Ubiquitous Joint Research Articles

The 2022 Stockholm+50 Moment in the Era of a Planetary Crisis: Some Lessons for the Scholars and the Decision-makers

The Stockholm+50 Conference (2-3 June 2022) has been perceived as a low-key affair and a missed opportunity. The moral halo that ushered the world into global environmental consciousness, led by the Prime Ministers of Sweden (Olof Palme) and India (Indira Gandhi) at the first UN Conference on the Human Environment (UNCHE) held in Stockholm (5–16 June 1972) seemed to be missing at the 2022 Stockholm+50 Conference. This historic event coincided with the 30th anniversary of the UN Framework Convention on Climate Change (UNFCCC). The Stockholm+50 event, jointly hosted by Sweden and Kenya, ended as a ubiquitous joint Presidents’ Final Remarks to the Plenary issued by the two host countries. In spite of the call for action by the UN Secretary-General Antonio Guterres to address the “triple planetary crisis” driven by climate emergency, biodiversity loss and pollution and waste, the Stockholm+50 outcome took the shape of ten-point summarized recommendations. It didn’t cause any ripples or resulted in a clarion call that could shake the conscience of peoples and nations to arise for everting the existential planetary crisis. The 2022 Stockholm+50 Moment at best remained a timid acknowledgement of things going terribly wrong in the past fifty years (1972–2022). Yet, no world leader stepped forward to don the mantle “to rescue” the world from the “environmental mess” as urged by the UNSG in his 2 June 2022 inaugural address. The heads of government and delegations seemed to lack the requisite courage befitting the momentous occasion for a decisive course correction in the global environmental regulatory policies, legal instruments and the environmental governance architecture. What would it entail to address the planetary crisis? It brings to the fore some lessons from the 2022 Stockholm+50 Moment that presents an ideational challenge for scholars of International Law and International Relations as well as the UN system, multilateral environmental treaty processes, international institutions and the decision-makers of the sovereign states.

Melbourne Metro Tunnel Project - Numerical Analysis Of Anisotropic Rock Mass For State Library Station

The Metro Tunnel Project is delivering twin nine-kilometre rail tunnels in Melbourne, Australia. In addition to the tunnels, five new underground stations are being constructed. Two of the new stations – State Library and Town Hall – are complex cavern and adit excavations located in Melbourne’s City Centre which will directly connect to the existing City Loop Stations. The State Library station, located predominantly underneath Swanston Street and a busy tram route, was surrounded by a mixture of modern, educational and heritage developments requiring the excavation sequence and primary support to be designed to ensure minimal surface impacts. To simulate the anisotropic rock mass response to the excavation of the State Library Station, FLAC3D numerical analysis was undertaken. The analysis adopted the ubiquitous joint constitutive model approach and was used to assess the performance of the primary lining design and to determine the impacts the predicted ground displacements may have on the surrounding structures.

Probability of failure and factor of safety in the design of interramp angles in a large open iron ore mine

This paper shows the importance of performing probabilistic analyses in open pits, especially for mine planning, which can lead to more efficient ore extraction and meeting the acceptability criteria for safety in mine slopes. Three-dimensional stability analyses were performed to evaluate the future geometry of a large open pit for iron ore extraction in Brazil. The strength parameters of the lithologies were calibrated using ruptures in the pit walls. After determining the factors of safety (FoSs) from the calibrated parameters, probabilistic analyses were performed using the total range of values of each parameter under different field conditions to verify the reliability of the initial analysis. In this sense, it was possible to plot the probability of failure (PoF) and the FoS on the graph of slope height versus slope interramp angle (IRA) for the future pit in each lithology. IRA recommendations are made for two scenarios: (1) the best scenario: dry without ubiquitous joints and (2) the worst scenario: the water table at 10 m depth with ubiquitous joints in the most unfavourable direction. The results show that probabilistic evaluation is an important tool for establishing alert mechanisms in slopes that can be termed stable.

