and OXB schemes of mode conversion. In the cases of highly over dense, low safety factor and low aspect ratio plasmas, ω/Ωce is rather close to two at the UHR layer and the second harmonic cyclotron damping can take place along the ray trajectory just after OXB mode conversion, depending on the parameters. Here, ω is the wave frequency and Ωce is the local cyclotron frequency. It is shown that direct mapping also works in this case as well. The direct mapping technique is based on above picture of EB wave propagation and absorption, and is useful to guide the ray tracing analyses and cross-check the ray tracing results.

Probabilistic stability analyses of layered excavated slopes

The random finite-element method (RFEM) is employed to study the effect of vertical spatial soil variability on the stability of layered excavated slopes. Particular emphasis of the paper is on the critical or ‘worst-case’ vertical spatial correlation length, at which the probability of slope failure reaches a maximum. The RFEM results indicate that layered slopes with a relatively low mean factor of safety or a relatively high coefficient of variation of soil strength are most likely to display the ‘worst-case’ phenomenon. The ‘worst-case’ phenomenon is explained by observing the failure mechanisms in layered soils where the critical spatial correlation length optimises the number of horizontal paths of weaker soil available for the mechanism to pass through.

A finite element study of welded aluminum shoe-base light pole details

Cantilevered light poles are examples of lightly damped, slender structural systems subjected to wind (cyclic) loads making fatigue life analysis necessary. Experimental and numerical studies performed on welded aluminum shoe-base details often found on cantilevered light poles included thirty-five fatigue tested in the Structures Laboratory of the University of Akron that provided the basis for the analytical study described in this article. Twenty-two of the thirty-five specimens failed and the remainder taken as run-outs. In an attempt to understand the fatigue behavior of the welded aluminum details, parametric studies using ANSYS examined bolt circle diameter, fillet weld leg-size, socket depth, and tube thickness. An increase in the bolt circle diameter of 27% results in about a 50% increase in the local stress adjacent to the fillet weld, and a reduction in tip deflection. A 50% increase in the fillet weld leg-size from 6.35 mm (0.25 in.) to 9.5 mm (0.375 in.) corresponds to about a 14% increase in the local stress. Increasing the shoe-base socket depth by 51% leads to an increase of 36% in the local stress. An increase in the thickness of 40% from 6.35 mm (0.25 in.) to 8.9 mm (0.35 in.) reflects a 60% increase in local stress. The analysis demonstrated that the lowest factor of safety was observed adjacent to the toe of the fillet weld. Thermographic measurements confirmed the existence of a hot spot near the weld toe on the tube.

The Hay Inclined Plane in Coalbrookdale (Shropshire, England): Analysis through Computer-Aided Engineering

This article analyzes the ‘Hay inclined plane’ designed by the English engineer and entrepreneur William Reynolds and put into operation in 1792 to facilitate the transport of vessels between channels at different levels using an inclined plane. To this end, a study of computer-aided engineering (CAE) was carried out using the parametric software Autodesk Inventor Professional, consisting of a static analysis using the finite-element method (FEM) of the 3D model of the invention under real operating conditions. The results obtained after subjecting the mechanism to the two most unfavorable situations (blockage situation of the inertia flywheel and emergency braking situation) indicate that, with the exception of the braking bar, the rest of the assembly is perfectly designed and dimensioned. In particular, for the blockage situation, the point with the greatest stress is at the junction between the inertia flywheel and the axle to which it is attached, the maximum value of von Mises stress being at that point (186.9 MPa) lower than the elastic limit of the cast iron. Also, at this point the deformation is very low (0.13% of its length), as well as the maximum displacement that takes place in the inertia flywheel itself (22.98 mm), and the lowest safety factor has a value of 3.51 (located on the wooden shaft support), which indicates that the mechanism is clearly oversized. On the other hand, the emergency braking situation, which is technically impossible with a manual operation, indicates that the braking bar supports a maximum von Mises stress of 1025 MPa, above the elastic limit of the material, so it would break. However, other than that element, the rest of the elements have lower stresses, with a maximum value of 390.7 MPa, and with safety factors higher than 1.7, which indicates that the mechanism was well dimensioned.

