Failure Probability Pf Research Articles

River quality management: Integrating uncertainty, failure probability, and assimilation capacity

Managing river water quality is challenging due to uncertainties in hydraulic and hydrologic parameters. This study integrates the symmetric exponential function (SEF) approach for solving the advection-dispersion equation with the Monte Carlo method in MATLAB. This combination allows us to explore the river's assimilation capacity and the failure probability (Pf) of maintaining desired water quality standards. Here, Pf represents the likelihood of pollutant concentrations exceeding acceptable limits under varying river conditions. A key contribution of this study is the introduction of a novel equation, developed using the Genetic Programming (GP) soft computing tool, to calculate assimilation capacity considering the failure probability of water quality provision. This equation provides a valuable tool for risk assessment in water resource management by quantifying pollutant assimilation dynamics. Its robustness is validated through high Coefficient of Determination (R2) and Overall Index (OI) values near 1, along with low Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). The study identifies critical river characteristics, such as flow velocity and pollutant load, significantly influencing the reliability index (β). By outlining how adjustments in these parameters can achieve a target reliability index (β=4.526), our study offers a practical approach to safeguarding river ecosystems. For example, increasing flow velocity by 76 % can shift the river from a safe state (Pf=3×10−5) to a hazardous state (Pf=1), while a 44 % decrease in velocity allows for 57 % more pollutant assimilation. These findings highlight the importance of flow control as a cost-effective strategy for mitigating high pollutant concentrations and ensuring sustainable water quality management. By integrating numerical approaches with reliability sampling methods and soft computing techniques, this study enhances understanding of river system dynamics and supports informed decision-making for protecting water resources.

Analytical method of incorporating failure probability to predict the fatigue life of ultra-high-performance concrete (UHPC)

This study predicted the fatigue life (N) of UHPC incorporated with different volume fractions (Vf = 0.0%, 0.5%, 1.0%, 1.5% and 2.0%) of steel fiber under flexural cyclic loading at various stress levels (S). The Weibull distribution, a two-parameter model, was utilized to estimate the distribution of fatigue life in UHPC. Subsequently, three methods were employed to calculate the parameters: the graphical method, the method of moments, and the method of maximum likelihood. The averaged values of these parameters were then obtained to enhance the accuracy of the estimation. The results are presented in the form of S-N diagrams, which depict the quantitative relationship between stress (S) and fatigue life (N). This relationship was determined using the Wohler equation, the modified Wohler equation, and the power equation. By employing these equations, the flexural fatigue strength of UHPC can be accurately predicted. Subsequently, the fatigue failure probability (Pf) was incorporated to enhance the reliability of the S-N quantitative relation. The fatigue testing results were presented in the form of S-N-Pf curves, which comprehensively reflect the relationship between stress, fatigue life, and failure probability. Furthermore, the mathematical relation of the S-N-Pf curves was derived to predict the fatigue life of UHPC with a given failure probability, providing a more comprehensive and accurate assessment of its fatigue behavior.

Global Sensitivity Analysis of Structural Reliability Using Cliff Delta

This paper introduces innovative sensitivity indices based on Cliff’s Delta for the global sensitivity analysis of structural reliability. These indices build on the Sobol’ method, using binary outcomes (success or failure), but avoid the need to calculate failure probability Pf and the associated distributional assumptions of resistance R and load F. Cliff’s Delta, originally used for ordinal data, evaluates the dominance of resistance over load without specific assumptions. The mathematical formulations for computing Cliff’s Delta between R and F quantify structural reliability by assessing the random realizations of R > F using a double-nested-loop approach. The derived sensitivity indices, based on the squared value of Cliff’s Delta δC2, exhibit properties analogous to those in the Sobol’ sensitivity analysis, including first-order, second-order, and higher-order indices. This provides a framework for evaluating the contributions of input variables on structural reliability. The results demonstrate that the Cliff’s Delta method provides a more accurate estimate of Pf. In one case study, the Cliff’s Delta approach reduces the standard deviation of Pf estimates across various Monte Carlo run counts. This method is particularly significant for FEM applications, where repeated simulations of R or F are computationally intensive. The double-nested-loop algorithm of Cliff’s Delta maximizes the extraction of information about structural reliability from these simulations. However, the high computational demand of Cliff’s Delta is a disadvantage. Future research should optimize computational demands, especially for small values of Pf.

