Application of importance sampling method in sliding failure simulation of caisson breakwaters

It is assumed that the storm wave takes place once a year during the design period, and N histories of storm waves are generated on the basis of wave spectrum corresponding to the N-year design period. The responses of the breakwater to the N histories of storm waves in the N-year design period are calculated by mass-spring-dashpot mode and taken as a set of samples. The failure probability of caisson breakwaters during the design period of N years is obtained by the statistical analysis of many sets of samples. It is the key issue to improve the efficiency of the common Monte Carlo simulation method in the failure probability estimation of caisson breakwaters in the complete life cycle. In this paper, the kernel method of importance sampling, which can greatly increase the efficiency of failure probability calculation of caisson breakwaters, is proposed to estimate the failure probability of caisson breakwaters in the complete life cycle. The effectiveness of the kernel method is investigated by an example. It is indicated that the calculation efficiency of the kernel method is over 10 times the common Monte Carlo simulation method.     

Dynamic response and sliding distance of composite breakwaters under breaking and non-breaking wave attack

Over the last 15 years improved awareness of wave impact induced failures has focused attention on the need to account for the dynamic response of maritime structures to wave impact load. In this work a non-linear model is introduced that allows evaluating the effective design load and the potential sliding of caisson breakwater subject to both pulsating and impulsive wave loads. The caisson dynamics is modelled using a time-step numerical method to solve numerically the equations of motion for a rigid body founded on multiple non-linear springs having both horizontal and vertical stiffness. The model is first shown to correctly describe the dynamics of caisson breakwaters subject to wave attack, including nonlinear features of wave–structure–soil interaction. Predictions of sliding distances by the new method are then compared with measurements from physical model tests, showing very good agreement with observations. The model succeeds in describing the physics that stands behind the process and is fast, accurate and flexible enough to be suitable for performance design of caisson breakwaters.     

Application of Importance Sampling Method in Sliding Failure Simulation of Caisson Breakwaters

It is assumed that the storm wave takes place once a year during the design period, and N histories of storm waves are generated on the basis of wave spectrum corresponding to the N-year design period. The responses of the breakwater to the N histories of storm waves in the N-year design period are calculated by mass-spring-dashpot mode and taken as a set of samples. The failure probability of caisson breakwaters during the design period of N years is obtained by the statistical analysis of many sets of samples. It is the key issue to improve the efficiency of the common Monte Carlo simulation method in the failure probability estimation of caisson breakwaters in the complete life cycle. In this paper, the kernel method of importance sampling, which can greatly increase the efficiency of failure probability calculation of caisson breakwaters, is proposed to estimate the failure probability of caisson breakwaters in the complete life cycle. The effectiveness of the kernel method is investigated by an example. It is indicated that the calculation efficiency of the kernel method is over 10 times the common Monte Carlo simulation method.     

沉箱式防波堤静力与动力稳定性设计体型分析

将沉箱式防波堤滑移和倾覆稳定性设计方法分为三类：静力设计方法、不允许沉箱出现滑移和摇摆角的动力设计方法、控制沉箱滑移量和摇摆角的动力设计方法。建立了满足给定抗滑和抗倾安全系数条件下，按静力设计方法确定沉箱尺度的控制方程，研究了波浪条件和安全系数取值对沉箱长宽比的影响。通过动力数值计算分析了沉箱长宽比对沉箱滑移量和摇摆角的影响，并与传统静力设计理论进行了比较，讨论了控制沉箱滑移量和摇摆角的动力设计方法的可行性。     

Dynamic Stability Analysis of Caisson Breakwater in Lifetime Considering the Annual Frequency of Severe Storm

