Department of Civil Engineering, Universitas Katolik Parahyangan, Bandung, 40141, Indonesiaof loose sand with fungus

This article presents an innovative method of bio-mediated soil improvement for increasing the shear strength of loose sand.The improvement is realized by mixing the loose sand with the inoculum of Rhizopus oligosporus,a kind of fungus widely used in food industry for making Indonesian tempeh.The objective of this article is to investigate the performance and mechanism of mixing tempeh inoculum as a binding agent of loose sand particles.The inoculum dosage,water content of loose sand,and curing time were examined for identifying the increment of unconfined compressive strength(q_u)of the samples.The results showed that q_u of the treated samples increased when the inoculum dosage was elevated.It shows that 5.24%inoculum could yield 68 kPa of q_u,and 5%water content and 3 d curing time produced the maximum q_u.Moreover,the mechanism of hypha and mycelium in binding the soil particles was clearly observed using a digital microscope and scanning electron microscope.

Liquefaction susceptibility and deformation characteristics of saturated coral sandy soils subjected to cyclic loadings-a critical review

Coral sandy soils widely exist in coral island reefs and seashores in tropical and subtropical regions.Due to the unique marine depositional environment of coral sandy soils,the engineering characteristics and responses of these soils subjected to monotonic and cyclic loadings have been a subject of intense interest among the geotechnical and earthquake engineering communities.This paper critically reviews the progress of experimental investigations on the undrained behavior of coral sandy soils under monotonic and cyclic loadings over the last three decades.The focus of coverage includes the contractive-dilative behavior,the pattern of excess pore-water pressure(EPWP)generation and the liquefaction mechanism and liquefaction resistance,the small-strain shear modulus and strain-dependent shear modulus and damping,the cyclic softening feature,and the anisotropic characteristics of undrained responses of saturated coral sandy soils.In particular,the advances made in the past decades are reviewed from the following aspects:(1)the characterization of factors that impact the mechanism and patterns of EPWP build-up;(2)the identification of liquefaction triggering in terms of the apparent viscosity and the average flow coefficient;(3)the establishment of the invariable form of strain-based,stress-based,or energy-based EPWP ratio formulas and the unique relationship between the new proxy of liquefaction resistance and the number of cycles required to reach liquefaction;(4)the establishment of the invariable form of the predictive formulas of small strain modulus and strain-dependent shear modulus;and(5)the investigation on the effects of stress-induced anisotropy on liquefaction susceptibility and dynamic deformation characteristics.Insights gained through the critical review of these advances in the past decades offer a perspective for future research to further resolve the fundamental issues concerning the liquefaction mechanism and responses of coral sandy sites subjected to cyclic loadings associated with seismic events in marine environments.

Nonlinear Study on the Mechanical Performance of Built-Up Cold-Formed Steel Concrete-Filled Columns under Compression

Given their numerous functional and architectural benefits,such as improved bearing capacity and increased resistance to elastic instability modes,cold-formed steel(CFS)built-up sections have become increasingly developed and used in recent years,particularly in the construction industry.This paper presents an analytical and numerical study of assembled CFS two single channel-shaped columns with different slenderness and configurations(backto-back,face-to-face,and box).These columns were joined by double-row rivets for the back-to-back and box configurations,whereas they were welded together for the face-to-face design.The built-up columns were filled with ordinary concrete of good strength.Finite element models were applied,using ABAQUS software,to assess mechanical performance and study the influence of assembly techniques on the behavior of cold-formed columns under axial compression.Analytical approaches based on Eurocode 3 and Eurocode 4 recommendations for un-filled and concrete-filled columns respectively were followed for the numerical analysis,and concrete confinement effects were also considered per American Concrete Institute(ACI)standards for face-to-face and box configurations.The obtained results indicated a good correlation between the numerical results and the proposed analytical methodology which did not exceed 8%.The failure modes showed that the columns failed due to instabilities such as local and global buckling.

