Global Safety Factor Research Articles

Seismic analysis of nailed vertical excavation using pseudo-dynamic approach

An attempt has been made to study the behavior of nailed vertical excavations in medium dense to dense cohesionless soil under seismic conditions using a pseudo-dynamic approach. The effect of several parameters such as angle of internal friction of soil (ϕ), horizontal (kh) and vertical (kv) earthquake acceleration coefficients, amplification factor (fa), length of nails (L), angle of nail inclination (α) and vertical spacing of nails (Sv) on the stability of nailed vertical excavations has been explored. The limit equilibrium method along with a planar failure surface is used to derive the formulation involved with the pseudo-dynamic approach, considering axial pullout of the installed nails. A comparison of the pseudo-static and pseudo-dynamic approaches has been established in order to explore the effectiveness of the pseudo-dynamic approach over pseudo-static analysis, since most of the seismic stability studies on nailed vertical excavations are based on the latter. The results are expressed in terms of the global factor of safety (FOS). Seismic stability, i.e., the FOS of nailed vertical excavations is found to decrease with increase in the horizontal and vertical earthquake forces. The present values of FOS are compared with those available in the literature.

Seismic analysis of soil nail performance in deep excavation

Deep excavation is a common part of development to utilize underground space in densely populated areas. Protection of contiguous building and properties is a primary design concern space. Soil nailing is one such technique to exchange conventional retaining system for deep excavation. It will also donate to significant saving in cost and time of construction compared to conventional retaining systems. In this study an attempt has been made to have a deep vertical excavation on ground of 10 m height using soil nail wall. Also studied the enactment of soil nail wall under different nail inclination to horizontal i.e., Ѳ = 0° and Ѳ = 15° with water table. The finite element analysis of soil nail wall was carried to study the behavior of maximum horizontal wall displacement, maximum horizontal nail displacement, base heave, maximum axial force in nail, maximum shear force in nail, maximum bending moment in nail under both static and seismic conditions using PLAXIS 2D. The process of construction is carried out in stages and a value of Global factor of safety (FSG) is maintained above 1.5 to make sure its stability. The length of nail has a major impact on the behavior of soil nail wall system; increase in nail length will increase the FSG. Results of the numerical analysis direct that the use of soil nail wall is desirable to impart stability to retaining systems.

Three-dimensional stability of landslides based on local safety factor

Unlike the limit equilibrium method (LEM), with which only the global safety factor of the landslide can be calculated, a local safety factor (LSF) method is proposed to evaluate the stability of different sections of a landslide in this paper. Based on three-dimensional (3D) numerical simulation results, the local safety factor is defined as the ratio of the shear strength of the soil at an element on the slip zone to the shear stress parallel to the sliding direction at that element. The global safety factor of the landslide is defined as the weighted average of all local safety factors based on the area of the slip surface. Some example analyses show that the results computed by the LSF method agree well with those calculated by the General Limit Equilibrium (GLE) method in two-dimensional (2D) models and the distribution of the LSF in the 3D slip zone is consistent with that indicated by the observed deformation pattern of an actual landslide in China.

Reliability assessment of ultimate limit state of twin caverns

ABSTRACTConstruction of a cavern in close proximity to an existing cavern modifies the state of stresses and movements in a zone around the existing cavern, as some degree of interaction between these two caverns generally takes place. This study investigates the interaction of two parallel caverns and the influence of such interaction on stress-induced global stability in terms of a global factor of safety. A series of finite difference analyses were performed to derive the global factor of safety of a system of two parallel and adjacent caverns. A mathematical response surface model was then built using the multivariate adaptive regression splines (MARS) approach and a series of charts based on this surrogate model were developed to relate the global factor of safety to the critical parameters. The built MARS model is of high accuracy and is simple to interpret and can be used to perform probabilistic assessment of ultimate limit state of twin caverns.

Predictive models of ultimate and serviceability performances for underground twin caverns

The construction of a new cavern modifies the state of stresses and displacements in a zone around the existing cavern. For multiple caverns, the size of this influence zone depends on the ground type, the in situ stress, the cavern span and shape, the width of the pillar separating the caverns, and the excavation sequence. Performances of underground twin caverns can be unsatisfactory as a result of either instability (collapse) or excessive displacements. These two distinct failures should be prevented in design. This study simulated the ultimate and serviceability performances of underground twin rock caverns of various sizes and shapes. The global factor of safety is used as the criterion for determining the ultimate limit state and the calculated maximum displacement around the cavern opening is adopted as the serviceability limit state criterion. Based on the results of a series of numerical simulations, simple regression models were developed for estimating the global factor of safety and the maximum displacement, respectively. It was proposed that a proper pillar width can be determined based on the threshold influence factor value. In addition, design charts with regard to the selection of the pillar width for underground twin rock caverns under similar ground conditions were also developed.