Three-dimensional analysis of excavation face stability of shallow tunnels

Several studies have been focused on minimizing construction risks of underground works. However, additional studies regarding excavation face stability, which has great influence on global performance of shallow tunnels, will offer more security criteria to engineers. The aim of this work is to compare the results from an existing analytical and a numerical method in assessing the behavior of the excavation face subjected to different overburden depth and ground conditions. Typical parameters of shallow soils were considered for all simulations. The analytical method was applied to assess the excavation face pressure for different tunnel covers. Numerical methods were applied using ABAQUS 3D® finite elements software, which considered a continuous, homogeneous medium in a 6-meter-wide tunnel excavated at different depths, and assessed the need for support and stabilization pressure on the face. Furthermore, the influence of a well on the excavation line was also considered for such assessment. As result, excavation face was defined as stable by the analytical method; nevertheless, it was obtained a very low safety factor. On the other hand, results from the numerical method showed the need to apply pressure on the excavation face. Those limit support pressure values at tunnel face showed a direct correlation with the increase of cover-to-tunnel diameter ratio. Finally, the numerical method showed a more realistic result when compared with the analytical method.

Synergic effects of biochar and polyacrylamide amendments on the mechanical properties of silt loam soil under coastal reclamation in China

Recent surveys have reported severe erosion and slope collapse caused by a combination of the poor structure of silt loam and heavy rainfall in reclaimed areas of China. Biochar and polyacrylamide (PAM) have been widely used as amendments to protect soil from degradation and enhance plant growth. However, few studies have focused on their synergic effects on soil mechanical properties. In this study, biochar and PAM were incorporated into silt loam at rates of 0%, 2%, and 5% and 0‰, 0.4‰, and 1‰, respectively, to investigate the extent to which biochar and PAM additions affect soil consistency limits and shear strength and to evaluate the slope reliability under natural conditions. The results show that the plastic limit (PL) and liquid limit (LL) were significantly enhanced by amendments of 5% biochar and 1‰ PAM. Soil consistency limits were significantly correlated with the soil 3D fractal dimension (FD), μ-CT porosity and electrical conductivity (EC). Amendment of coastal silt loam soil with biochar resulted in decreased cohesion. The application of PAM reduced the negative effect of biochar on cohesion and considerably increased the cohesion value of the silt loam. The results of the slope stability analysis were closely related to the shear strength parameters. Biochar-amended silt loam soil in the coastal area exhibited a much lower factor of safety (FS) compared with the control soil, irrespective of the level of the water and the slope angle within the slope system. A PAM amendment in coastal silt loam soil increased the FS significantly (P < 0.05) and minimized the negative effects on the FS that was caused by the biochar amendment. Therefore, biochar and PAM could be applied to silt loam soil together to improve soil quality to enhance the slope stability under coastal reclamation in China.

Tokamak parameter regimes with low toroidal momentum diffusivity

The strong, sharp flow structures that are seen frequently in tokamak cores, and large amplitude spontaneous global toroidal rotation are both surprising in light of current theories where toroidal flow evolution is dominantly diffusive. Mechanisms for spontaneously generating strong poloidal shear flows have been extensively investigated, but these processes were thought not to apply to toroidal flows. We confirm, however, that there is a regime with near-zero toroidal momentum diffusivity, where toroidal flow structures are spontaneously generated, as shown in earlier global gyrokinetic simulations. This allows strong rotation with negligible applied external torque, and the regime where this occurs is also favourable for strong turbulence stabilisation by rotation. The transition to low momentum diffusivity occurs for tight aspect ratio, low safety factor and at low levels of heat flux, in agreement with a simple zero-dimensional model for the flow–turbulence interaction.

Insights into the recent Kotropi landslide of August 2017, India: a geological investigation and slope stability analysis

The paper describes the recent devastating landslide of Kotrupi, Himachal Pradesh in India which had claimed many human lives and properties along its course on 13 August 2017. This event was the third reactivation of the slide as per data available. The study for this landslide involves a preliminary investigation of the site and comparison of pre- and post-event slope stability analysis. Other than rainfall, the combined effect of differential weathering rate of the debris and soil layers, low material strength, and the presence of a fault zone was found to be the primary cause of instability. The analysis was carried out with the geotechnical investigation and numerical modeling with the help of finite element model-based Phase 2 simulator. The significant findings of this paper include numerical simulation of pre- and post-event slide as stated under unsaturated and saturated condition. The study finds a low factor of safety of the present slope. The unstable condition of the slope may trigger another event of the same intensity shortly.