3D Modelling of Excavation-Induced Anisotropic Responses of Deep Drifts at the Meuse/Haute-Marne URL

Understanding the excavation-induced fractured zone (EFZ) around drifts is paramount in the context of the deep geological disposal for nuclear waste since fractures can introduce pathways for the migration of radionuclides. Drifts in the Meuse/Haute-Marne Underground Research Laboratory (URL) have been essentially excavated following the two main directions of major and minor horizontal stresses. Field observations on the two drifts GCS (parallel to major horizontal stress direction) and GED (parallel to minor horizontal stress direction) in the URL show anisotropic shapes of EFZ around drifts through both orientations and anisotropic convergences. These anisotropic responses resulted from the inherent and/or induced anisotropies of the host rock as well as the anisotropic stress field. This study focuses on 3D numerical modelling of excavation-induced anisotropic responses including shape and extent of EFZ, and short-term convergences of drifts. The main assumption is that the failure of claystone material is due to fracturing along weakness planes (ubiquitous joints) and the failure of the rock matrix. The ubiquitous joint failure is represented by perfectly plastic models for both tensile and shear yield functions. Their orientation is determined from the stress state based on the fracture mechanics, which includes tensile, longitudinal splitting and shear (conjugate planes) cracks. The rock matrix is assumed to be elastoplastic with hardening, softening and residual behaviours. Confining pressure dependency for the post-peak behaviour with a brittle–ductile transition is taken into account for the rock matrix. The proposed model is implemented into a commercial numerical software FLAC3D. The main features of the implemented model are shown by the simulation of laboratory triaxial compression tests, as well as field observation within the URL. In particular, comparisons between 3D simulations of GCS and GED drifts with in situ observations shows promising results, which demonstrates advances of present model with respect to existing models.

Deformation Analysis of the Rock Surrounding a Tunnel Excavated through a Gently Dipping Bed

To investigate the deformation and stability of the rock surrounding a tunnel excavated through layered rock, a three-dimensional numerical simulation was conducted to compare and analyze the right line of the YD2K100+560–630 two-stage docking cross-section of the Yuelongmen Tunnel using a ubiquitous joint model. Based on 3-D numerical simulations, the following conclusions were drawn: (1) The excavation on the construction entrance side significantly disturbed the construction exit side, and the exit side was more disturbed in the steeply dipping layer than in the gently dipping layer. (2) The influence of the dip angle of the laminae on the uplift of the tunnel invert was greater than the influence on the tunnel vault settlement when the laminae were oriented perpendicular to the trend of the tunnel and two-stage docking excavation was used. (3) When two-stage excavation was applied to gently inclined laminated rock, there was an obvious disturbance to both the top of the tunnel (less than one time the diameter of the through face; and to the bottom of the tunnel within 0.5 time the diameter of the through face on the side with the stopping construction exit side during the tunnelling process. When tunnel excavation was conducted against the trend of the layer, there was obvious disturbance to the top of the tunnel within 0.5 time the diameter of the through face and to the bottom of the tunnel within one time the diameter of the entrance face) on the construction exit side during the tunnelling process due to the presence of laminae. The excavation on the construction entrance side significantly disturbed the construction exit side. When docking and penetrating layered rock tunnels, priority should be given to docking and penetrating in the direction corresponding to the layers, and temporary support on the exit side should be strengthened to ensure the deformation stability of the surrounding rock mass.

Application of the Slope Coefficient of the Equivalent M–C Criterion in Layered Rock Mass Engineering

The slope coefficient ω is defined based on the insufficiency of the area equivalent method, the slope of the equivalent M–C criterion obtained from the instantaneous equivalent, and the optimal first‐order approximation to reduce the error between the simulated value and the measured value of the surrounding rock and ensure the safety of the project. Different ω conditions are set to obtain multiple equivalent M–C strength parameter combinations. The above combinations are input to the ubiquitous joint model of FLAC3D, and the surrounding rock strength of layered tunnels with different inclination angles (0°, 30°, 45°, 60°, and 90°) is corrected. The results show that (1) after the tunnel excavation is completed, the displacement of key points (e.g., the vault and waist) increases when the slope coefficient is increased and the deviator stress decreases when the slope coefficient is increased. (2) After the area equivalent method is revised, the displacement and the deviator stress are more significantly affected by the inclination of the rock strata than the uncorrected ones, suggesting that the equivalent area can more effectively highlight the anisotropy characteristics of the layered surrounding rock. (3) After the simulation results of the displacement and the deviator stress at the respective key point are comprehensively modified, the optimal slope coefficient corresponding to each rock layer inclination is obtained, and the area is optimized by ensuring reasonableness to reduce the error between the simulated value and the measured value. (4) The layered surrounding rock at a dip angle of 30° is studied. The development of the plastic zone is promoted when the slope coefficient is increased, and the rock shear failure and the joint shear failure occur simultaneously on both sides of its axis.