Extended wet sieving method for determination of complete particle size distribution of general soils

The traditional standard wet sieving method uses steel sieves with aperture?0.063 mm and can only determine the particle size distribution(PSD)of gravel and sand in general soil.This paper extends the traditional method and presents an extended wet sieving method.The extended method uses both the steel sieves and the nylon filter cloth sieves.The apertures of the cloth sieves are smaller than 0.063 mm and equal 0.048 mm,0.038 mm,0.014 mm,0.012 mm,0.0063 mm,0.004 mm,0.003 mm,0.002 mm,and 0.001 mm,respectively.The extended method uses five steps to separate the general soil into many material sub-groups of gravel,sand,silt and clay with known particle size ranges.The complete PSD of the general soil is then calculated from the dry masses of the individual material sub-groups.The extended method is demonstrated with a general soil of completely decomposed granite(CDG)in Hong Kong,China.The silt and clay materials with different particle size ranges are further examined,checked and verified using stereomicroscopic observation,physical and chemical property tests.The results further confirm the correctness of the extended wet sieving method.

Effect of eccentric and inclined loading on the bearing capacity of strip footing placed on rock mass

This paper deals with the bearing capacity determination of strip footing on a rock mass in hilly area by considering the influence of inclined and eccentric loading. Applying the generalized HoekBrown failure criterion, the failure behavior of the rock mass is modeled with the help of the power cone programming in the lower bound finite element limit analysis framework. Using bearing capacity factor(Ns), the change in bearing capacity of the strip footing due to the occurrence of eccentrically inclined loading is presented. The variations of the magnitude of Ns are obtained by examining the effects of the Hoek-Brown rock mass strength parameters(uniaxial compressive strength(sci), disturbance factor(D), rock parameter(mi), and Geological Strength Index(GSI)) in the presence of different magnitudes of eccentricity(e) and inclination angle(λ) with respect to the vertical plane, and presented as design charts. Both the inclined loading modes, i.e., inclination towards the center of strip footing(+λ) and inclination away from the center of strip footing(-λ), are adopted to perform the investigation. In addition, the correlation between the input parameters and the corresponding output is developed by utilizing the artificial neural network(ANN). Additionally, from sensitivity analysis, it is observed that inclination angle(λ) is the most sensitive parameter. For practicing engineers, the obtained design equation and design charts can be beneficial to understand the bearing capacity variation in the existence of eccentrically inclined loading in mountain areas.

Mechanical Property and Microstructure of Cement Mortar with Carbonated Recycled Powder

Carbonated recycled powder as cementitious auxiliary material can reduce carbon emissions and realize high-quality recycling of recycled concrete.In this paper,microscopic property of recycled powder with three carbonation methods was tested through XRD and SEM,the mechanical property and microstructure of recycled powder mortar with three replacement rates were studied by ISO method and SEM,and the strengthening mechanism was analyzed.The results showed that the mechanical property of recycled powder mortar decreased with the increasing of replacement rate.It is suggested that the replacement rate of recycled powder should not exceed 20%.The strength index and activity index of carbonated recycled powder mortar were improved,in which the flexural strength was increased by 27.85%and compressive strength was increased by 20%at the maximum.Recycled powder can be quickly and completely carbonated,and the improvement effect of CH pre-soaking carbonation was the best.The activity index of carbonated recycled powder can meet the requirements of Grade II technical standard for recycled powder.Microscopic results revealed the activation mechanism of carbonated recycled powder such as surplus calcium source effect,alkaline polycondensation effect and carbonation enhancement effect.

Seismic performance evaluation of hybrid coupled shear wall system with shear and flexural fuse-type steel coupling beams

Replaceable flexural and shear fuse-type coupling beams are used in hybrid coupled shear wall(HCSW)systems,enabling concrete buildings to be promptly recovered after severe earthquakes.This study aimed to analytically evaluate the seismic behavior of flexural and shear fuse beams situated in short-,medium-and high-rise RC buildings that have HCSWs.Three building groups hypothetically located in a high seismic hazard zone were studied.A series of 2D nonlinear time history analyses was accomplished in OpenSees,using the ground motion records scaled at the design basis earthquake level.It was found that the effectiveness of fuses in HCSWs depends on various factors such as size and scale of the building,allowable rotation value,inter-story drift ratio,residual drift quantity,energy dissipation value of the fuses,etc.The results show that shear fuses better meet the requirements of rotations and drifts.In contrast,flexural fuses dissipate more energy,but their sectional stiffness should increase to meet other requirements.It was concluded that adoption of proper fuses depends on the overall scale of the building and on how associated factors are considered.

