Exact analytical solutions of nonlinear problems of tsunami wave run-up on slopes with different profiles

A review of papers investigating tsunami wave run-up on a beach is given and the control parameters of the problem are revealed. There are two such parameters in the case of ideal fluid: the bottom sloping angle and the breaking parameter. A stage-by-stage approach for finding run-up characteristics is formulated: the linear calculation of shoreline oscillations and the subsequent non-linear transformation of the solution according to the Riemann method. Solution of the nononedimensional problems of wave run-up on a beach in the linear formulation is obtained.     

Simplified formulae for designing coastal forest against tsunami run-up: one-dimensional approach

In the present study, laboratory experiments were conducted to validate the applicability of a numerical model based on one-dimensional nonlinear long-wave equations. The model includes drag and inertia resistance of trees to tsunami flow and porosity between trees and a simplified forest in a wave channel. It was confirmed that the water surface elevation and flow velocity by the numerical simulations agree well with the experimental results for various forest conditions of width and tree density. Further, the numerical model was applied to prototype conditions of a coastal forest of Pandanus odoratissimus to investigate the effects of forest conditions (width and tree density) and incident tsunami conditions (period and height) on run-up height and potential tsunami force. The modeling results were represented in curve-fit equations with the aim of providing simplified formulae for designing coastal forest against tsunamis. The run-up height and potential tsunami forces calculated by the curve-fit formulae and the numerical model agreed within ± 10% error.     

Revealing effect of bathymetry over tsunami run-up through factor analysis

The east coast of Tamil Nadu, particularly Chennai–Nagapattinam was worstly affected by the 2004 tsunami. Run-up shows remarkable variation of 2–8 m with maximum at Cuddalore port and minimum at Marina beach. Factors like width of dislocation, source distance, orientation of the coastline, and bathymetry guide tsunami surge. While most of the parameters are similar in characteristics for the entire coast, it is presumed that variation in bathymetry have played an imperative role in guiding run-up. Based on gradient bathymetry, up to 50 km off the coast was classified into five classes, viz shallow, moderate, and steep continental slope and continental shelf. Statistical analysis was performed between offshore bathymetry and run-up. The results clearly indicate that moderate slopes have guided tsunami to attain maximum height. While steeper slope have acted as barriers and gentle slopes have shoaled tsunami surge resulting in reduced run-up height. The study offers early but potentially meaningful guidance on the role of bathymetry on run-up.     

Determination of mangrove forest performance in reducing tsunami run-up using physical models

Coastal ecosystems such as mangroves fringing tropical coastlines have been recognized as natural protectors of the coastal areas against destructive attack of a tsunami. In this paper, the authors aim to investigate the interaction of a tsunami wave on a typical mangrove forest and to determine its performance in reducing the run-up. A laboratory experiment using a hydraulic flume with a mangrove forest model was carried out in which tests were conducted by varying the vegetation widths of 0, 1, 2 and 3?m and average densities of 8, 6 and 4 trees per 100?cm² using a scale ratio of 1:100. Two conditions of water levels were considered in the experiments at several tsunami wave heights between 2.4 and 14?cm. The dam break method used in the experiments produced two types of waves. At low water condition, a bore was developed and subsequently, a solitary wave was produced during high water. The results of the experiments showed that in general, vegetation widths and densities demonstrate a dampening effect on tsunami run-up. A larger vegetation width was found to be more effective in dissipating the wave energy. The first 1?m width of mangrove forest could reduce 23?C32?% during high water and 31?C36?% during low water. Increasing the mangrove forest width to 2 and 3?m could further increase the average percentage of run-up reduction by 39?C50?% during high water and 34?C41?% during low water condition. It was also observed that densities of the mangrove forest do not influence the run-up reduction as significantly as the forest widths. For mangrove forest densities to be significantly enough to reduce more tsunami run-up, an additional density of 4 trees/100?m² needs to be provided. The experiments also showed that mangrove roots are more effective in reducing the run-up compared to the trunks and canopies. The experiments managed to compare and present the usefulness of mangrove forests in dissipating wave energy and results produced are beneficial for initiating design guidelines in determining setback limits or buffer zones for development projects in mangrove areas.     