The Influence of Water Level Fluctuation Reservoir Stability of the Earth Dam

A large dam construction failure which caused in reservoir by ground water level fluctuations very extreme. Construction of earth dam failures can be avoided if the conditions of the dam slopes are in stable condition. This research discusses the influence of reservoir water level fluctuations on the stability of the earth dam models in the laboratory by analyzing the stress-strain and deformation using PLAXIS program version 8.2. Implementation of the research done in stages which include testing properties of the building blocks of the model earth dam and physical modelling in laboratory experiments with variations in soil types, namely: a mixture of 90% sand-silt 10%, and 80% sand-silt 20% and 100% soil. The slope of the model on the upstream 1: 1 and 1: 1.5, while in the downstream dam slope was maintained constant 1:1. Instrumentation used includes 6 soil moisture sensors with three accuracy of 2%, 1 deformation pressure sensor with detection range, 3 dial gauges, capacity level 1 meter with accuracy 2%. Furthermore, analysis on the stability of the earth dam modelling in laboratory tests using PLAXIS version 8.2. The results of this analysis are total displacement Plaids, total stress, total strain, pour water pressure and the safe rate (safety factor). Based on the review of the three nodal, at upstream slope of the dam are same, the effective value of the largest stresses occur in the model 10% soil 90% sand with the upstream slope 1:1, that is equal to -16.52 kN / m2 lowering phase. Total value of largest stresses occur in the model 20% soil 80% sand with the upstream slope 1:1, that is equal to -12.89kN/m2 phase rising 3 phase displacement (vertical displacements, the total displacements, the total incremental displacements and incremental strains), the largest value occurs in the model 100% of the land, the vertical displacements 8.12 x10−6 m, the total large displacements 3.92 x 10−5 m, 1.43 x 10−5 m total incremental displacements and incremental strains for-1.75 x 10−2. Lowest safety factor (critical condition) due to raising and lowering of water level in the upstream occurred at a slope 1:1 at 1.4710.

Kink instabilities of the post-disruption runaway electron beam at low safety factor

Realization of a high-current (approaching 1 MA) post-disruption runaway electron (RE) beam in DIII-D yields controlled access to very low edge safety factor (qa) conditions. This enables unique observation and study of low-order kink instabilities in post-disruption plasmas where the current is carried entirely by relativistic REs. The conventional external kink stability boundary (in terms of qa and internal inductance, ℓi) is found to accurately predict the operational space of the RE beam, with qa limited to ≈2. Kink instabilities appear with a characteristic growth rate of a few tens of microseconds (which is comparable to the Alfven time) and ultimately cause complete loss of the RE population on a similar time-scale. This characteristic RE loss time is significantly faster than observations away from the qa ≈ 2 stability limit and implies both higher peak heat loading but also less chance of destructive magnetic to kinetic energy conversion via RE beam regeneration. With large enough kink amplitude no RE beam regeneration is observed, indicating the magnetic to kinetic energy conversion was inhibited. Instability structure analysis reveals that early instabilities at high qa () are likely internal or resistive kinks (at higher poloidal mode number), while at qa ≈ 2 the most destructive instabilities are either internal or external kinks with low-order poloidal mode number (m = 2). The HXR loss magnitude is found to be proportional to the perturbed magnetic field and exhibits a helical spatial pattern. These observations are novel for present-day tokamaks yet will potentially be very common in high current tokamaks such as ITER, where predicted RE beam equilibrium evolutions cross the qa ≈ 2 stability boundary.

Evaluation of Slope Stability Considering the Preservation of the General Patrimonial Cemetery of Guayaquil, Ecuador

Inefficient blasting techniques and poor closure management of the old quarry that existed during the 1970s in the area of the actual General Patrimonial Cemetery of Guayaquil resulted in an almost vertical slope of approximately 50 m in height and an intense induced fracturing that weakened the rock mass. This led to the loss of stability and increased material detachment, which damaged the infrastructure of the graveyard representing a risk to visitors and workers. The aim of this research is to evaluate the slope stability through a geotechnical analysis that allows decision-making to recover and preserve the safety of the area. In this work, we used structural measurements and observations made in the field, as well as a three-dimensional model of the slant generated by photographs taken by a drone. Slope Mass Rating (SMR) and Chinese Slope Mass Rating (CSMR) rankings were used to evaluate stability, susceptibility to rockfall was determined using a theoretical–practical procedure, and the safety factor was calculated using the Morgenstern–Price method. The analysis of the geomechanical classifications yielded a low stability value of the slope, which was in accordance with the high susceptibility to rockfall and with the low safety factor. Based on these results, we recommend the application of systematic bolt and shotcrete for stabilization.