Optimising deep mixed soil zones in land reclamation projects

The use of deep soil mixing technologies has become increasingly common in North America following its widespread development and adoption in Japan and Scandinavia. This research project considered how design of soft soils stabilised with deep soil mixing may be optimised to satisfy global slope stability requirements to assist the construction of large reclaimed land projects. The land reclamation case that was studied in the present paper deals with raising the elevation of a terrestrial area above a tidal or flood zone, where the water table is close or at the original grade. In this work, the effect of several key design parameters on the global factor of safety against slope failure for a land reclamation project was studied using limit equilibrium slope stability analyses. The parametric analyses considered design parameters, including the thickness of the soft soil layer, as well as the strength, width and location of a stabilised soil zone. The purpose of this work is to provide guidelines for the preliminary design of ground improvements for future land reclamation projects using deep soil mixing methods by identifying design parameters that have the most significant impact on the global factor of safety.

Solutions for stability of anchored earth slopes subjected to seismic loading

The limit analysis approach is paid more attention to in the stability analysis of slopes subjected to seismic loading. However, the solutions obtained from the approaches are in general limited to a designated slope or the same kind of slopes. It seems that a wide applicability of the solutions in their present form is rather difficult. Based on the kinematic theorem and the assumption of combined log-spiral rotational failure mechanism, the integral formulation for expressing the rate of external work rate due to soil weight and seismic loading is derived under the framework of pseudo-static method considering the complex geometrical configurations and the multilayer soils in slopes with multi-row anchors. Further, the work-energy balance equation is established, and the analytical expressions for the global factors of safety (FS) and the yield acceleration coefficient of anchored slopes are obtained by using the strength reduction technique combined with the optimization method. Moreover, the permanent displacement with Newmark's method is also solved. Several representative examples are employed to validate the analytical solutions, and some comparisons of the FSs and the corresponding critical sliding surfaces obtained by various methods are also made. The results show that the analytical approach can yield the high-accuracy solutions and is widely applicable to the seismic stability analysis of complex slopes with multi-row anchors. Finally, a practical case is analyzed using the proposed approach. ©2016, Editorial Office of Chinese Journal of Geotechnical Engineering. All right reserved.

Design of Geostructural Systems

AbstractThis paper begins with an extensive review of the literature covering the development of design rules for geostructural systems, beginning with traditional global safety factors and developing through partial factors for loads and resistances, and then considering the use of mobilization factors to limit soil strains. The paper then aims to distinguish two possible functions for geotechnical factors: to compensate for the uncertainty regarding soil strength, and to limit soil deformations that could compromise the associated structure before the soil strength can be fully mobilized, whatever it is. At present, design procedures generally conflate and confuse ultimate limit state (ULS) checks and serviceability limit state (SLS) deformation checks. Furthermore, most geotechnical engineers wrongly associate ULS with soil failure rather than with structural failure. The paper addresses this fundamental confusion by advocating mobilizable strength design (MSD), which is based on assumed soil-structure...

Reliability Analysis of Bearing Capacity of Square Footing on Soil with Strength Anisotropy Due to Layered Microstructure

Abstract The paper deals with reliability analysis of square footing on soil with strength anisotropy. The strength of the soil has been described with identified anisotropic strength criterion dedicated to geomaterials with layered microstructure. The analysis assumes dip angle α and azimuth angle β which define direction of lamination of the structure to be random variables with given probability density functions. Bearing capacity being a function of these variables is approximated based on results of deterministic simulations obtained for variety of orientations. The weighted regression method by Kaymaz and McMahon within the framework of Response Surface Method is used for the approximation. As a result of analysis, global factor of safety that corresponds to assumed value of probability of failure is determined. The value of the safety factor denotes the ratio between the value of the design load and the mean value of bearing capacity which is needed to reduce the probability of failure to the acceptable level. The procedure of calculating the factor has been presented for two different cases. In the first case, no information about lamination direction of the soil has been provided and thus all the orientations are assumed to be equally probable (uniform distribution). In the second case, statistical information including mean, variance and assumed probability distribution for both α and β angle is known. For the latter case, using results obtained for few different values of mean of angle α, also the influence of strength anisotropy on the value of global factor of safety is shown.