Laboratory experiments of tsunami run-up and withdrawal in patchy coastal forest on a steep beach

Laboratory experiments were carried out to study tsunami flow dynamics in the presence of patchy macro-roughness, representing coastal forest, on a 1:10 steep beach. The experimental setup included four cross-shore rows of roughness patches affixed to the dry beach in a staggered array, such that 12 % of the staggered array region had higher roughness. The flow field during run-up and withdrawal was quantified using point measurements of velocity and flow depth at 20 locations, while high-resolution video was used to track bore position during run-up. Data analysis revealed that while inundated area was marginally impacted when patchy roughness was present, flow depths and flow force were, respectively, increased by more than 40 and 30 % in some areas within the patch array; a decrease in flow force was also observed in some areas. Alongshore variation in flow depth, induced by the roughness patches, was most pronounced during withdrawal. These findings suggest that patchy macro-roughness, like that created by coastal forest, will simultaneously lead to increased protection in some areas and decreased protection in others.     

土坡稳定分析简化Bishop法的数值解

建立了适于边坡稳定分析简单的平面直角坐标系,得到了该坐标系下的边坡稳定分析瑞典圆弧法的积分表达式,与张天宝法进行了验证和对比;提出了基于边坡稳定分析简化Bishop法原理的积分法,推导了其安全系数Fs积分表达式,编制了数值积分计算和图形处理程序,并进行了工程应用,实践证明该方法的正确性。     

一种改进的公路边坡稳定性模糊评价方法研究

考虑影响公路边坡稳定性信息的不完整性、随机性和模糊性,以最大熵原理和工程模糊集理论为基础,并采用综合赋权法确定指标权重,提出了一种改进的公路边坡稳定性模糊评价方法。该模型充分利用影响因素的信息,以广义加权距离表示待评价样本与标准样本的差异,从优化条件中获得相对隶属度,并依据加权平均原则对边坡样本等级进行识别。该模型应用于常吉和吉怀高速公路边坡稳定性评价中,将评价结果与模糊综合模型和属性识别模型的结果以及边坡实际情况进行对比验证,体现了其较好的一致性,并且结果更合理。同时,该模型具有较小的信息熵值,表明其评价的不确定性小,可靠性较高,是一种边坡稳定性评价分析新方法,可在相关工程领域中应用推广。     

Identification of tsunami deposits considering the tsunami waveform: An example of subaqueous tsunami deposits in Holocene shallow bay on southern Boso Peninsula, Central Japan

This study proposes a tsunami depositional model based on observations of emerged Holocene tsunami deposits in outcrops located in eastern Japan. The model is also applicable to the identification of other deposits, such as those laid down by storms. The tsunami deposits described were formed in a small bay of 10–20-m water depth, and are mainly composed of sand and gravel. They show various sedimentary structures, including hummocky cross-stratification (HCS) and inverse and normal grading. Although, individually, the sedimentary structures are similar to those commonly found in storm deposits, the combination of vertical stacking in the tsunami deposits makes a unique pattern. This vertical stacking of internal structures is due to the waveform of the source tsunamis, reflecting: 1) extremely long wavelengths and wave period, and 2) temporal changes of wave sizes from the beginning to end of the tsunamis.

The tsunami deposits display many sub-layers with scoured and graded structures. Each sub-layer, especially in sandy facies, is characterized by HCS and inverse and normal grading that are the result of deposition from prolonged high-energy sediment flows. The vertical stack of sub-layers shows incremental deposition from the repeated sediment flows. Mud drapes cover the sub-layers and indicate the existence of flow-velocity stagnant stages between each sediment flow. Current reversals within the sub-layers indicate the repeated occurrence of the up- and return-flows.