Influence of root suction on tensile strength of Chrysopogon zizanioides roots and its implication on bioslope stabilization

Root tensile strength is an important factor controlling the performance of bio-slope stabilization works. Due to evapotranspiration and climate factors, the root moisture content and its suction can vary seasonally in practice and may not equal soil suction. The influences of suction and root moisture contents were investigated on Chrysopogon zizanioides (vetiver grass) root tensile strength. The root specimens were equilibrated with moist air in different suction conditions (0, 10, 20, and 50 kPa), prior to root tension tests. The root-water characteristic curve or relationship between root moisture and suction, was determined. The increase in suction resulted in decreased tensile strengths of the grass roots, particularly those with diameter of about 0.2 mm, which constituted 50.7% of all roots. For 1 mm roots, the tensile strength appeared to be unaffected by suction increase. The average root tensile strengths were used to estimate the root cohesion in slope stability analysis to find variation of safety factors of a bioengineered slope in different suction conditions. The analysis showed that the critical condition of slope with the lowest factor of safety would happen when the soil suction was zero and the root suction was high. Such condition may occur during a heavy rain period after a prolonged drought.

New insights on the cardiac safety factor: Unraveling the relationship between conduction velocity and robustness of propagation

Cardiac conduction disturbances are linked with arrhythmia development. The concept of safety factor (SF) has been derived to describe the robustness of conduction, but the usefulness of this metric has been constrained by several limitations. For example, due to the difficulty of measuring the necessary input variables, SF calculations have only been applied to synthetic data. Moreover, quantitative validation of SF is lacking; specifically, the practical meaning of particular SF values is unclear, aside from the fact that propagation failure (i.e., conduction block) is characterized by SF < 1. This study aims to resolve these limitations for our previously published SF formulation and explore its relationship to relevant electrophysiological properties of cardiac tissue. First, HL-1 cardiomyocyte monolayers were grown on multi-electrode arrays and the robustness of propagation was estimated using extracellular potential recordings. SF values reconstructed purely from experimental data were largely between 1 and 5 (up to 89.1% of sites characterized). This range is consistent with values derived from synthetic data, proving that the formulation is sound and its applicability is not limited to analysis of computational models. Second, for simulations conducted in 1-, 2-, and 3-dimensional tissue blocks, we calculated true SF values at locations surrounding the site of current injection for sub- and supra-threshold stimuli and found that they differed from values estimated by our SF formulation by <10%. Finally, we examined SF dynamics under conditions relevant to arrhythmia development in order to provide physiological insight. Our analysis shows that reduced conduction velocity (Θ) caused by impaired intrinsic cell-scale excitability (e.g., due to sodium current a loss-of-function mutation) is associated with less robust conduction (i.e., lower SF); however, intriguingly, Θ variability resulting from modulation of tissue scale conductivity has no effect on SF. These findings are supported by analytic derivation of the relevant relationships from first principles. We conclude that our SF formulation, which can be applied to both experimental and synthetic data, produces values that vary linearly with the excess charge needed for propagation. SF calculations can provide insights helpful in understanding the initiation and perpetuation of cardiac arrhythmia.

Stability of bioreactor landfills with leachate injection configuration and landfill material condition

In this study, the design factors of bioreactor landfill were investigated using the coupled leachate-infiltration and slope-stability analyses for various conditions of leachate injection, subgrade, and landfill waste. The factor of safety (FS) decreased with leachate injection where larger and faster reduction of FS was observed for higher injection pressure. The upper-placed injection pipes within landfill induced larger wet zone. The number of injection pipe indicated some effect on FS for the lower-placed case. The optimum location of injection pipes was at heights above Y/H = 0.33. The highest location of injection pipes should be identified considering landfill property and geometry conditions. Shallower and smaller slip surface within landfill was formed for strong subgrade whereas deeper, larger slip surface with lower FS was formed for soft subgrade. For low-compaction landfills, leachate injection reached the steady state and perched leachate was formed. The values of FS for high- and low-compaction cases were similar for soft subgrade indicating that the compaction of landfill waste does not affect the overall stability of landfill significantly for soft subgrades.