Stability Evaluation of Slope Based on Global Sensitivity Analysis

The uncertainty of parameters will have a significant impact on slope stability, where sensitivity analysis is a commonly used method in uncertainty research. However, traditional sensitivity analysis method costs much computation time. When calculating the sensitivity index of one parameter, all other parameters are taken as fixed values, and the uncertainty of all parameters cannot be considered simultaneously. Therefore, the variance-based and the moment-independent global sensitivity analysis (GSA) methods are both introduced to determine the influence of geotechnical parameters on slope stability in this study. To solve the importance index of GSA, the least angle regression algorithm, the kernel density estimation, and orthogonal polynomial estimation methods are developed to obtain variance-based importance index and the moment-independent importance index, respectively. The proposed methods allow all variables to change simultaneously within their variation range and have high computational efficiency. The results are in good at with those obtained by the variance-based Monte Carlo simulation method, which is considered as the exact solution forobtaining the importance index. The influence of the correlation between the shear strength parameters (c and φ) on the importance index is also studied, which indicates that the negative correlation will have a great impact on the importance index, which in turn affects the safety assessment of slope. Three engineering cases have been studied for engineering application, and the compared results indicate that the impact of the geotechnical parameters uncertainty on the safety factor (Fs) and failure probability (pf) are different. Therefore, the approaches based on GSA which can integrate the Fs with pf will be a promising approach for slope stability evaluation.

Study on biaxial bending fatigue performance of Engineered Cementitious Composites (ECC)

Structural components such as bridge deck, highway pavement and thin-walled roof dome often are subjected to the biaxial and even multi-axis stress state due to the external load. Also, the fatigue effect cannot be ignored due to the moving vehicle load in the design of these structures. If engineering cementitious composites (ECC) is used in the above traditional concrete structures, their performance, such as easy cracking and short service life can be greatly improved. However, the biaxial bending fatigue performance of ECC should be analyzed in detail. At present, the biaxial bending test methods of cement-based materials include biaxial bending test (BFT) and centrally loaded round panel test (RPT). This study used both RPT and BFT test methods to analyze the biaxial fatigue performance of ECC and used four-point bending test (4PBT) uniaxial fatigue test as a reference. The stress levels S were set as 0.5, 0.6 and 0.7. The uniaxial and biaxial bending fatigue failure procedures of ECC were analyzed by plotting the three-stage deflection development curve, the fatigue damage and strain relationship curve based on the linear cumulative fatigue damage theory, and the S–N curve. The fatigue life of ECC biaxial bending specimens was greater than that of uniaxial bending specimens. At S = 0.5, the fatigue life: BFT > RPT. At S = 0.6, the fatigue life of BFT and RPT specimens was close. At S = 0.7, the fatigue life: BFT < RPT. With increasing stress level, the fatigue life of BFT specimen decreases more than that of RPT specimen. The lognormal distribution model and Weibull distribution model were used to fit the uniaxial and biaxial bending fatigue life of ECC, respsectively. Using the double logarithmic fatigue equation, fatigue life under the failure probability PF of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 was derived. The survival rate represents the level of safety reservation, which could provide reference and basis for the design of ECC bridge deck and highway pavement with different safety reservation requirements.