The tsunami deposits are vertically divided into four depositional units, Tna to Tnd in ascending order, reflecting the temporal change of wave sizes in the tsunami wave trains. Unit Tna is relatively fine-grained and indicative of small tsunami waves during the early stage of the tsunami. Unit Tnb is a protruding coarse-grained and thickest-stratified division and is the result of a relatively large wave group during the middle stage of the tsunami. Unit Tnc is a fine alternation of thin sand sheets and mud drapes, deposited from waning waves during the later stage of the tsunami. Unit Tnd is deposited during the final stage of the tsunami and is composed mainly of suspension fallout. Cyclic build up of these sub-layers and depositional units cannot be explained by storm waves with short wave periods of several to ten seconds common in small bays.     

On the solution of steady unconfined seepage towards semi-infinite slopes

Analytical solutions for the two-dimensional problem of unconfined seepage towards semi-infinite slopes are described. The analysis employs complex variable techniques. Conformal mappings have been used to reduce the problem to solving an ordinary differential equation. The resulting integrals are presented in terms of special functions. The solutions for the location of the phreatic surface and the exit point have been obtained in parametric form. Some additional results and asymptotic expansions of the solutions are also presented. The numerical results have been calculated and plotted for different values of the slope angle in dimensionless co-ordinate space.     

An empirical coverage test for theg-sample problem

A nonparametricg-sample empirical coverage test has recently been developed for univariate continuous data. It is based upon the empirical coverages which are spacings of multiple random samples. The test is capable of detecting any distributional differences which may exist among the parent populations, without additional assumptions beyond randomness and continuity. The test can be effective with the limited and/or unequal sample sizes most often encountered in geologic studies. A computer program for implementing this procedure, G-SECT 1, is available.     

An empirical strength criterion for heterogeneous tuff

An empirical failure criterion is formulated by expressing the second invariant of stress deviation at failure as a function of the first invariant of stress, key parameter, and volume. Strength data from Apache Leap tuff specimens are analyzed as a demonstration example. The density variable included as a key parameter for this tuff minimizes the effect of heterogeneity caused by nonuniform distribution of pores, mineralogy, inclusions, welding and grain bonding. The criterion incorporates all principal stresses and the scale effect, and hence allows predicting the strength toward in-situ conditions. The proposed derivation improves the correlations between test results and failure envelope for the heterogeneous tuff. The criterion formulated from the uniaxial and triaxial test data adequately predicts the strengths for biaxial compression tests.     

A simple model for calculating tsunami flow speed from tsunami deposits

This paper presents a simple model for tsunami sedimentation that can be applied to calculate tsunami flow speed from the thickness and grain size of a tsunami deposit (the inverse problem). For sandy tsunami deposits where grain size and thickness vary gradually in the direction of transport, tsunami sediment transport is modeled as a steady, spatially uniform process. The amount of sediment in suspension is assumed to be in equilibrium with the steady portion of the long period, slowing varying uprush portion of the tsunami. Spatial flow deceleration is assumed to be small and not to contribute significantly to the tsunami deposit. Tsunami deposits are formed from sediment settling from the water column when flow speeds on land go to zero everywhere at the time of maximum tsunami inundation. There is little erosion of the deposit by return flow because it is a slow flow and is concentrated in topographic lows. Variations in grain size of the deposit are found to have more effect on calculated tsunami flow speed than deposit thickness. The model is tested using field data collected at Arop, Papua New Guinea soon after the 1998 tsunami. Speed estimates of 14 m/s at 200 m inland from the shoreline compare favorably with those from a 1-D inundation model and from application of Bernoulli's principle to water levels on buildings left standing after the tsunami. As evidence that the model is applicable to some sandy tsunami deposits, the model reproduces the observed normal grading and vertical variation in sorting and skewness of a deposit formed by the 1998 tsunami.     