The influence of soil plasticity on the seismic performance of bridge piers on caisson foundations

This paper investigates the role of soil plasticity on the seismic performance of bridge piers founded on cylindrical caissons through a numerical study where the geometrical and mechanical properties of the caisson and the pier, as well as the weight of the deck, are varied. Numerical models of the soil-caisson-pier-deck systems are subjected to six real acceleration time histories differing in frequency content, strong-motion duration and intensity. Three-dimensional coupled dynamic analyses are carried out in the time domain in terms of effective stresses, assuming an undrained response for the foundation soils. The studied systems are designed to be characterised by the same safety factors under static vertical loads, to evaluate the seismic performance of different systems endowed with similar mobilised shear strength, and by a low pseudo-static factor of safety to promote the activation of plastic mechanisms during seismic shaking. To reproduce the initial state of stress around the caissons, the effects induced by the construction stages are also simulated in the analyses through a simplified procedure.Seismic performance of the systems is evaluated comparing the maximum and the permanent deck drift ratios with corresponding threshold values related to ultimate limit states. It is shown that seismic performance is strongly related to the ratio between the fundamental periods of the flexible-base system and the soil, as well as to the strong motion duration. The range of systems and input properties for which soil plasticity is significant is identified, thus avoiding excessive overestimates of earthquake-induced displacements and inertial forces on the superstructure.

A hybrid Monte Carlo-Simulated Annealing approach for reliability analysis of slope stability considering the uncertainty in water table level

Slope stability analysis is one of the most challenging problems in geotechnical engineering. Due to the uncertainty involved in the problem, probabilistic methods are recently utilized to estimate the probability of slope failure. In this study, the slope stability is presented as an optimization problem and the Simulated Annealing (SA) method is used to identify the slip surface with the minimum safety factor. The SA algorithm is then integrated with the Monte Carlo sampling method to calculate the probability of slope failure. Next, the groundwater level is added to the problem formulation as a random variable to model the uncertainty for cases where the groundwater table is not accurately determined. The results of the analysis showed that for slopes with low safety factors, the uncertainty of the groundwater table worsens the condition and increases the failure probability. Moreover, the parametric study showed that the insufficient understanding of groundwater level distribution and the assumption of uniform distribution further increases the failure probability. The results of this study are presented in the form of a probability curve against the groundwater table. This presentation has practical applications in real projects.

Geo-Environmental and Structural Problems of the First Successful True Pyramid, (Snefru Northern Pyramid) in Dahshur, Egypt

Significantly, Snefru northern pyramid is the first successful true complete Pyramid was built in Egypt. It has suffered from different kinds of geo-environmental impact and other mechanical and dynamic actions; aspects of structural deficiency and building material decay are recorded and monitored. The scope of this pilot study is to ensure the structure stability and weathering vulnerability of the building materials of Snefru northern pyramid under different environmental, geotechnical and seismic loading conditions. It has been achieved through the following steps: (1) Evaluation of the building materials; includes the integrated petrography study, petro-physical and geo-mechanical testing (2) Estimations of relevant factors affecting these building materials (3) integrated modeling of the pyramid geo-environment conditions. The present study reveals that the Snefru pyramid is considered the only composite pyramid structure, which is composed of local Dolomitic sandstone body blocks which had been quarried from Dahshur plateau, and joining with pure hydraulic lime mortars and covered with imported casing limestone layers from Tura Formations. Stripped from its limestone casing, this pyramid reveals the reddish sandstone used to build its core. This explains its modern-day name, the red Pyramid. The detailed analytical study proved that this important monument present poor engineering properties and low safety factors for both static and seismic loading. The present study indicates the dependence of the mechanical properties on the petro-physical and the geochemical properties of the studied construction materials. Modeling the properties indicates a reliable correlation between the different parameters. Consequently a well-focused strengthening and retrofitting program is deemed necessary.

Probabilistic assessment of rock slopes stability using the response surface approach – A case study

This paper examines the stability condition of a jointed rock slope in the south western region of Saudi Arabia using deterministic and probabilistic approaches, under both dry and wet conditions. The study area is characterized by complex geology in rugged terrains. The stability analysis is carried out using the code FLAC3D to generate a 3-dimensional, ubiquitous joint model, to determine the influence of the dominant, unfavourable discontinuity orientation with respect to the slope face. The deterministic analysis is first implemented using the mean values of the selected random variables, namely the dip, dip direction and friction angle of the dominant discontinuity set, and the stability condition is assessed with a factor of safety based on the classical frictional joint constitutive model. A Box-Behnken design (BBD) approach is then adopted to create the surface response function as a second order polynomial for the factor of safety. To do so, fifteen FLAC3D models are generated in accordance with the BBD. Based on this, 10,000 simulations of different slope realizations are carried out using Monte-Carlo simulation technique, and the probability of unsatisfactory of performance of the rock slope is assessed. It is shown that the probabilistic approach provides more insight and confidence in the stability condition of the rock slope, both under dry and steady state heavy rainfall conditions. A discussion is presented on the significance of accepting lower safety factors when heavy rainfall conditions are encountered.