Application of artificial intelligence in predicting the residual mechanical properties of fiber reinforced concrete (FRC) after high temperatures

The practical application of Artificial Intelligence (AI) approaches in estimating the mechanical properties of fiber-reinforced concrete (FRC) subjected to high temperatures was initiated by developing a dataset including concrete mixtures, geometrical and mechanical properties of fiber, and temperatures. The dataset contains compressive strength, tensile strength, and modulus of elasticity of concrete with two distinct types of fiber, i.e., steel and polypropylene with an extensive range of temperatures from 100 to 1200 ℃. The dataset determined the gaps in the literature and showed FRC with high fiber aspect ratios and higher content of fiber (>0.8%) are not studied enough. The AI-based models showed that steel fiber-reinforced concrete (SFRC) has higher residual compressive strength compared with polypropylene fiber-reinforced concrete (PFRC). An increase in steel fiber diameter and length resulted in a higher compressive strength ratio at all temperatures. Moreover, higher PP fibers content and longer PP fibers decrease the rate of tensile strength degradation. A large probabilistic analysis was performed, and it showed that the failure probability (Pf) for PFRC is independent of W/B ratios and is almost 50%;. In contrast, for SFRC, W/B ratios between 0.4 to 0.5 have lower failure probability in comparison with other W/B ratios. Moreover, Pf for both fibers at a W/B ratio of 0.5 is almost independent of fiber content. Furthermore, the critical temperature resulting in failure (defined as the residual strength ratio less than 0.5) for SFRC and PFRC is 550 ℃ and 430 ℃, respectively.

Influence of hot-dip galvanization on the fatigue performance of high-strength bolted connections

In the present work, the influence of hot-dip galvanization (HDG) on the fatigue behaviour of high-strength bolted details is investigated through a set of 15 constant-amplitude tests. Cyclic behaviour of coated specimens is hence compared against results for unprotected samples drawn from literature, i.e., both with reference to neutral and aggressive exposure conditions. Namely, while behaviour of coated samples is moderately inferior as respect to uncoated ones in dry air (–6 % in terms of characteristic fatigue strength, probability of failure PF = 5 %, confidence interval CI = 75 %), their performance still complies with European normative requirements for double covered joints, and galvanization proves to be highly effective when corrosion is likely to occur (with a characteristic strength increase of [+12 %; +52 %]). Finally, fractography analyses on both uncoated and coated specimens were performed, suggesting that hydrogen embrittlement may play a role in reducing fatigue strength of coated joints, that is, especially within the high-cycle fatigue regime.

Reliability-based analysis of seismic bearing capacity of shallow strip footings resting on soils with randomly varying geotechnical and earthquake parameters

Seismic bearing capacity of strip footings is a challenging task for geotechnical engineers due to its stochastic framework instigated by the natural uncertainties incorporated into geotechnical properties and earthquake parameters. Consequently, the introduction of the random field theory into reliability analysis may provide power tools to succor designers check how reliable their designs. This paper aims to assess the seismic bearing capacity of shallow strip footings resting on soils with randomly varying parameters. Bearing capacity formulas for purely cohesive and cohesive-frictional soils are considered. The influence of the type of the autocorrelation functions (ACFs), the scale of fluctuations (SOFs) and the coefficient of variation (COV) of the random parameters are investigated. Statistical moments, probability density function (PDF) and failure probability (Pf) of the seismic bearing capacity are computed. It is shown that the Single Exponential (SNE) ACF is the most appropriate function to characterize the spatial variability of the soil properties since it provides conservative results. On other hand, the results indicate that the increase in the coefficients of variation (COV) of the cohesion or the friction angle increases the variability of the seismic bearing capacity while this variability remains unaffected when the COV of the seismic coefficient increases. The results also highlight that the effect of the vertical SOF on the PDF and the failure probability is much more significant than that of the horizontal SOF. In addition, the mean seismic bearing capacity fluctuates slightly as the horizontal or vertical SOF increases so that the increment of variation is between 0.4% and 2% for the both two soil types.