In the dynamic stability analysis of a caisson breakwater, most of current studies pay attention to the motion characteristics of caisson breakwaters under a single periodical breaking wave excitation. And in the lifetime stability analysis of caisson breakwater, it is assumed that the caisson breakwater suffers storm wave excitation once annually in the design lifetime. However, the number of annual severe storm occurrence is a random variable. In this paper, a series of random waves are generated by the Wen Sheng-chang wave spectrum, and the histories of successive and long-term random wave forces are built up by using the improved Goda wave force model. It is assumed that the number of annual severe storm occurrence is in the Poisson distribution over the 50-year design lifetime, and the history of random wave excitation is generated for each storm by the wave spectrum. The response histories of the caisson breakwater to the random waves over 50-year design lifetime are calculated and taken as a set of samples. On the basis of the Monte Carlo simulation technique, a large number of samples can be obtained, and the probability assessment of the safety of the breakwater during the complete design lifetime is obtained by statistical analysis of a large number of samples. Finally, the procedure of probability assessment of the breakwater safety is illustrated by an example.     

Dynamic Stability Analysis of Caisson Breakwater in Lifetime Considering the Annual Frequency of Severe Storm

In the dynamic stability analysis of a caisson breakwater, most of current studies pay attention to the motion characteristics of caisson breakwaters under a single periodical breaking wave excitation. And in the lifetime stability analysis of caisson breakwater, it is assumed that the caisson breakwater suffers storm wave excitation once annually in the design lifetime. However, the number of annual severe storm occurrence is a random variable. In this paper, a series of random waves are generated by the Wen Sheng-chang wave spectrum, and the histories of successive and long-term random wave forces are built up by using the improved Goda wave force model. It is assumed that the number of annual severe storm occurrence is in the Poisson distribution over the 50-year design lifetime, and the history of random wave excitation is generated for each storm by the wave spectrum. The response histories of the caisson breakwater to the random waves over 50-year design lifetime are calculated and taken as a set of samples. On the basis of the Monte Carlo simulation technique, a large number of samples can be obtained, and the probability assessment of the safety of the breakwater during the complete design lifetime is obtained by statistical analysis of a large number of samples. Finally, the procedure of probability assessment of the breakwater safety is illustrated by an example.     

Expected Sliding Distance of Vertical Slit Caisson Breakwater

Evaluating the expected sliding distance of a vertical slit caisson breakwater is proposed. Time history for the wave load to a vertical slit caisson is made. It consists of two impulsive wave pressures followed by a smooth sinusoidal pressure. In the numerical analysis, the sliding distance for an attack of single wave was shown and the expected sliding distance during 50 years was also presented. Those results were compared with a vertical front caisson breakwater without slit. It was concluded that the sliding distance of a vertical slit caisson may be over-estimated if the wave pressure on the caisson is evaluated without considering vertical slit.     

Probabilistic distribution of the maximum wave height

A new method of treating maximum wave height as a random variable in reliability analysis of breakwater caissons is proposed. The maximum wave height is expressed as the significant wave height multiplied by the so-called wave height ratio.The proposed wave height ratio is a type of transfer function from the significant wave height to the maximum wave height.Under the condition of a breaking wave, the ratio is intrinsically nonlinear. Therefore, the probability density function for the     

直立防波堤振动──滑移运动分析的模型和方法

建立了一个动力系统模型及相应分析方法,对破碎波冲击作用下直立式防波堤的振动-滑移运动过程进行数值模拟,预测特殊波浪力作用下防波堤可能出现的滑移量.用本文模型和方法对一沉箱防波堤在破碎波作用下的运动过程进行了计算,并分析了沿基床顶面的滑移对沉箱位移、摇摆角、滑移力和倾覆力矩的影响.     