Predictive active control of building structures using LQR and artificial intelligence

This study presents a neural network-based model for predicting linear quadratic regulator(LQR)weighting matrices for achieving a target response reduction.Based on the expected weighting matrices,the LQR algorithm is used to determine the various responses of the structure.The responses are determined by numerically analyzing the governing equation of motion using the state-space approach.For training a neural network,four input parameters are considered:the time history of the ground motion,the percentage reduction in lateral displacement,lateral velocity,and lateral acceleration,Output parameters are LQR weighting matrices.To study the effectiveness of an LQR-based neural network(LQRNN),the actual percentage reduction in the responses obtained from using LQRNN is compared with the target percentage reductions.Furthermore,to investigate the efficacy of an active control system using LQRNN,the controlled responses of a system are compared to the corresponding uncontrolled responses.The trained neural network effectively predicts weighting parameters that can provide a percentage reduction in displacement,velocity,and acceleration close to the target percentage reduction.Based on the simulation study,it can be concluded that significant response reductions are observed in the active-controlled system using LQRNN.Moreover,the LQRNN algorithm can replace conventional LQR control with the use of an active control system.

Synthesis of plant-based biogenic jarosite nanoparticles using Azadirachta indica and Eucalyptus gunni leaf extracts and its application in Fenton degradation of dicamba

Bio-jarosite,an iron mineral synthesized biologically using bacteria,is a substitute for iron catalysts in the Fenton oxidation of organic pollutants.Iron nanocatalysts have been widely used as Fenton catalysts because they have a larger surface area than ordinary catalysts,are highly recyclable,and can be treated efficiently.This study aimed to explore the catalytic properties of bio-jarosite iron nanoparticles syn-thesized with green methods using two distinct plant species:Azadirachta indica and Eucalyptus gunni.The focus was on the degradation of dicamba via Fenton oxidation.The synthesized nanoparticles exhibited different particle size,shape,surface area,and chemical composition characteristics.Both particles were effective in removing dicamba,with removal efficiencies of 96.8%for A.indica bio-jarosite iron nano-particles(ABFeNPs)and 93.0%for E.gunni bio-jarosite iron nanoparticles(EBFeNPs)within 120 min of treatment.Increasing the catalyst dosage by 0.1 g/L resulted in 7.6%and 43.0%increases in the dicamba removal efficiency for EBFeNPs and ABFeNPs with rate constants of 0.025 min^(-1) and 0.023 min^(-1),respectively,confrming their catalytic roles.Additionally,the high efficiency of both catalysts was demonstrated through five consecutive cycles of linear pseudo-first-order Fenton oxidation reactions.

Direct scaling of residual displacements for bilinear and pinching oscillators

The estimation of residual displacements in a structure due to an anticipated earthquake event has increasingly become an important component of performance-based earthquake engineering because controlling these displacements plays an important role in ensuring cost-feasible or cost-effective repairs in a damaged structure after the event.An attempt is made in this study to obtain statistical estimates of constant-ductility residual displacement spectra for bilinear and pinching oscillators with 5%initial damping,directly in terms of easily available seismological,site,and model parameters.None of the available models for the bilinear and pinching oscillators are useful when design spectra for a seismic hazard at a site are not available.The statistical estimates of a residual displacement spectrum are proposed in terms of earthquake magnitude,epicentral distance,site geology parameter,and three model parameters for a given set of ductility demand and a hysteretic energy capacity coefficient in the case of bilinear and pinching models,as well as for a given set of pinching parameters for displacement and strength at the breakpoint in the case of pinching model alone.The proposed scaling model is applicable to horizontal ground motions in the western U.S.for earthquake magnitudes less than 7 or epicentral distances greater than 20 km.