A Novel Sampling Method Based on Normal Search Particle Swarm Optimization for Active Learning Reliability Analysis

In active learning reliability methods, an approximation of limit state function (LSF) with high precision is the key to accurately calculating the failure probability (Pf). However, existing sampling methods cannot guarantee that candidate samples can approach the LSF actively, which lowers the accuracy and stability of the results and causes excess computational effort. In this paper, a novel candidate samples-generating algorithm was proposed, by which a group of evenly distributed candidate points on the predicted LSF of performance function (either the real one or the surrogate model) could be obtained. In the proposed method, determination of LSF is considered as an optimization problem in which the absolute value of performance function was considered as objective function. After this, a normal search particle swarm optimization (NSPSO) was designed to deal with such problems, which consists of a normal search pattern and a multi-strategy framework that ensures the uniform distribution and diversity of the solution that intends to cover the optimal region. Four explicit performance functions and two engineering cases were employed to verify the effectiveness and accuracy of NSPSO sampling method. Four state-of-the-art multi-modal optimization algorithms were used as competitive methods. Analysis results show that the proposed method outperformed all competitive methods and can provide candidate samples that evenly distributed on the LSF.

Slope Failure Risk Assessment Considering Both the Randomness of Groundwater Level and Soil Shear Strength Parameters

Conducting research on slope failure risk assessment is beneficial for the sustainable development of slopes. There will be various failure modes considering both the randomness of the groundwater level and soil shear strength parameters. Based on the integrated failure probability (IFP), the traditional failure risk analysis needs to count all failure modes, including the failure probability (Pf) and failure risk coefficient (C), one-by-one. A new slope failure risk assessment method that uses the sum of the element failure risk to calculate the overall failure risk is proposed in this paper and considers both the randomness of the groundwater level and soil shear strength parameters. The element failure probability is determined by their location information and failure situation; the element failure risk coefficient is determined by their area. It transforms the complex overall failure risk problem into a simple element failure risk problem, which simplifies the calculation process and improves the calculation efficiency greatly. The correctness is verified with the systematic analysis of a classical case. The results show that the slope failure probability and failure risk are greatly increased from 1.40% to 3.30% and 0.829 m2 to 2.094 m2 with rising groundwater level, respectively.

Insight from a Physical-Based Model for the Triggering Mechanism of Loess Landslides Induced by the 2013 Tianshui Heavy Rainfall Event

Rainfall-induced landslides pose a significant threat to human life, destroy highways and railways, and cause farmland degradation in the Loess Plateau. From 19 June 2013 to 26 July 2013, continuous and heavy rainfall events occurred in the Tianshui area, Gansu Province. This strong rainfall process included four short-term serious rainfall events and long-term intermittent rainfall, triggering many shallow loess landslides. To improve our understanding of this rainfall process as the triggering mechanism of the loess landslides, we conducted the physical-based spatiotemporal prediction of rainfall-induced landslides. By utilizing precipitation data recorded every 12 h from the rain gauge stations and 51 soil samples from within a 50 km radius of the study area, we predicted 1000 physical-based model-calculated pictures of potential landslides, and the slope failure probability (Pf) of the study area was obtained by Monte Carlo simulations. The model was validated by the actual landslide data of the 2013 heavy rainfall event, and the effects of the precipitation process and the trigger mechanism on the landslides were discussed. The results showed that the fourth rainfall event had the best prediction ability, while the third event had the second-best prediction ability. There was a solid linear link between the antecedent precipitation (Pa) and the predicted landslide area (Pls) based on the fitting relationship, indicating that antecedent rainfall may play a significant role in the occurrence of landslides in the region. By comparing the distribution of the predicted results of the four heavy rainfall events with the actual landslide, we observed that the first two rainfall processes may not have been the main reason for slope failure, contributing only to prepare for the landslides in the later period. The superposition of the fourth and third rainfall events finally determined the spatial distribution characteristics of the landslide induced by the 2013 heavy rainfall event.