An approach for estimating the largest probable tsunami from far-field subduction zone earthquakes

Following the recent unexpected earthquake events of 2004 and 2011, it can be cautiously extrapolated that all major subduction zones bearing the capacity to produce mega-earthquake events will eventually do so given enough time, irrespective of the lack of such in the relatively short historical record. This notion has led to an effort of assigning maximum earthquake magnitudes to all major subduction zones, either based on geological constraints or based on size–frequency relations, or a combination of both. In this study, we utilize the proposed maximum magnitudes to assess tsunami hazard in Central California in the very long return periods. We also assessed tsunami hazard following an alternative methodology to calculate maximum magnitudes, which uses scaling relations for subduction zone earthquakes and maximum fault rupture scenarios found in literature. A sensitivity analysis is performed for Central California that is applicable to any coastal site in the Pacific Rim and can readily provide a strong indication for which subduction zones beam the most energy toward a study area. The maximum earthquake scenarios are then narrowed down to a few candidates, for which the initial conditions are examined in more detail. The chosen worst-case scenarios for Central California stem from the Alaska–Aleutian subduction zone that beams more energy and generates the biggest amplitude waves toward the study area. The largest tsunami scenario produces maximum free surface elevations of 15 m and run-up heights greater than 20 m.     

An empirical strength criterion for jet grouted soilcrete

Based on experimental data, this paper presents an empirical strength criterion for jet grouted soilcrete. Cylindrical specimens drilled from construction sites were tested to investigate the strength characteristics of soilcrete. Experiments conducted include the uniaxial compression test, Brazilian test and the triaxial compression test. It was found that soilcrete density increases with increasing depth. The uniaxial compressive strengths obtained were significantly greater than the design values suggested by the JSG Association of Japan. Experimental Poisson's ratios varied from 0.12 to 0.22, which are closer to that for concrete than that for native soil. Based on test results, a parabolic-type empirical criterionτ_ff = N·σ_ff + T_o)^M is proposed to describe the strength behaviour of soilcrete under low and tensile stress regions.     

全球海啸地震震源机制解及海啸成因探讨

海啸作为五大海洋自然灾害之一,严重威胁着人类生命财产安全。近些年来,国内外学者对地震海啸进行了大量研究,主要针对海啸的生成、传播、爬高和淹没的数值模拟,以及古海啸沉积物进行研究,但是对于海啸地震震源机制的研究还比较欠缺,尤其是缺乏对震级小于6.5的海啸地震的研究。针对我国的地震海啸研究现状,强调震级小于6.5地震引发海啸的问题不容忽视。本文归纳整理了全球766次地震海啸,利用三角图分类基本法则对海啸地震震源机制解进行分类,并对其中341个发生在1976年后的海啸地震进行震源机制解分析,对其中633次海啸浪高进行统计学方法分析研究。本文认为逆冲型、正断型、走滑型和奇异型机制地震均能引发海啸,逆冲型地震引发的海啸占比最大,震级小于6.5级地震引发的海啸的浪高也有高达10 m的情况,也能产生巨大破坏性。逆冲型、正断型、奇异型地震可直接引起海底地形垂向变化,进而引发海啸,而走滑型地震引发海啸则可能有两种原因,一种是走滑型地震并非纯走滑型而是带有正断或逆冲分量从而引发海啸,另外一种是走滑型地震引发海底滑坡导致海底地形变化进而产生海啸。从海啸地震震源深度分析,能产生海啸的地震震源深度97%以上都是浅源地震,主要集中在30 km深度以内,但是也有中深源地震海啸。本文综合海啸地震的震源特点、我国地理位置以及以往海啸发生的情况,认为未来我国沿海地区威胁性的地震海啸主要集中在马尼拉海沟和台湾海峡区域,在今后海啸预警方面需要格外重视这些区域,通过建立完善海啸预警系统来减少损失。     

Evaluation of tsunami impacts on shallow marine sediments: An example from the tsunami caused by the 2003 Tokachi-oki earthquake, northern Japan