Rotation of the Stress Tensor in a Westerly Granite Sample During the Triaxial Compression Test

We simulated the spatiotemporal modelling of 3D stress and strain distributions during the triaxial compression laboratory test on a westerly granite sample using finite-difference numerical modelling implemented with FLAC3D software. The modelling was performed using a ubiquitous joint constitutive law with strain softening. The applied procedure is capable of reproducing the macroscopic stress and strain evolution in the sample during triaxial deformation until a failure process occurs. In addition, we calculated focal mechanisms of acoustic emission (AE) events and resolved local stress field orientations. This detailed stress information was compared with that from numerical modelling. The comparison was made based on the 3D rotation angle between the cardinal axes of the two stress tensors. To infer the differences in rotation, we applied ANOVA. We identified the two time levels as the plastic deformation phase and the after-failure phase. Additionally, we introduced the bin factor, which describes the location of the rotation scores in the rock sample. The p values of the test statistics F for the bin and phase effects are statistically significant. However, the interaction between them is insignificant. We can, therefore, conclude that there was a significant difference in the time between the rotation means in the particular bins, and we ran post hoc tests to obtain more information where the differences between the groups lie. The largest rotation of the stress field provided by the focal mechanisms of AE events from the numerically calculated stress field is observed in the edge bins, which do not frame the damage zone of the sample.

Impact of smoking on the incidence and post-operative complications of total knee arthroplasty: A systematic review and meta-analysis of cohort studies.

Osteoarthritis and rheumatoid arthritis are the most ubiquitous joint disorders which cause tremendous loss of life quality and impose an economic burden on society. At present, the treatment options for these two diseases comprise non-operative and surgical treatments, among those total knee arthroplasty (TKA). Various studies have recognized smoking as a significant risk factor for post-operative complications. Therefore, the purpose of this study was to examine the impact of smoking on the incidence and post-operative complications after a TKA by a systematic review and meta-analysis. The research was performed using PUBMED, Cochrane Library and EMBASE, extracting data from thirteen suitable studies and incorporating 2,109,482 patients. Cohort studies evaluating the impact of smoking on TKA with sufficient data were included for the study, and cohort studies without a proper control group and complete data were excluded from the analysis. A fixed-effects or random-effects model was used to measure the pooled risk ratio or hazard ratio with 95% confidence interval (CI). Compared to non-smokers, smokers had a significantly lower incidence of TKA (p < 0.01). However, smokers had a higher incidence of total complications (p = 0.01), surgical complications (p < 0.01), pneumonia (p < 0.01), and revision surgery (p = 0.01). No significant difference in the risk of blood transfusion (p = 0.42), deep vein thrombosis (p = 0.31), pulmonary embolism (p = 0.34), urinary tract infection (p = 0.46), or mortality (p = 0.39) was found between smokers and non-smokers. In conclusion, the study indicated that tobacco has two diametrically opposite effects on TKA patients: (1) Tobacco increases the incidence of surgical complications, pneumonia and revision after TKA; (2) It decreases the overall risk of being a candidate for TKA.

Investigation of Failure Mechanism of Inclined Coal Pillars: Numerical Modelling and Tensorial Statistical Analysis with Field Validations