Finite element-based reliability analysis of RC bridge piers subjected to the combination of barge impact and blast loads

In this paper, the reliability analysis of a girder bridge pier is presented when exposed to the combinations of barge collision and blast loads based on the finite element (FE) simulations performed in LS-DYNA and the Monte Carlo algorithm performed in MATLAB. An improved reliability analysis approach is proposed for the bridge pier under combined loads using the residual dynamic resistance capacities of the impacted bridge pier when subjected to sequential blast loading rather than utilizing the static resistance capacities of the pier columns which are commonly employed by conventional fault tree analysis. In the first step of the proposed framework, the response surface method (RSM) using the Box-Behnken design (BBD) method is employed for fitting the structural response surfaces and the internal forces of the pier columns obtained from the FE simulations. Then, the reliability analysis results including the failure probability (Pf) and corresponding reliability index (β) are calculated using the Monte Carlo algorithm in MATLAB. Finally, the sensitivities of Pf and β to various barge collision and blast loading parameters are assessed, and fragility curves are plotted for the reliability analysis results. From the reliability analysis of the pier under combined loads, it is found that the failure probabilities of the pier resulting from the proposed method are greater than those from the conventional method based on the static capacities of the pier. Therefore, the conventional static-based method provides an unconservative approach and the residual dynamic capacities of the impacted and damaged pier should be considered under the sequential blast loading for reliability analysis of the pier under combined loads.

Flexure fatigue strength and failure probability of self compacting concrete made with RCA and blended cements

The examination of the fatigue strength of self-compacting concrete (SCC) under flexural loads is the prime objective of the present investigation. SCC comprises recycled concrete aggregates (RCA) and blended cements, i.e., either silica fume (SF) or metakaolin (MK), which differentiates it from the reference mix. Fatigue life data has been accumulated by conducting flexural fatigue tests on beam specimens of size 100 mm × 100 mm × 500 mm. The existing fatigue equations based on SN relationships have been tested with the experimental data and proposed to predict the flexural fatigue strength for SCC constituting RCA and blended cements. An approach based on failure probability (Pf) has also been adopted for the prediction of flexural fatigue strength of SCC mixes. Therefore, SNPf curves have been generated for various SCC mixes under consideration. Several mathematical equations have also been proposed for various SCC mixes to predict the flexure fatigue strength at the desired level of failure probability (Pf). Endurance limit has also been evaluated for various SCC mixes. The introduction of blended cements in SCC mixes constituting RCA enhances the endurance limit, but the enhancement of endurance limit is most prominent in SCC mix containing RCA and MK.

Slope reliability analysis using Bayesian optimized convolutional neural networks

PurposeThis paper aims to develop an effective framework which combines Bayesian optimized convolutional neural networks (BOCNN) with Monte Carlo simulation for slope reliability analysis.Design/methodology/approachThe Bayesian optimization technique is firstly used to find the optimal structure of CNN based on the empirical CNN model established in a trial and error manner. The proposed methodology is illustrated through a two-layered soil slope and a cohesive slope with spatially variable soils at different scales of fluctuation.FindingsThe size of training data suite, T, has a significant influence on the performance of trained CNN. In general, a trained CNN with larger T tends to have higher coefficient of determination (R2) and smaller root mean square error (RMSE). The artificial neural networks (ANN) and response surface method (RSM) can provide comparable results to CNN models for the slope reliability where only two random variables are involved whereas a significant discrepancy between the slope failure probability (Pf) by RSM and that predicted by CNN has been observed for slope with spatially variable soils. The RSM cannot fully capture the complicated relationship between the factor of safety (FS) and spatially variable soils in an effective and efficient manner. The trained CNN at a smaller the scale of fluctuation (λ) exhibits a fairly good performance in predicting the Pf for spatially variable soils at higher λ with a maximum percentage error not more than 10%. The BOCNN has a larger R2 and a smaller RMSE than empirical CNN and it can provide results fairly equivalent to a direct Monte Carlo Simulation and therefore serves a promising tool for slope reliability analysis within spatially variable soils.Practical implicationsA geotechnical engineer could use the proposed method to perform slope reliability analysis.Originality/valueSlope reliability can be efficiently and accurately analyzed by the proposed framework.