A combined approach of field geology and numerical simulation was conducted for evaluating the tsunami impacts on the shelf sediments. The 2003 Tokachi-oki earthquake, M 8.0, that occurred on 25 September 2003 off southeastern Hokkaido, northern Japan, generated a locally destructive tsunami. Maximum run-up height of the tsunami waves reached 4 m above sea level. In order to estimate the tsunami impacts on shallow marine sediments, we compared pre- and post-tsunami marine sediments in water depths of 38–112 m in terms of grain size, sedimentary structure, and microfossil content. Decreases of fine fractions, especially finer than very fine sand, which led to coarsen the mean grain size, were detected in the inner shelf of the northern part of the study area. Foraminiferal assemblages also changed in the coarsened sediments. On the other hand, the other shelf sediments largely unchanged or slightly fined. We also simulated the tsunami wave velocity and direction, and grain size entrained by the modeled tsunami. The numerical simulation resulted in that the 2003 tsunami could transport very fine sand in water depths shallower than 45–95 m at the northern part of the study area. This is comparable with the actual grain-size changes after the tsunami had passed. However, some storms and tidal currents might also be possible to stir the surface sediments after the pre-tsunami survey, so we could not conclude that the grain-size changes had been caused only by the tsunami. Nevertheless, a combined approach of sampling and modeling was powerful for estimating the tsunami impacts under the sea.     

Integrated tsunami intensity scale based on maxima of tsunami amplitude and induced current

As with earthquakes, river floods, water waves, and wind intensities, a tsunami intensity has to be synthetic and comprehensive to be efficient. Tsunami impact is complex because the effects can be felt on the beach, on inundated areas and also at berths and anchors. Within the same local area, a tsunami may severely impact the population on the coast, while its effects may be negligible on marine bodies (boats). Most existing tsunami intensity scales are based either on water elevation or on induced currents. However, it is commonly admitted that both variables should be considered simultaneously. Several existing intensity scales were integrated and were made consistent with each other. An original intensity scale is then derived based on analysis of the interdependency between the maxima of tsunami amplitude and induced current: The dimension of the couple composed by two variables is analyzed, in particular through the derivation of a linear relationship using the long wave theory and the use of a fully nonlinear numerical experiment. Our intensity scale is particularly well adapted to numerical studies, for which the two variables are naturally derived within an entire computational grid. Once the tsunami intensity scale was set up, it was briefly applied to a particular case study: the impact of the Sumatra tsunami, dated December 26, 2004, on the coast of Sri Lanka. Indeed, the tsunami scales proposed herein represent an initial framework of study and can be further improved through new or revisited tsunami observations.

     

An empirical model for plagioclase equilibrium in hydrous melts

Heat capacity models for anorthite (An) and albite (Ab) crystal and supercooled liquid, together with the assumption of ideal mixing of these components were used to derive average values of enthalpy and volume of melting from phase equilibrium data that are in significant disagreement with some recently published thermodynamic data. In an effort to find a means of calculating both liquidus temperature and crystal composition of plagioclase for a given hydrous melt composition, the activity models for feldspar components in hydrous melts and solubility calculations suggested by Burnham (1975) and the enthalpy data above were tested by comparing predicted and observed liquidi. These assumptions lead to satisfactory agreement in the systems Ab-An-H₂O and Ab-Si₄O₈-H₂O but liquidi in the system An-Si₄O₈-H₂O and complex systems differ radically from those calculated. For hydrous complex melts an empirical model using the above solubility and activity assumptions was fit to experimental data on coexisting melt and plagioclase compositions. Despite the demonstrable theoretical limitations of the assumptions involved, this empirical model apparently balances inaccuracies and reproduces the original data with absolute mean errors for 66 experiments of 17°C and 5 mol% An. It is sufficiently precise for use in kinetic crystallization models and may be useful as a geothermometer in some applications; it is probably not sufficiently accurate to be used as a geobarometer.     

An empirical model for predicting flakiness in cone crushing

A fundamental understanding of the factors influencing particle shape is of central importance for optimisation of the output quality from crushing plants for aggregate production. The literature reports that the wear on and setting of a cone crusher influence particle shape, The fact that wear on and the setting of a cone crusher influence particle shape is considered common knowledge and is also reported in the literature. To date, no mathematical model for predicting particle shape has been presented.