波致海床滑动稳定性计算方法及滑动失稳特征研究

波浪引起的海床不稳定性是海洋工程中需要考虑的重要问题。在对现有波致海床滑动稳定性计算方法进行分析的基础上,提出了一种波致海床滑动稳定性计算的全应力状态法,将其与现有计算方法进行了对比分析,并进一步研究了波致砂土海床和软土海床的滑动失稳特征。结果分析表明,全应力状态法在波致海床滑动稳定性分析中具有较好的适用性。对于砂土海床,其滑动稳定性受饱和度的影响较大,且当海床计算厚度约为0.2倍波长时对应的滑动深度最大。波浪作用下坡度不超过2°的均质软土海床,其最危险滑动面的位置仅与波长有关,其滑动深度约为0.21倍波长,滑动面半弦长约为0.33倍波长;海床表面的波压力数值只影响其安全系数的大小,而不影响其滑动深度。     

Probabilistic Distribution of the Maximum Wave Heigh

A new method of treating maximum wave height as a random variable in reliability analysis of breakwater caissons is proposed. The maximum wave height is expressed as the significant wave height multiplied by the so-called wave height ratio. The proposed wave height ratio is a type of transfer function from the significant wave height to the maximum wave height. Under the condition of a breaking wave, the ratio is intrinsically nonlinear. Therefore, the probability density function for the variable cannot be easily defined. In this study, however, it can be derived from the relationship between the maximum and significant waves in a nonbreaking environment. Some examples are shown to validate the derived probability density function for the wave ratio parameter. By introducing the wave height ratio into reliability analysis of caisson breakwater, the maximum wave height can be used as an independent and primary random variable, which means that the risk of caisson failure during its lifetime can be evaluated realistically.     

近破波作用下沉箱式防波堤运动特性的模型实验研究

对近破波作用下沉箱式防波堤的运动特性进行了模型实验研究。实验中测量了沉箱模型与基床的摩擦系数、基床刚度和阻尼系数;不同水位情况下作用于沉箱模型上的近破波波压力时程;近破波作用下沉箱模型的位移和转角响应时程等,并与数学模型计算结果进行了比较分析。实验结果表明,若沉箱的滑移力大于沉箱与基床间的摩擦力,在连续波浪作用下,沉箱将连续出现间歇式滑移运动,数学模型可较好地模拟这一运动过程。     

Vibrating-Rocking Motion of Caisson Breakwater Under Breaking Wave Impact

The possible motions of a caisson breakwater under dynamic load excitation include vibrating, vibrating-sliding and vibrating-rocking motions. The models of vibrating motion and vibrating-sliding motion have been proposed in an early paper. In this paper, a model of vibrating-rocking motion of caisson breakwaters under breaking wave impact is presented, which can be used to simulate the histories of vibrating-rocking motion of caisson breakwaters. The effect of rocking motion on the displacement, rotation, sliding force and overturning moment of breakwaters is investigated. In case the overturning moment exceeds the stability moment of a caisson, the caisson may only rock. The caisson overturns only in case the rocking angle exceeds the critical angle. It is shown that the sliding force and overturning moment of breakwaters can be reduced effectively due to the rocking motion. It is proposed that some rocking motion should be allowed in breakwater design.     

沉箱式防波堤蛇行破坏的期望滑移量模型

防波堤是港工建筑物中的一个重要组成部分,主要作用为保护港湾免受波浪、冰、沙等海洋动力因素的侵袭.综合以往的相关文献,对于防波堤断面破坏形式,如滑移、倾覆、地基滑动等有了非常充分的研究,可以定量计算出其损坏程度.而对于防波堤平面形态的损坏,如蛇行破坏等,只是较深入研究了失效机理,并没有一个能够定量计算其后果的模型.本文第一部分将期望滑移量模型和绕射模型结合,建立了计算半无限长沉箱式防波堤在使用期限内蛇行破坏程度的模型.第二部分则利用实测的波浪数据设计并计算了一个沉箱式防波堤实例.结果表明,各个堤段的期望滑移量呈现出一定周期性变化的规律,堤头附近区域的滑移量远大于较远的堤段,这对于防波堤施工过程中的堤头防护具有参考价值.本文为建立防波堤平面形态损坏定量计算模型提供了一种思路.     