Experimental and numerical investigation on the stability of a high arch dam with typical problems of nonsymmetry: Baihetan Dam, China

High arch dams present nonsymmetry problems, both on topological and geological conditions at dam site, and are inevitable in many projects. Their influence is unfavorable to the performance of the dam-foundation system, and the mechanism needs to be studied to find proper treatments in giant rock engineering. Baihetan Dam is a high arch dam with typical nonsymmetry problems, and is studied in this paper as an example. A geomechanical model test was conducted focusing on features of deformation and failure phenomena, and a numerical calculation based on a nonlinear finite element method (FEM) was performed on it. Deformation reinforcement theory was particularly involved in the FEM calculation to quantize and describe the instability status of structure and proved to be reliable. It is found that the nonsymmetrical profile causes the allocation of arch thrust to be asymmetrical, leading to an approximately equivalent rotation of asymmetric axis of deformation. This phenomenon contributes to causing local regions of the dam to be under an extra large tension or compression in the overload process. The asymmetrical geological conditions, characterized by many developed tectonic surfaces in the left abutment, are revealed to threaten the stability of the rock mass. Global safety factors of the dam decrease as a consequence, when comparing the results with other dams of similar dam height. In the end, the revised definition of Lombardi’s slenderness coefficient was proposed considering nonsymmetry of the profile.

COMPARISONS ON THE RESPONSE OF SHALLOW GEOTHERMAL ENERGY PILE EMBEDDED IN SOFT AND FIRM SOILS

Shallow geothermal energy pile, particularly the one used in tropical countries, is a sustainable geostructure system that transforms the soil surrounding the geostructure as a heat sink, for building cooling purposes. Thermal loads stored in the soil will cause thermally induced settlement. A series of laboratory tests were performed to study the behaviour of model energy piles installed in kaolin soil with soft and firm consistencies. Twelve tests which included thermal load tests (35˚C and 40˚C) and thermo-axial load tests (100 N and 200 N, combined with thermal loads) were performed. The pile response to thermal and thermo-axial loads were attributed to the soil consistency and the magnitude of the loads applied to the pile head. Firm soils produce lower thermally induced settlement, due to higher level of restraint compared to soft soils. To ensure that the thermo-axial settlement does not exceed the limiting settlement, the recommended global factor of safety used for soft soil and firm soils subjected to 40˚C thermal load should be more than 4.0 and 2.5, respectively.

An Analysis of Excavation Support Safety Based on Experimental Studies

Abstract The article presents the results of inclinometric measurements and numerical analyses of soldier-pile wall displacements. The excavation under investigation was made in cohesive soils. The measurements were conducted at points located at the edge of the cantilever excavation support system. The displacements of the excavation support observed over the period of three years demonstrated the pattern of steady growth over the first two months, followed by a gradual levelling out to a final plateau. The numerical analyses were conducted based on 3D FEM models. The numerical analysis of the problem comprise calculations of the global structural safety factor depending on the displacement of the chosen points in the lagging and conducted by means of the φ/c reduction procedure. The adopted graphical method of safety estimation is very conservative in the sense that it recognizes stability loss quite early, when one could further load the medium or weaken it by further strength reduction. The values of the Msf factor are relatively high. This is caused by the fact that the structure was designed for excavation twice as deep. Nevertheless, the structure is treated as a temporary one.

Safety assessment of punching shear failure according to the level of approximation approach

AbstractThe fib Model Code for Concrete Structures 2010 introduced the concept of levels of approximation (LoA) as a strategy for simplifying the procedures involved in preliminary design stages or the design of non‐critical structural elements while still providing the tools for engineers to use state‐of‐the‐art techniques in the assessment of existing structures or in the advanced stages of design for critical structural elements. In this paper, this concept is applied to the determination of the punching shear resistance of reinforced concrete slabs. A procedure is validated for the highest LoA involving non‐linear finite element analysis (NLFEA) with multi‐layered shell elements and the critical shear crack theory (CSCT). The safety format proposed for use in the safety verification assisted by NLFEA is based on the definition of a global resistance safety factor. A semi‐probabilistic approach is followed, based on the assumption of a lognormal distribution for the resistance and on an estimate of its coefficient of variation. This approach is validated by means of a comparison with the results from a probabilistic analysis.The LoA approach is initially applied to the study of statically determinate slabs supported on one column to verify the effectiveness of the procedure presented here compared with other validated methods available in the literature. The paper concludes with a case study illustrating the application of the proposed procedure to a bridge deck slab and highlighting the benefits of using a higher LoA.

