probability density function curve for the liquefaction safety factor and reliability assessment, an. 12[r]

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Abstract. During an earthquake, seismic waves propagate vibrations that carry energy from the source of the shaking outwards. Seismic waves can be distinguished by the **velocity** and shape of propagation. The **velocity** of waves depends on the elastic properties and density of the soil layers through which the waves pass. **Probabilistic** analysis of earthquake waves can be used as an eective tool to evaluate inherent uncertainty in the soil properties and the resulting uncertainty in site classication. In this research, the jointly distributed random variables method is used for **probabilistic** analysis and reliability assessment of the **shear** **wave** **velocity** relationship. The selected stochastic parameters are density, elastic modulus and Poisson's ratio which are modeled using truncated normal probability distribution functions. The results are compared with the Monte Carlo simulation, point estimated method and rst order second moment method. Comparison of the results indicates very good performance of the proposed **approach** for assessment of reliability. It is shown that this method can correctly predict the inuence of stochastic input parameters and capture the expected probability distribution of **shear** **wave** **velocity** correctly. It is also shown that the modulus of elasticity is the most eective parameter in **shear** **wave** **velocity**.

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In the simplified stress-**based** **approach** for **liquefaction** analysis, seismic demand is calculated as the cyclic **shear** stress ratio applied by an earthquake (CSR) and the cyclic resistance ratio (CRR) of the soil (capacity) is estimated from a correlation with an in-situ test. Earthquake-induced CSR can be estimated using the Seed and Idriss (1971) simplified procedure or numerical methods such as finite element method **based** seismic response analysis. The simplified procedure provides CRR of a level-ground (no **shear** stress bias) for an effective overburden pressure of 100 kPa. Cyclic **liquefaction** is deemed to occur when CSR exceeds CRR. Semi-empirical relationships between CRR and SPT or CPT penetration resistance have been extensively studied by many researchers. Determining CRR from in-situ **shear** **wave** **velocity** measurement can be a particularly useful alternative for sites underlain by soils that are difficult to penetrate or extract undisturbed samples. Robertson, et al. (1992) present one of the earliest boundary curves between **liquefaction** and non- **liquefaction** cases using a limited field database. **Based** on cases of **liquefaction** and non-**liquefaction** for 26 earthquakes and more than 70 different sites, Andrus and Stokoe (2000) developed relationships between CRR and VS1 which are the current state of practice for evaluating **liquefaction** potential using VS1.

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The **probabilistic** relationship proposed by Liao et al. employs a larger number of case history data points than were used by Seed et al. (1984), but this larger number of data points is the result of less severe screening of points for data quality. This relationship was developed using the maximum likelihood esti- mation method for **probabilistic** regression (binary regression of logistic models). A largely judgmental correction was made for sampling bias, and this significantly affected the final relation- ships. Liao et al. sought, but failed to find, a significant impact of fines content on the regressed relationship between SPT penetra- tion resistance and **liquefaction** resistance, and so developed reli- able curves [Fig. 2(a)] only for “clean” sandy soils (soils with less than 12% fines). This was a landmark effort in its time, and it set high standards for those that followed.

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Group **velocity** dispersion data of surface waves travelling through the central portion of the Philippine Sea were used to construct a one-dimensional (1-D) upper mantle **shear** **wave** model, ARC-1. Several studies have been done to reveal the lateral variations of the upper mantle structure in the Philip- pine Sea region since Kanamori and Abe (1968). Seekins and Teng (1977) studied on the laterally heterogeneous structure in the upper mantle beneath the Philippine Sea with using seismograms recorded at Guam which is the WWSSN sta- tion located at the eastern edge of the Philippine Sea. They regionalized the Philippine Sea plate into three sub regions according to its topographic features. Shiono et al. (1980) also made a surface **wave** analysis using group **velocity** dis- persion data. They investigated waveforms which traversed western (West) and eastern (East) Philippine Sea. Senna et al. (1990) and Oda and Senna (1994) divided the Philippine Sea region and its marginal region into seven sub regions ac- cording to the topographic features and obtained a 1-D **shear** **wave** **velocity** structure for each sub region using group ve- locity dispersion data. As to body **wave** analysis, Iidaka et al. (1989) is the only study to investigate the lateral hetero- geneity of the upper mantle in the Philippine Sea.

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And the **shear** **wave** **velocity** of rock can be influenced by porosity, fluid saturation, fractures, pressure and tem- perature (Toksoz et al. 1976). Hence the near-surface **shear** **wave** **velocity** is subjected to a variety of environ- ment conditions, such as crustal stress, ground surface perturbation and atmospheric forcing. Many researchers have observed change of near-surface **velocity** caused by strong motion (Hobiger et al. 2012; Nakata and Snieder 2011; Niu et al. 2008), plate motion (Nakata and Snieder 2012a; Takagi and Okada 2012), volcanic eruption (Bren- guier et al. 2008, 2011), earth tide (Hillers et al. 2015a, b), seasonal variations, including temperature, precipitation, groundwater level; sea level, wind and so on (Clements and Denolle 2018; Meier et al. 2010; Richter et al. 2014; Sen-Schönfelder and Wegler 2006; Tsai 2011; Wang et al. 2017).