明基床开孔沉箱不规则波反射系数试验研究

通过二维波浪水槽物模试验,在考虑消浪室相对宽度、相对水深、相对波高、开孔率对反射系数的影响基础上,针对明基床开孔沉箱的工程应用,引入相对基床高度新的影响因素,通过控制单一变量原则分析各因素和反射率的关系,采用多元回归给出明基床开孔沉箱不规则波浪反射系数的计算公式,对明基床开孔沉箱的消浪机理进行了有益的探索,研究成果为工程设计及应用提供了一种简捷可靠的计算方法。     

An improved ‘Battjes’ method for predicting the probability of extreme waves

The Battjes method for predicting the 50 or 100-year design wave was developed to allow for the possibility that the highest wave in a 50 or 100 year period may occur during the second highest storm or even in lower storms. It uses the probability distribution of individual waves. It is first shown that a slightly different logical approach removes some of the problems encountered with the use of the method. It is then shown that it actually uses a different definition of return period to that used by the classic method because if two or more waves in a severe storm exceed H₅₀, then these are counted as separate events. A formula is developed which considers each storm as one event, but still takes account of the possibility of the highest wave in 50 years not coming from the most severe storm. Computation using this formula shows that it reduces H₅₀ by about 3% relative to the Battjes method.     

Vibrating-Sliding Motion of Caisson Breakwaters Under Various Breaking Wave Impact Forces

Sliding is one of the principal failure types of caisson breakwaters and is an essential content of stability examination in caisson breakwater design. Herein, the mass-spring-dashpot model of caisson-base system is used to simulate the vi-brating-sliding motion of the caisson under various types of breaking wave impact forces, i.e., single peak impact force, double peak impact force, and shock-damping oscillation impact force. The effects of various breaking wave impacts and the sliding motion on the dynamic response behaviors of caisson breakwaters are investigated and the calculation of relevant system parameters is discussed. It is shown that the dynamic responses of the caisson are significantly different under different types of breaking wave impact forces even when the amplitudes of impact forces are equal. The amplitude of dynamic response of the caisson is lower under single peak impact excitation than that under double peak impact or shock-damping oscillation impact excitation. Though the disp     

Numerical investigation on evolving failure of caisson foundation in sand using the combined Lagrangian-SPH method

Caisson foundations are often used in offshore engineering. However, for an optimum design understanding the failure process of a caisson during its installation and the subsequent external loadings is crucial. This paper focuses on the evolving failure of a caisson foundation in sand by advanced numerical modeling. A combined Lagrangian-smoothed particle hydrodynamics method is adopted to deal with the large deformation analysis. The method with parameters are first calibrated and validated by a simulation of cone penetration test in sand. The results of an experimental campaign of a caisson in the same sand are selected and validated for the numerical model. Then, more representative loading combinations are designated for numerical modeling of failure process and mode. Furthermore, three additional caisson dimensions D/d?=?0.5, 1.5, and 2.0 (changing the ratio of caisson diameter D to skirt length d while keeping the same soil-structure surface contact area) are simulated under six representative combined loading paths. Based on that, the influence of caisson dimension to the failure process and mode is investigated. All results are helpful to estimate all possible sliding surfaces under different monotonic combined loading paths for further limit analysis.     

空间节省型堰式沉箱波浪反射与结构优化试验研究

为了同时提升消浪效果和节省海岸空间,对低反射防波堤进行改进,提出了一种空间节省型堰式沉箱结构。通过物理模型试验研究了堰式沉箱在规则波作用下的消能机理,然后采用单因子分析法分析了相对淹没深度、波陡和相对波高对反射系数的影响,并且利用SPSS软件对无因次参数进行非线性回归分析得到了反射系数计算公式。结果表明,内堰消浪室可以形成良好的波能耗散机制,随着有效消浪室个数的增多,消浪效果逐渐增强,使得反射系数的最小值和最大值较非透空直立结构分别降低了60%～90%和10%～30%。基于以上研究成果,给出关于特征水位与内堰的相对位置关系的合理建议,并总结了堰式沉箱结构的优化设计要点,对实际工程应用具有一定的指导意义。