Analysis of the failure mechanism of inclined coal pillars is one of the complicated issues. The wide variability of dip angles of inclined coal pillars makes it more complex. The asymmetric stress distribution and the tendency of shearing along the bedding planes make the inclined coal pillars to behave differently from the flat coal pillars. There is a need for in-depth investigation of the failure mechanism for addressing the instability problems of the inclined coal pillars. Most of the literature quantifies only the magnitudes of the mean principal stresses by classical statistics. As the stress is a second-order tensor having six independent components, the classical statistics is not appropriate to calculate the mean and variability of the principal stresses at the onset of failure of the pillars. In this paper, a comprehensive analysis is done to understand the complex failure mechanism of the inclined coal pillar using numerical modelling as well as tensorial statistics and validated the results with field measurement data of failure cases. The failure mechanism is analysed by quantification of the characteristics of the inclined coal pillars by the principal-stress magnitude and its orientation, induced at the time of failure. Since the spatial variability of the magnitudes and orientations of the induced principal stresses exist within the inclined coal pillars, the mean induced principal stresses $$\left( {\overline{{\sigma_{1} }} {, }\;\overline{{\sigma_{2} }} {\text{ and }}\overline{{\sigma_{3} }} } \right)$$ are used to quantify the stress states within it. The failure stress states within the coal pillars having different dip angles are generated by the calibrated elasto-plastic numerical modelling with the ubiquitous joint model. Several statistical parameters are calculated to quantify the stress-tensor variability and the correlation among the stress-tensor components. It is found that the correlation coefficients among the shear components increase significantly with the increase of the coal pillar dip angle. Therefore, the inclined coal pillars are highly susceptible to shear failure. The magnitudes, as well as orientations of the mean induced principal stresses within the coal pillars obtained through numerical modelling, are quantified by the tensorial as well as classical statistics. It is found that the magnitude of the mean major induced principal stress $$\left( {\overline{{\sigma_{1} }} } \right)$$ at the time of failure, i.e. the strength of the pillar decreases with the increase of the dip angles. The validation of the results with the actual stress measurement data shows that all the failed pillar cases are correctly predicted by the tensorial statistical approach whereas the classical statistical approach does not effectively predict the actual failed condition of the pillars. The study would help to characterise the behaviour of the inclined pillars and address the instability issues for safe and efficient mining of inclined coal seams.

Effect of Closely Spaced, Non-Persistent Ubiquitous Joint on Tunnel Boundary Deformation: A Case Study from Himachal Himalaya

The stability of an underground tunnel excavated in a jointed rock mass is studied using the field investigation and numerical modelling. This research aims to numerically analyze the rockmass behavior as a function of closely spaced non-persistent joints. For this purpose, the Kainchi-mod Nerchowck twin tunnels (Himachal Pradesh, India) is chosen for the in-depth analysis. The host rock encountered is mainly gray sandstone and maroon sandstone with many closely spaced, non-persistent joints, dipping critically into the tunnel. The detailed rockmass properties were collected from the field and intact rock properties were tested in the laboratory. A series of finite element numerical simulations were conducted based on the filed/laboratory data with different values of joint spacing, including the actual values of field joint spacing. It was found that the extent of deformation above the excavation was predominantly controlled by the joint spacing. The results of this study provide an explicit correlation between geometrical features of the rock mass with the total displacement values around the excavation. The study will help the engineers to design an appropriate support system for heavily jointed rocmkass.

A numerical study on mechanical behavior of jointed rock masses after tunnel excavation

The tunnel in jointed rock masses is prone to be overbroken and then gives rise to collapse, yet the failure modes of jointed rock masses are still poorly understood. This paper investigates anisotropic deformations and failure modes of tunnels in jointed rock masses. For this purpose, five series of numerical models are modeled for a severe tunnel overbreak occurring on the Panlongshan tunnel. The ubiquitous joint model is used to consider the shearing and tensioning effects of the bedding and joint structures. The factors affecting anisotropic deformation and failure of rock masses, such as bedding spacing (s), joint dip angles (θ), and joint spacing (d), are discussed. The results demonstrate that for the stratified rock masses (without joint), the maximum settlement around the tunnel is located at the roof, and the separation of “virtual blocks” along the bedding planes is a basic failure mode; for stratified rock masses containing joints, the maximum deformation surrounding the tunnel appears in the joint position, and failure happens through a combined rotation, sliding, and falling mechanism. Our study can also reveal that with the increase of the number of joints, the plastic zone at the joint positions has a developing tendency towards the deep part. The more complex the joint structures in jointed rock masses are, the more unstable rock masses are formed.

Stability Analysis of Jointed Rock Slope by Strength Reduction Technique considering Ubiquitous Joint Model

In order to study the failure mechanism and assess the stability of the inlet slope of the outlet structure of Lianghekou Hydropower station, the strength reduction method considering the ubiquitous joint model is proposed. Firstly, two‐dimension numerical models are built to investigate the influence of the dilation angle of ubiquitous joints, mesh discretization, and solution domain size on the slope stability. It is found that the factor of safety is insensitive to the dilation angle of ubiquitous joints and the solution domain size but sensitive to the mesh discretization when the number of elements less than a certain threshold. Then, a complex three‐dimension numerical model is built to assess the stability of the inlet slope of the outlet structure of Lianghekou Hydropower station. During the strength reduction procedure, the progressive failure process and the final failure surface of the slope are obtained. Furthermore, the comparison of factors of safety obtained from strength reduction method and analytical solutions indicates that the effect of vertical side boundaries plays an important role in the stability of jointed rock slope, and the cohesive force is the main contribution to the resistant force of vertical side boundaries.