Weibull reliability plots to study the strain rate effect on interfacial strengths of carbon fiber reinforced epoxy composites

AbstractTwo‐parameter Weibull reliability plots are utilized to determine the effects of strain rate on the interfacial strengths of unidirectional carbon fiber reinforced epoxy (CFRE) composites. Laminate specimens with two different fiber orientations are tested to failure under flexural loading. Type 1 laminates with fibers running parallel to specimen length (fiber orientation of 0° with respect to specimen span length) enable measuring inter‐laminar shear strength (ILSS) of the interface (between adjacent lamina) with locus of failure along beam mid ply. Seventy‐two type 1 laminates are tested at five levels of flexural strain rates: 1.89 * 10−5 to 9.37 * 10−2 s−1. Type 2 laminates with fibers running perpendicular to specimen length (fiber orientation of 90° with respect to specimen span length) enable measuring intra‐laminar (matrix/fiber) peel strength (ILPS) for tensile (mode I) strength of the matrix/fiber interface with locus of failure at beam bottom ply. Thirty‐six type 2 laminates are tested at three levels of flexural strain rates: 2.09 * 10−5 to 3.49 * 10−3 s−1. For each level of strain rate, Weibull plots are constructed. Stress values at failure probability (Pf) of 63.1% are assigned as strength values. The results show a slight decrease of the Weibull modulus, m, with increasing strain rates. The modulus decreases from 12.37 to 10.49 and from 11.11 to 9.68, for laminates type 1 and 2, respectively. For laminates type 1, ILSS increases with increasing strain rates rising 16.1% over the range of the tested strain rates. For laminates type 2, ILPS increases with increasing strain rates rising 38.1% over the range.

Probabilistic Evaluations of Prescribed Safety Margins in Eurocode 7 for Spread Foundations

According to the design code Eurocode 7, analysis procedures require reaching a prescribed safety margin, based on the conditions of levelling design action and design resistance. Such semi-probabilistic procedures do not result in a consistent equivalent value of the Overall Factor of Safety (OFS), neither in individual analysis nor in different tasks in geotechnical engineering. Furthermore, the implementation of different calculation approaches in Eurocode 7 also does not guarantee an equal probability of the occurrence of a relevant limit state. A comparative analysis is conducted for an example of a centrically loaded spread foundation on homogenous, isotropic, and coarse-grained soil, according to procedures in Eurocode 7, Design Approach 3. An algorithm is developed to estimate failure probability, taking into consideration the relevant statistical characteristics of each calculation parameter. A significant influence of the statistical characteristics of the relevant sample is emphasized. The degree of required modification of the equivalent Overdesign Factor (ODF) and the Overall Factor of Safety (OFS), based on the criterion of the required reliability index β and failure probability pf , is quantified.

RELIABILITY-BASED INVESTIGATION ON THE COMPRESSIVE STRENGTH OF COMMONLY USED NIGERIAN TIMBER SPECIES

This paper considers the compressive strength both parallel and perpendicular to grain of not less than twenty Nigerian-grown timber species out of which, six commonly used ones were selected and their compressive resistance assessed under certain loads. First, it was found out that the basic compressive stress perpendicular to the grain of timber is about 22% of the basic compressive stress parallel to grain. A reliability assessment was then carried out using the First Order Reliability Method (FORM) to investigate the performance of a column section of 250 x 250mm and 300 x 300mm for the six Nigerian-grown timber species. Lophira alata was found to be the most reliable with a Probability of failure Pf = 2.78 x 10-3 and 7.1 x 10-2 under an axial load of 1000kN and 2000kN respectively. This was followed by Anogeissus leiocarpus with Pf = 2.53 x 10-2 and 5.26 x 10-3 under an axial load of 1000kN and 1500kN respectively. Others that followed were ‘Iroko’(Chlorophora excelsa),‘Abura’ (Mitragyna ciliata),‘Afara’ (Terminalia superba), and ‘Obeche’(Triplochiton scleroxylon), in the order of descending performance. It can been established from this study that, ‘Ekki’ (Lophira alata) and African birch (Anogeissus leiocarpus) could be suitable for bridge piles and piers, railways or related structures that require compressive members with high axial capacity whereas, ‘Abura’, ‘Obeche’, ‘Afara’ and ‘Abura’ would be best suitable for buildings.