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rock peak ground acceleration (PGA) hazard curves for one of the locations. This figure also shows the corresponding soil PGA hazard curve, transformed from the rock curves using the soil/rock amplification relation presented in [15]. These soil PGA hazard curves correspond to Eq. 5. Each of the circle symbols on the hazard curve in Figure 4 indicates where a magnitude-distance deaggregation matrix value [Eq. 6] is available to use in ASHLES. Figure 5 is an example ground motion deaggregation matrix for one point along the hazard curve. As an observation for this particular site at this example ground motion and hazard level, the highest peaks are coming from the dominating contribution to ground motion hazard of the Hayward-Rodgers Creek (63%) and San Andreas (17%) faults, identifiable from their distinguishing magnitude and distance distributions. This deaggregation matrix indicates that much of the remaining PGA hazard contribution is coming from nearby (0 to 10km) smaller magnitude events not associated with any given fault. Deaggregation matrices for different points along a hazard curve will indicate differing relative contributions by the various seismic sources. As discussed above, and indicated by the summation over a i in Eq. 17, the evaluation of annual probability of **liquefaction**

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We utilized the **shear** **wave** **velocity** information of 243 boreholes. These boreholes were drilled during geotech- nical studies for different projects such as hotels, residential and commercial buildings. Downhole **shear** **wave** profiling has been done by Zamin Physics Consulting Engineering Company. Mashhad is spiritual capital of Iran and more than 20 million tourists and pilgrims visit the city annually. Hence tendency increases to construct high- raised commercial buildings, malls, and hotels. The main aim of downhole Vs measuring are determining seis- mic soil classification **based** on 2800 Iranian Seismic Code. Most of the boreholes were drilled to depth of 30 m although some continue more than 30 meters. The Vs profiles scattered throughout the city are shown in Figure 1. 2.3. Method

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During the experiments, the nylon wires were first pre- stretched to the maximum tension of 57 N. A single unipolar **wave** pulse was then manually generated by perturbing the first metal rod, and the tension was subsequently dropped to 12.4 N by releasing the lever during propagation. In order to avoid the superposition of boundary reflections with the waves we wanted to study, the release of the lever was timed so that the waveform would always be in the center of the system when the tension dropped. The tension drop happens in a fraction of a period. Figure 4 shows the propagation measured during an experiment: the axes represent the time elapsed and the spatial coordinates of each rod expressed by rod number; due to the limited field of view of the camera, the extremal rods were not imaged and therefore do not appear in the plot. The color scheme represents the ampli- tude of rotation of each bar, so that the bright yellow “bands” essentially correspond to the positive forward trav- eling **wave**. At time t 1:5 s the effects of the tension drop can be seen. A reflected **wave** appears as the broad band that moves backwards from right to left, with its negative ampli- tude represented in dark blue. In addition, broadening of the

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When considering this model, there may be a question of the validity of binding structure defects to the grid and assessing the impact of cell size on the resulting fragmentation spectrum because when changing the cell size, the spatial distribution of the initial inhomogeneities will change fundamentally. This point was analyzed in detail and the following conclusions were made. The selected grid step, in fact, determines the level of the structure **modeling**, at the same time at any level there are distributed real inhomogeneities, which act as triggers and initiate the formation of microcracks. At the atomic level, the inhomogeneities are dislocations and other defects of the crystal lattice. In larger scale analysis, grains and grain boundaries act as defects. In macro analysis, the inhomogeneities are already microcracks and other relatively large stress concentrators. Thus, the **approach** with the distribution of strength characteristics is applicable for any cell size, however, as in any other algorithm using grid approximation, the cell size should be sufficient to ensure the necessary accuracy (in this case – the accuracy of the definition of the fragmentation spectrum).

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Abstract-- In This paper we will present a new methodology for **modeling** and optimization of maintenance costs, in a different and innovate way, and highlights, management methods **based** on the process **approach**, as recommended by the ISO 9000, mainly, this new method get their strategy from the Unity of Value Added (UVA). An application of this hybrid method to calculate maintenance costs is detailed.

Abstract—This paper presents a parsimonious Bayesian indoor **wave** propagation model for predicting signal power in multi-wall multi-ﬂoor complex indoor environments. The received power is modeled as a Bayesian multiple regression model. The parameters of the model are assessed and validated using a two-tier validation strategy in which Bayes factor and posterior probability are used in the ﬁrst tier and second tier, respectively. The performance of the two-tier strategy is then assessed using Bayesian information criterion. The proposed indoor propagation model is tested in a two-storey building with access points operating at 2.4 GHz.