Response of shallow geothermal energy pile from laboratory model tests

In shallow geothermal energy pile systems, the thermal loads from the pile, transferred and stored in the soil will cause thermally induced settlement. This factor must be considered in the geotechnical design process to avoid unexpected hazards. Series of laboratory model tests were carried out to study the behaviour of energy piles installed in kaolin soil, subjected to thermal loads and a combination of axial and thermal loads (henceforth known as thermo-axial loads). Six tests which included two thermal load tests (35°C and 40°C) and four thermo-axial load tests (100 N and 200 N, combined with 35°C and 40°C thermal loads) were conducted. To simulate the behaviour of geothermal energy piles during its operation, the thermo-axial tests were carried out by applying an axial load to the model pile head, and a subsequent application of thermal load. The model soil was compacted at 90% maximum dry density and had an undrained shear strength of 37 kPa, thus classified as having a firm soil consistency. The behaviour of model pile, having the ultimate load capacity of 460 N, was monitored using a linear variable displacement transducer, load cell and wire thermocouple, to measure the pile head settlement, applied axial load and model pile temperature. The acquired data from this study was used to define the thermo-axial response characteristics of the energy pile model. In this study, the limiting settlement was defined as 10% of the model pile diameter. For thermal load tests, higher thermal loads induced higher values of thermal settlement. At 40°C thermal load an irreversible settlement was observed after the heating and cooling cycle was applied to the model pile. Meanwhile, the pile response to thermo-axial loads were attributed to soil consistency and the magnitude of both the axial and thermal loads applied to the pile. The higher the thermoaxial loads, the higher the settlements occurred. A slight hazard on the model pile was detected, since the settlement occurred was greater than the limiting value when the pile was loaded with thermo-axial loads of 40°C and 200 N. It is therefore recommended that the global factor of safety to be applied for energy pile installed in firm soil should be more than 2.3 to prevent any hazard to occur in the future, should the pile also be subjected to thermal load of 40°C or greater.

Deterministic and probabilistic multi-modal analysis of slope stability

Traditional slope stability analysis involves predicting the location of the critical slip surface for a given slope and computing a safety factor at that location. However, for some slopes with complicated stratigraphy several distinct critical slip surfaces can exist. Furthermore, the global minimum safety factor in some cases can be less important than potential failure zones when rehabilitating or reinforcing a slope. Existing search techniques used in slope stability analysis cannot find all areas of concern, but instead converge exclusively on the critical slip surface. This paper therefore proposes the use of a holistic multi modal optimisation technique which is able to locate and converge to multiple failure modes simultaneously. The search technique has been demonstrated on a number of benchmark examples using both deterministic and probabilistic analysis to find all possible failure mechanisms, and their respective factors of safety and reliability indices. The results from both the deterministic and probabilistic models show that the search technique is effective in locating the known critical slip surface while also establishing the locations of any other distinct critical slip surfaces within the slope. The approach is of particular relevance for investigating the stability of large slopes with complicated stratigraphy, as these slopes are likely to contain multiple failure mechanisms.

Regression models for estimating ultimate and serviceability limit states of underground rock caverns

Performances of underground rock caverns can be unsatisfactory as a result of either instability (collapse) or excessive movements. Collapse refers to ultimate limit state failure, in which the stresses exceed the strength of the rock masses. Failure of the serviceability limit state refers to excessive deformations resulting in difficulties during excavation such as lining placement and reinforcement installation. Both distinct limit states may need to be considered in design. This study used numerical modeling to assess both the ultimate and the serviceability limit states of underground single and twin rock caverns. The global factor of safety is used as the criterion for the ultimate limit state and the calculated percent strain around the cavern opening is adopted as the serviceability limit state criterion. Based on the numerical results, simple regression models were developed for estimating the global factor of safety and the induced percent strain of the single and twin caverns, respectively. Charts for assessing cavern stability for preliminary design use were developed. In addition, the use of the critical strain concept and the elastic and design line methodology to limit the induced strains was discussed.

ANCHORED WALL DESIGN: COMPARING THE GLOBAL AND PARTIAL FACTORS OF SAFETY INCORPORATING THE AUSTRALIAN STANDARDS

A versatile and user-friendly model has been developed for evaluating the factor of safety of anchored sheet-pile structures, using both global factors of safety (GFS) and partial factors of safety (PFS) methods, abiding AS 4678 standard, an Australian standard for retaining wall design. The developed model is aimed to determine the following features: (i) depth of embedment, (ii) total wall height for determining the amount of material required, (iii) the length of anchor, (iv) the anchor force and (v) the maximum moment acting on the sheet-pile wall. Key findings are highlighted based on the design calculations. This study incorporates different design scenarios including layered soil, line loads and uniformly distributed surcharge loads to draw comparisons between the GFS and PFS methods. Many examples are used to validate the outputs of the program. The results indicate that the PFS method is preferred for design strength and safety aspects, whereas the GFS method is adopted for cost effectiveness and simplicity of design calculations. The limitations of the Australian standard AS 4678-2002 are discussed in order to identify the superiority of one method over another.