Identification of time-varying system and energy-based optimization of adaptive control in seismically excited structure

The combination of structural health monitoring and vibration control is of great importance to provide components of smart structures.While synthetic algorithms have been proposed,adaptive control that is compatible with changing conditions still needs to be used,and time-varying systems are required to be simultaneously estimated with the application of adaptive control.In this research,the identification of structural time-varying dynamic characteristics and optimized simple adaptive control are integrated.First,reduced variations of physical parameters are estimated online using the multiple forgetting factor recursive least squares(MFRLS)method.Then,the energy from the structural vibration is simultaneously specified to optimize the control force with the identified parameters to be operational.Optimization is also performed based on the probability density function of the energy under the seismic excitation at any time.Finally,the optimal control force is obtained by the simple adaptive control(SAC)algorithm and energy coefficient.A numerical example and benchmark structure are employed to investigate the efficiency of the proposed approach.The simulation results revealed the effectiveness of the integrated online identification and optimal adaptive control in systems.

Engineering behaviour of in situ cored deep cement mixed marine deposits subjected to undrained and drained shearing

The deep cement mixing(DCM)is used to improve the capacity and reduce the settlement of the soft ground by forming cemented clay columns.The investigation on the mechanical behaviour of the DCM samples is limited to either laboratory-prepared samples or in-situ samples under unconfined compression.In this study,a series of drained and undrained triaxial shearing tests was performed on the in-situ cored DCM samples with high cement content to assess their mechanical behaviours.It is found that the drainage condition affects significantly the stiffness,peak and residual strengths of the DCM samples,which is mainly due to the state of excess pore water pressure at different strain levels,i.e.being positive before the peak deviatoric stress and negative after the peak deviatoric stress,in the undrained tests.The slope of the failure envelope changes obviously with the confining pressures,being steeper at lower stress levels and flatter at higher stress levels.The strength parameters,effective cohesion and friction angle obtained from lower stress levels(c′0 andφ′0)are 400 kPa and 58°,respectively,which are deemed to be true for design in most DCM applications where the in-situ stress levels are normally at lower values of 50-200 kPa.Additionally,the computed tomography(CT)scanning system was adopted to visualize the internal structures of DCM samples.It is found that the clay pockets existing inside the DCM samples due to uneven mixing affect markedly their stress-strain behaviour,which is one of the main reasons for the high variability of the DCM samples.

In situ digital testing method for quality assessment of soft soil improvement with polyurethane

This study purposes an in situ testing method on quality assessment of soil improvement.Factual drilling data includes the spatial distribution and in situ strength of untreated and treated soil along three different drillholes measured by on-site drilling monitoring method.These factual drilling data can characterize the degree of soil improvement by penetration injection with permeable polyurethane.Result from on-site drilling monitoring shows that the linear zones represent constant drilling speeds shown in the plot of drill bit advancement vs.net drilling time,which indicates the spatial distributions of soil profile.The soil profile at the study site is composed of four layers,which includes fill,untreated silty clay,treated silty clay,and mucky soil.The results of soil profile are verified by the parallel site loggings.The constant drilling speeds profile the coring-resistant strength of drilled soils.By comparing with the untreated silty clay,the constant drilling speeds of the treated silty clay have been decreased by 13.0-62.8%.Two drilling-speed-based indices of 61.2%and 65.6%are proposed to assess the decreased average drilling speed and the increased in situ strength of treated silty clay.Laboratory tests,i.e.uniaxial compressive strength(UCS)test,have been performed with core sample to investigate and characterize in situ strength by comparing that with drilling speeds.Results show that the average predicted strengths of treated silty clay are 2.4-6.9 times higher than the average measured strength of untreated silty clay.The UCS-based indices of 374.5%and 344.2%verified the quality assessment(QA)results by this new in situ method.This method provides a cost-effective tool for quality assessment of soil improvement by utilizing the digital drilling data.

Multi-scale analysis of carbon mineralization in lime-treated soils considering soil mineralogy