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.

Stability Analysis of Rock Structure in Large Slopes and Open-Pit Mine: Numerical and Experimental Fault Modeling

Deep open-pit mines and large rock slopes expose many diverse rock lithologies and geological structures (e.g., faults, bedding planes) that may reduce the integrity of slopes. Numerical modeling is a powerful tool for simulating these structures; however, there are few guidelines and methods for calibrating/validating and implementing faults in a numerical model. This paper presents a novel laboratory method to calibrate numerical models and highlights the challenges in simulating faults. One of the main issues in reliable modeling of faulted rock structure is the scarcity of experimental analyses in the laboratory under the controlled conditions. Moreover, a comprehensive evaluation of the effect of using the conventional fault modeling methods on the stability of rock structures is required, as well as a benchmarking between theoretical and experimental results. This research combines theory and experiment, to fill the existing gaps, using numerical simulation and laboratory measurements. Using FLAC3D software, the sensitivity and comparative analyses are carried out for the numerical simulations to investigate the stability of rock slopes on large and small scales (overall open-pit slope and bench slope), and the fault zones. The weak zone (WZ), ubiquitous-joint (UJ), and interface (IF) techniques are the widely used methods in the modeling to capture fault slip mechanisms. The factor of safety (FOS) of the slope is monitored upon variation of the design parameters, such as fault and rock mass mechanical properties, fault types, and modeling framework (e.g., mesh density, convergence ratio). In addition, parameters such as shear displacement and shear stress are investigated to deduce the failure mechanism of the studied models. Finally, laboratory tests were performed to calibrate the modeling results and approximate the agreement between theoretical and experimental results. The results of sensitivity analysis showed that choosing an adequately low convergence ratio is critical for estimating FOS. However, beyond a certain convergence ratio, below 10−7, this change is negligible (less than 5%). The results of mesh density sensitivity analysis indicate that the FOS values are insensitive to the mesh density in the WZ method (less than 5% change in FOS), the IF method shows the median sensitivity (5–12% change in FOS), and the UJ method is the most sensitive (FOS values improves by ~ 31%). Comparison between laboratory test and numerical modeling (FOSlab = 1.71, FOSWZ = 1.51, FOSIF = 1.62, and FOSUJ = 1.76) indicates a good agreement between the UJ and IF methods and the laboratory model (~ 3–5% discrepancy). It needs to be mentioned that these analyses/tests are not to favor one method over the other, but rather to emphasize the pros and cons of each within the assumptions of this study.

Assessment of the Strength of Inclined Coal Pillars through Numerical Modelling based on the Ubiquitous Joint Model

The inclined coal pillars, formed during the underground extraction of the inclined coal seam, are different from the flat coal pillars due to the high strength anisotropy of the inclined bedded rock, and the asymmetrical stress distribution. To ease the manoeuvring of the men and machinery in the inclined coal mine, the pillars are developed along the apparent dip. Thus, the pillars become rhombus-shaped with acute-angled corners which crush rapidly due to the high stress concentration. No suitable formula is found to estimate the strength of the inclined coal pillar that incorporates all these factors. Thus, the use of the available coal pillar strength formulae may endanger the extraction of the inclined coal seams. This study elucidates the procedures to estimate the strength of the inclined coal pillars by the numerical modelling technique. The ubiquitous joint model is used to simulate the shearing characteristics of the inclined strata. The parametric study shows that the strength of the inclined coal pillars decreases with the increase of the dip of the coal seams. It is also obtained that the strength of the pillars decreases with the decrease of the value of the acute angle of the corners. The peak stress distribution and the strain accumulation over the inclined pillars at the time of failure are plotted in three-dimensional graphs which show the asymmetrical characteristics of the inclined coal pillars. The analysis of variance shows that the dip of the coal seams and the acute angles of the corners have a statistically significant effect on the strength of the inclined coal pillars. Based on the results of the simulation, the best fit relation is established by the multivariate non-linear regression technique to estimate the strength of the inclined coal pillars. The coefficient of determination (R2) and the root mean square error of the model are obtained as 0.92 and 0.065, respectively. The validation of the developed model has been carried out by the stable and failed inclined pillar cases of different underground inclined coal mines in India. Comparisons of the safety factors, obtained from the developed model and the flat pillar strength formula, indicate that the flat pillar strength formula overestimates the strength of the inclined coal pillars. The developed model can be used to design the inclined coal pillars for safe extraction of inclined coal seams.