New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

This article presents new sensitivity measures in reliability-oriented global sensitivity analysis. The obtained results show that the contrast and the newly proposed sensitivity measures (entropy and two others) effectively describe the influence of input random variables on the probability of failure Pf. The contrast sensitivity measure builds on Sobol, using the variance of the binary outcome as either a success (0) or a failure (1). In Bernoulli distribution, variance Pf(1 − Pf) and discrete entropy—Pfln(Pf) − (1 − Pf)ln(1 − Pf) are similar to dome functions. By replacing the variance with discrete entropy, a new alternative sensitivity measure is obtained, and then two additional new alternative measures are derived. It is shown that the desired property of all the measures is a dome shape; the rise is not important. Although the decomposition of sensitivity indices with alternative measures is not proven, the case studies suggest a rationale structure of all the indices in the sensitivity analysis of small Pf. The sensitivity ranking of input variables based on the total indices is approximately the same, but the proportions of the first-order and the higher-order indices are very different. Discrete entropy gives significantly higher proportions of first-order sensitivity indices than the other sensitivity measures, presenting entropy as an interesting new sensitivity measure of engineering reliability.

The role of the geological uncertainty in a geotechnical design – A retrospective view of Freeway No. 3 Landslide in Northern Taiwan

The importance of the geological model in a geotechnical engineering project has long been recognized. However, the uncertainty associated with the geological model has rarely been quantified and explicitly considered in the geotechnical design. This paper explores the role of the geological model uncertainty and the benefit of reducing such uncertainty in a geotechnical design. To this end, the landslide that occurred on 25 April 2010 at 3.3 K of Freeway No. 3 in Northern Taiwan, referred to herein as NH-3 Slope, is re-analyzed with an assumed geological model (a dip-slope model in this case) under various uncertainty scenarios. Traditionally, the design (i.e., a choice of design parameters such as slope height, slope angle, and supporting anchors) of a rock slope seeks to satisfy a target factor of safety (FS). In the case of NH-3 Slope, the apparent dip angle of the slip surface along the dip direction of slope constitutes the geological model of concern. Different survey techniques produce data with varying degrees of error (or uncertainty) in the measured apparent dip angle. For example, data from a Regional Geological Map (RGM) typically yields an estimate of the bedding plane attitude with a significant level of uncertainty due primarily to low data density. In contrast, LiDAR can significantly reduce the uncertainty of the derived bedding plane attitudes. By lowering this uncertainty, the variation (or uncertainty) in the computed FS may be reduced, which tends to yield a lower failure probability (Pf), given other conditions being the same. The benefit of lowering the geological model uncertainty in a geotechnical design is demonstrated through a retrospective analysis of the NH-3 Slope.

Risk-Based Warning Decision Making of Cascade Breaching of the Tangjiashan Landslide Dam and Two Smaller Downstream Landslide Dams

Mega earthquakes or serious rainfall storms often cause crowded landslides in mountainous areas. A large part of these landslides are very likely blocking rivers and forming landslide dams in series along rivers. The risks of cascading failure of landslide dams are significantly different from that of a single dam. This paper presented the work on risk-based warning decision making on cascading breaching of the 2008 Tangjiashan landslide dam and two small downstream landslide dams in a series along Tongkou River. The optimal decision was made by achieving minimal expected total loss. Cascade breaching of a series of landslide dams is more likely to produce a multi-peak flood. When the coming of the breaching flood from the upstream dam perfectly overlaps with the dam breaching flood of the downstream dam, a higher overlapped peak flood would occur. When overlapped peak flood occurs, the flood risk would be larger and evacuation warning needs to be issued earlier to avoid serious life loss and flood damages. When multi-peak flood occurs, people may be misled by the warning of the previous peak flood and suddenly attacked by the peak flood thereafter, incurring catastrophic loss. Systematical decision making needs to be conducted to sufficiently concern the risk caused by each peak of the breaching flood. The dam failure probabilityPflinearly influences the expected life loss and flood damage but does not influence the evacuation cost. The expected total loss significantly decreases withPfwhen the warning time was insufficient. However, it would not change much withPfwhen warning time is sufficient.