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middle part of central Java, north to Merapi and Lawu volcanoes, there is a large and very intense anomaly with a **velocity** decrease of up to 30% and 35% for P and S models, respectively. Inside this anomaly E-W orientation of fast **velocity** takes place, probably caused by regional extension stress regime. They observed that in a vertical section there is a faster horizontal velocities inside this anomaly that might be explained by layering of sediments and/or penetration of quasi-horizontal lenses with molten magma. Luehr et al [4] identiﬁed a large low **velocity** body in the crust which extends down to the upper mantle beneath Central Java. The **shear** **wave** signals recorded above this anomaly are strongly attenuated compared to the neighboring areas. Active volcanoes like Merapi, Sumbing, and Lawu are located at the edge of this anomaly between high and low **velocity** regions. In this paper we try to model the **shear** **wave** velocities in the crust between the Merapi and Lawu volcanoes anomaly (MLA) inferred from Love **wave** dispersion.

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Another significant limitation of existing ELM’s is a lack of openness regarding the model building process. In this process, a modeler must make choices regarding which predictor variables to include, how to pre-process these predictors, what model forms to use, and many more. When a modeler makes these decisions, either manually or as part of pre-programmed algorithm, they will naturally have some idea of what “good model performance” is and make their choices to achieve it. This notion of good performance can be concrete such as some statistical metric, **based** on engineering judgement and experience, or most often some combination of the two. While necessary to the **modeling** process, this introduces bias. Because these training methods and metrics are often not reported along with the finished product, practitioners and code writers cannot currently evaluate these model biases when selecting which relationships to use or recommend in guidance documents. Within this context of our own definition of “good model performance” we discuss the impacts of **modeling** choices and how they can be used in future model development.

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Inversion results show that most cracks have a relatively steep dip; however, the results for stations P06 and P11 indicate that the shallow dip of the cracks (<40°) may indeed be related to fractures associated with the overall shape of the Krafla-Leirhnúkur geothermal field, which stretches between the two regions of **shear** **wave** attenuation imaged by Einarsson (1978). As the source volume of most of our events lies between 1- 2 km depth, fractures at this depth are likely to be formed by deformation within the near- surface, extrusive part of the crust, dike injections, or the strike-slip across the divergent plate boundary. Figure 3.7 shows some of the major geological lineament structures to the north of Iceland. It seems that the NW-SE oriented fracture systems detected by this study could also be interpreted as the subsurface continuation of Dalvik Lineament. The magnitude of splitting delays is similar to what has been observed elsewhere within the Neovolcanic Zone of Iceland (Menke et al., 1994). The high scatter of time delays are also observed by Volti and Crampin (2003a, 2003b) and should be accounted for by similar explanations thereof.

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Classical tension field theory can represent the post-buckling behaviour of plate girders very well [9-11, 14-17]. In these models, **shear** resistance involves three stages: pre-buckling, post-buckling and collapse. In the pre-buckling stage, no buckling appears in the panel, and the principal tensile and compressive stresses are identical until elastic buckling happens. The elastic buckling strengths of plates under various conditions are given by Timoshenko [24]. In the post-buckling stage, stress redistribution occurs, with increase occurring especially in the directions of the tensile principal stresses. Any additional compressive stress after web **shear** buckling can effectively be neglected. In the collapse stage, four plastic hinges appear on the flanges, and finally the plate girder fails in a “sway” mechanism. In the proposed **analytical** model, for Class 1 beams, the **shear** response once again consists of three stages, which differ from those of tension field theory. These are the elastic, plastic and plastic post-buckling stages. The behaviour of the web panel of a Class 1 beam subject to **shear** and bending moment is compared with that of a plate girder in Fig. 3.

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standard deviation of the second Gaussian mixture respectively, Y is displacement measurements at X instances. No modifications are happened to linear regression implementation performed in the Lateral TTP algorithm. Regressions are not applied to lateral locations within ROE i.e. one excitation beam width deﬁned by (F/#)* from excitation center and extended over lateral range where the peak displacements remained above 1 m. The inverse slopes of these regression lines, with goodness-of-ﬁt metrics exceeding a threshold (R2 >0.8, 95% CI <0.2), represent the material’s local **shear** **wave** speeds. These speciﬁc goodness- of-ﬁt metrics is applied to all of the datasets presented throughout this manuscript. The material’s **shear** modulus is then estimated using Eq. 3 [31].

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As expected, group and phase speed values for a certain heart sample at a given stretch state were depth- and probe orientation-dependent, due to the varying myocardial fiber orientation across tissue thickness. The range of the resulting group speed values of all hearts corresponded to values previously reported in literature: 2-6 m/s for in vitro porcine hearts at 0% stretch [6]. Uniaxial stretching the myocardial slab increased the group and maximally excited phase speed, as could be seen from the 75 th percentile increase, but also from the increasing predicted marginal mean of each variable during stretching. This increase was mainly caused by an increase in **wave** speed for probe orientation angles oriented along the fiber direction for both cases. This trend was more convincing for group speed than for phase speed, as the GLM statistical model fit showed an adjusted R-squared value of 0.804 for group speed vs. a value of 0.415 for maximally excited phase speed (also related to the fewer data points for phase speed analysis). Furthermore, for maximally excited phase speed, tissue depth was the second most relevant factor in determining marginal mean phase speed for a mean heart at a mean depth, whereas this was the fourth relevant factor for the group speed. This is also noticed from the larger 95% confidence interval in Fig. 5 vs. Fig. 2.

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