Mineral carbonation is emerging as a reliable CO_(2) capture technology that can mitigate climate change.In lime-treated clayey soils,mineral carbonation occurs through the carbonation of free lime and cementitious products derived from pozzolanic reactions.The kinetics of the reactions in lime-treated clayey soils are variable and depend primarily on soil mineralogy.The present study demonstrates the role of soil mineralogy in CO_(2) capture and the subsequent changes caused by carbon mineralization in terms of the unconfined compressive strength(UCS)of lime-treated soils during their service life.Three clayey soils(kaolin,bentonite,and silty clay)with different mineralogical characteristics were treated with 4%lime content,and the samples were cured in a controlled environment for 7 d,90 d,180 d,and 365 d.After the specified curing periods,the samples were exposed to CO_(2) in a carbonation cell for 7 d.The non-carbonated samples purged with N2 gas were used as a benchmark to compare the mechanical,chemical-mineralogical,and microstructure changes caused by carbonation reactions.Experimental investigations indicated that exposure to CO_(2) resulted in an average increase of 10%in the UCS of limetreated bentonite,whereas the strength of lime-treated kaolin and silty clay was reduced by an average of 35%.The chemical and microstructural analyses revealed that the precipitated carbonates effectively filled the macropores of the treated bentonite,compared to the inadequate cementation caused by pozzolanic reactions,resulting in strength enhancement.In contrast,strength loss in lime-treated kaolin and silty clay was attributed to the carbonation of cementitious phases and partly to the tensile stress induced by carbonate precipitation.In terms of carbon mineralization prospects,lime-treated kaolin exhibited maximum carbonation due to the higher availability of unreacted lime.The results suggest that,in addition to the increase in compressive strength,adequate calcium-bearing phases and macropores determine the efficiency of carbon mineralization in lime-treated clayey soils.

High-efficiency Carbonation Modification Methods of Recycled Coarse Aggregates

To solve the problem of only surface carbonation and realize high-efficiency carbonation of recycled coarse aggregate,the method of carbonated recycled coarse aggregate with nano materials pre-soaking was first put forward.The carbonation effect of modified recycled coarse aggregate with three different carbonation methods was evaluated,and water absorption,apparent density and crush index of modified recycled coarse aggregate were measured.Combined with XRD,SEM,and MIP microscopic analysis,the high-efficiency carbonation strengthening mechanism of modified recycled coarse aggregate was revealed.The experimental results show that,compared with the non-carbonated recycled coarse aggregate,the physical and microscopic properties of carbonated recycled coarse aggregate are improved.The method of carbonation with nano-SiO_(2) pre-soaking can realize the high-efficiency carbonation of recycled coarse aggregate,for modified recycled coarse aggregate with the method,water absorption is reduced by 23.03%,porosity is reduced by 44.06%,and the average pore diameter is 21.82 nm.The high-efficiency carbonation strengthening mechanism show that the pre-socked nano-SiO_(2) is bound to the hydration product Ca(OH)_(2) of the old mortar with nano-scale C-S-H,which can improve the CO_(2) absorption rate,accelerate the carbonation reaction,generate more stable CaCO_(3) and nano-scale silica gel,and bond to the dense three-dimensional network structure to realize the bidirectional enhancement of nano-materials and pressurized carbonation.It is concluded that the method of carbonation with nano-SiO_(2) pre-soaking is a novel high-efficiency carbonation modification of recycled coarse aggregate.

Significance of including lid thickness and particle shape factor in numerical modeling for prediction of particle trap efficiency of invert trap

Sediment accumulation on the bed of open sewers and drains reduces hydraulic efficiency and can cause localized flooding.Slotted invert traps installed underneath the bed of open sewers and drains can eliminate sediment build-up by catching sediment load.Previous three-dimensional(3D)computational studies have examined the particle trapping performance of invert traps of different shapes and depths under varied sediment and flow conditions,considering particles as spheres.For two-dimensional and 3D numerical modeling,researchers assumed the lid geometry to be a thin line and a plane,respectively.In this 3D numerical study,the particle trapping efficiency of a slotted irregular hexagonal invert trap fitted at the flume bottom was examined by incorporating the particle shape factor of non-spherical sewage solid particles and the thicknesses of upstream and downstream lids over the trap in the discrete phase model of the ANSYS Fluent 2020 R1 software.The volume of fluid(VOF)and the realizable k-turbulence models were used to predict the velocity field.The two-dimensional particle image velocimetry(PIV)was used to measure the velocity field inside the invert trap.The results showed that the thicknesses of upstream and downstream lids affected the velocity field and turbulent kinetic energy at all flow depths.The joint impact of the particle shape factor and lid thickness on the trap efficiency was significant.When both the lid thickness and particle shape factor were considered in the numerical modeling,trap efficiencies were underestimated,with relative errors of-8.66%to-0.65%in comparison to the experimental values of Mohsin and Kaushal(2017).They were also lower than the values predicted by Mohsin and Kaushal(2017),which showed an overall overestimation with errors of-2.3%to 17.4%.