Analytical Prediction of the Shear Behaviour of Rock Joints with Quantified Waviness and Unevenness Through Wavelet Analysis

We present an analytical model for the shear behaviour of a rock joint with waviness and unevenness. The waviness and unevenness of a natural joint profile are quantitatively separated through wavelet analysis. The critical waviness and critical unevenness of a joint profile are subsequently determined. The degradation process of each-order asperity is predicted by considering the role of plastic tangential work in shear, by which the sheared-off asperity area and the dilation angle are quantified. Both the dilation angles of critical waviness and critical unevenness decay, as plastic tangential work accumulates. The analytical predictions are compared with the experimental data from direct shear tests on both regular- and irregular-shaped joints. Good agreement between analytical predictions and laboratory-measured curves demonstrates the capability of the developed model. Therefore, the model is capable of assessing the stability of rock-engineering structures with ubiquitous joints.

Numerical analysis of tunneling in slates with anisotropic time-dependent behavior

Slate is a metamorphic rock often contains a dense foliated texture called slaty cleavages or schistosities. The ease of split along the schistosities weakens the slate and its resistance to weathering and erosion. For the tunnel excavation in slate formations, it is common to observe anisotropic deformation; in addition, the deformation caused by stress release also shows time-dependent behavior. Hence, anisotropic and time-dependent behaviors must be taken into account to more properly estimate the deformation of tunnel excavation in slate formation. In this paper, the computer software FLAC with the ubiquitous-joint (UBI) model and the Burger-creep viscoplastic (CVISC) model was adopted for the analysis. To more efficiently obtain relevant parameters of those models, back calculations were performed by the automatic iterative tool Quick Macro. Coupling these two models, the new hybrid UBI/BUR model was developed and implemented as a UDM program, which can be applied for the FLAC analyses. The new model was calibrated by the monitoring data from a slate tunnel excavation project, i.e., the Wanta-Sunglin Project in Taiwan, then applied for detailed analyses. The results indicate that the hybrid model developed in this study is better than the conventional models, and can be used for the simulation of tunnel excavation in anisotropic time-dependent slate formations.

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.

Constitutive model for inherent anisotropic rocks: Ubiquitous joint model based on the Hoek-Brown failure criterion

This paper proposes an elasto-perfect plastic constitutive model (called Jhoek) linking two failure criteria to model the sliding and non-sliding failure modes of anisotropic rocks. For non-sliding failure mode, modified Hoek-Brown criterion with an explicit function of the rock parameter mi with orientation β is applied, while the single plane of weakness is simulating the sliding failure mode. Published experimental datasets of anisotropic rocks are used to validate this model. Jhoek could predict failure envelopes of rock samples under triaxial loading conditions at different orientation angles. Besides that, Jhoek model shows sensitivity to the intermediate principal stress in 3-dimensional cases.

Prediction of Mud Pressures for the Stability of Wellbores Drilled in Transversely Isotropic Rocks

Serious borehole instability problems are often related to the presence of weakness planes in rock formations. In this study, we investigated the stability of wellbores drilled along a principal direction and parallel to the weakness planes. We used three different strength criteria (weakness plane model, Hoek and Brown and Nova and Zaninetti) to calculate the mud pressures to avoid slip and tensile failure along the weakness planes. We identified the orientation of the weakness planes that generate the most critical slip condition as a function of the friction angle of the planes. We also identified the range of orientations of the weakness planes that corresponds with the lower mud pressure window. We confirmed the validity of the proposed relationships with comparative stability analyses by using analytical solutions and numerical simulations (Ubiquitous Joint Model, FLAC). We found that the mud pressures calculated with the Hoek and Brown criterion show a particular trend, which cannot be predicted by the weakness plane model. We provided two normalized stability charts to predict mud pressures to prevent slip along the weakness planes in the critical slip condition. Finally, we corroborated our findings by simulating the stability of wellbores drilled in the Pedernales Field (Venezuela) and in oil fields located in Bohai Bay (China).