The Three-Dimensional (3D) Numerical Stability Analysis of Hyttemalmen Open-Pit

Abstract The purpose of this paper was to perform the 3D numerical calculations allowing slope stability analysis of Hyttemalmen open pit (location Kirkenes, Finnmark Province, Norway). After a ramp rock slide, which took place in December 2010, as well as some other small-scale rock slope stability problems, it proved necessary to perform a serious stability analyses. The Hyttemalmen open pit was designed with a depth up to 100 m, a bench height of 24 m and a ramp width of 10 m. The rock formation in the iron mining district of Kirkenes is called the Bjornevaten Group. This is the most structurally complicated area connected with tectonic process such as folding, faults and metamorphosis. The Bjornevaten Group is a volcano-sedimentary sequence. Rock slope stability depends on the mechanical properties of the rock, hydro-geological conditions, slope topography, joint set systems and seismic activity. However, rock slope stability is mainly connected with joint sets. Joints, or general discontinuities, are regarded as weak planes within rock which have strength reducing consequences with regard to rock strength. Discontinuities within the rock mass lead to very low tensile strength. Several simulations were performed utilising the RocLab (2007) software to estimate the gneiss cohesion for slopes of different height. The RocLab code is dedicated to estimate rock mass strength using the Hoek-Brown failure criterion. Utilising both the GSI index and the Hoek-Brown strength criterion the equivalent Mohr-Coulomb parameters (cohesion and angle of internal friction) can be calculated. The results of 3D numerical calculations (with FLA3D code) show that it is necessary to redesign the slope-bench system in the Hyttemalmen open pit. Changing slope inclination for lower stages is recommended. The minimum factor of safety should be equal 1.3. At the final planned stage of excavation, the factor of safety drops to 1.06 with failure surface ranging through all of the slopes. In the case of a slope angle 70° for lower stages, FS = 1.26, which is not enough to provide slope stability. Another series of calculations were therefore performed taking water table lowering into consideration, which increases the global safety factor. It was finally evaluated, that for a water table level of 72 m the factor of safety equals 1.3, which is enough to assure global open-pit stability.

Quantitative deterministic versus probability analyses based on a safety margin criterion

This paper proposes a new criterion called the ratio of safety margin (RSM) for use in the areas of the global factor of safety, reliability and limit states analyses with reference to their respective allowable criteria. An equation for calculating RSM based on the reliability index is formulated. Efforts for proving the applicability of this criterion include a theoretical demonstration in a simple one-variable case; an investigation on a test problem involving two random variables, followed by a slope stability study on a 156 m high embankment dam and an illustrative example presented in a EuroCode 7 guidebook. Calculation of the ratios of safety margin in the three areas provides a quantitative way to accommodate the analytical results within the same theoretical framework and makes the outcomes mutually comparable and supportive, which is much more enlightening than that would be the case by considering only one of them. Calculating RSMs for reliability and limit states methods has also helped solve the key issue concerning the uniqueness of the partial factors calibrated from a particular ‘target case’.

Performance of hybrid MSE/Soil Nail walls using numerical analysis and limit equilibrium approaches

MSE/Soil Nail hybrid earth retaining walls provide a more economical design for applications in cut/fill situations than the traditionally used full height MSE and drilled shaft retaining walls. MSE/Soil Nail hybrid earth retaining walls use a soil nailed wall in the cut section and an MSE wall in the fill section. The paper demonstrates the results of instrumentation and monitoring an MSE/Soil Nail hybrid retaining wall system. Innovative 2D finite element models were used to simulate the behavior of the hybrid retaining wall system. The paper describes the philosophy of design of hybrid MSE/Soil Nail walls and the outline of circumstances which are favorable for such walls. In order to evaluate the global Factor of Safety (FOS) of the soil nail wall portion using the conventional limit-equilibrium design methods (LEM), two different methodologies to simulate the effect of the upper MSE walls were proposed. The obtained results of numerical and limit equilibrium approaches as a design methodology are presented for such type of walls, in this paper.The design of hybrid MSE/SN walls is complicated as it is a composite of two different reinforcement techniques, traditional limit equilibrium approaches cannot be used alone for design of such walls, it shall be supported by numerical methods for estimation of the global factor of safety and failure surface. The limit equilibrium approaches can be used for the estimation of internal stability and facing connection for both soil nails and mechanically stabilized walls.