A Bayesian multi-model inference methodology for imprecise momentindependent global sensitivity analysis of rock structures

Traditional global sensitivity analysis(GSA)neglects the epistemic uncertainties associated with the probabilistic characteristics(i.e.type of distribution type and its parameters)of input rock properties emanating due to the small size of datasets while mapping the relative importance of properties to the model response.This paper proposes an augmented Bayesian multi-model inference(BMMI)coupled with GSA methodology(BMMI-GSA)to address this issue by estimating the imprecision in the momentindependent sensitivity indices of rock structures arising from the small size of input data.The methodology employs BMMI to quantify the epistemic uncertainties associated with model type and parameters of input properties.The estimated uncertainties are propagated in estimating imprecision in moment-independent Borgonovo’s indices by employing a reweighting approach on candidate probabilistic models.The proposed methodology is showcased for a rock slope prone to stress-controlled failure in the Himalayan region of India.The proposed methodology was superior to the conventional GSA(neglects all epistemic uncertainties)and Bayesian coupled GSA(B-GSA)(neglects model uncertainty)due to its capability to incorporate the uncertainties in both model type and parameters of properties.Imprecise Borgonovo’s indices estimated via proposed methodology provide the confidence intervals of the sensitivity indices instead of their fixed-point estimates,which makes the user more informed in the data collection efforts.Analyses performed with the varying sample sizes suggested that the uncertainties in sensitivity indices reduce significantly with the increasing sample sizes.The accurate importance ranking of properties was only possible via samples of large sizes.Further,the impact of the prior knowledge in terms of prior ranges and distributions was significant;hence,any related assumption should be made carefully.

Using neural network modeling to improve the detection accuracy of land subsidence due to groundwater withdrawal

Despite the high efficiency of remote sensing methods for rapid and large-scale detection of subsidence phenomena,this technique has limitations such as atmospheric impact and temporal and spatial decorrelation that affect the accuracy of the results.This paper proposes a method based on an artificial neural network to improve the results of monitoring land subsidence due to groundwater overexploitation by radar interferometry in the Aliabad plain(Central Iran).In this regard,vertical ground deformations were monitored over 18 months using the Sentinel-1A SAR images.To model the land subsidence by a multilayer perceptron(MLP)artificial neural network,four parameters,including groundwater level,alluvial thickness,elastic modulus,and transmissivity have been applied.The model's generalizability was assessed using data derived for 144 days.According to the results,the neural network estimates the land subsidence at each ground point with an accuracy of 6.8 mm.A comparison between the predicted and actual values indicated a significant agreement.The MLP model can be used to improve the results of subsidence detection in the study area or other areas with similar characteristics.

Quantification of the concrete freeze–thaw environment across the Qinghai–Tibet Plateau based on machine learning algorithms

The reasonable quantification of the concrete freezing environment on the Qinghai–Tibet Plateau(QTP) is the primary issue in frost resistant concrete design, which is one of the challenges that the QTP engineering managers should take into account. In this paper, we propose a more realistic method to calculate the number of concrete freeze–thaw cycles(NFTCs) on the QTP. The calculated results show that the NFTCs increase as the altitude of the meteorological station increases with the average NFTCs being 208.7. Four machine learning methods, i.e., the random forest(RF) model, generalized boosting method(GBM), generalized linear model(GLM), and generalized additive model(GAM), are used to fit the NFTCs. The root mean square error(RMSE) values of the RF, GBM, GLM, and GAM are 32.3, 4.3, 247.9, and 161.3, respectively. The R^(2) values of the RF, GBM, GLM, and GAM are 0.93, 0.99, 0.48, and 0.66, respectively. The GBM method performs the best compared to the other three methods, which was shown by the results of RMSE and R^(2) values. The quantitative results from the GBM method indicate that the lowest, medium, and highest NFTC values are distributed in the northern, central, and southern parts of the QTP, respectively. The annual NFTCs in the QTP region are mainly concentrated at 160 and above, and the average NFTCs is 200 across the QTP. Our results can provide scientific guidance and a theoretical basis for the freezing resistance design of concrete in various projects on the QTP.

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.