Yan Xiang*,Shu-yan Fu,Kai Zhu,Hui YuanZhi-yuan Fanga,

aDam Safety Management Center of the Ministry of Water Resources,Nanjing Hydraulic Research Institute,Nanjing 210029,China

bState Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Nanjing Hydraulic Research Institute,Nanjing 210029,China

cCollege of Mechanics and Materials,Hohai University,Nanjing 210098,China

dSchool of Water Resources and Hydraulic Engineering,Yunnan Agricultural University,Kunming 650000,China

Seepage safety monitoring model for an earth rock dam under influence of high-impact typhoons based on particle swarm optimization algorithm

Yan Xianga,b,*,Shu-yan Fuc,d,Kai Zhub,Hui Yuana,b,Zhi-yuan Fanga,b

aDam Safety Management Center of the Ministry of Water Resources,Nanjing Hydraulic Research Institute,Nanjing 210029,China

bState Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Nanjing Hydraulic Research Institute,Nanjing 210029,China

cCollege of Mechanics and Materials,Hohai University,Nanjing 210098,China

dSchool of Water Resources and Hydraulic Engineering,Yunnan Agricultural University,Kunming 650000,China

Extreme hydrological events induced by typhoons in reservoir areas have presented severe challenges to the safe operation of hydraulic structures.Based on analysis of the seepage characteristics of an earth rock dam,a novel seepage safety monitoring model was constructed in this study.The nonlinear in fluence processes of the antecedent reservoir water level and rainfall were assumed to follow normal distributions. The particle swarm optimization(PSO)algorithm was used to optimize the model parameters so as to raise the fitting accuracy.In addition,a mutation factor was introduced to simulate the sudden increase in the piezometric level induced by short-duration heavy rainfall and the possible historical extreme reservoir water level during a typhoon.In order to verify the ef ficacy of this model,the earth rock dam of the Siminghu Reservoir was used as an example.The piezometric level at the SW1-2 measuring point during Typhoon Fitow in 2013 was fitted with the present model,and a corresponding theoretical expression was established.Comparison of fitting results of the piezometric level obtained from the present statistical model and traditional statistical model with monitored values during the typhoon shows that the present model has a higher fitting accuracy and can simulate the uprush feature of the seepage pressure during the typhoon perfectly.

Monitoring model;Particle swarm optimization algorithm;Earth rock dam;Lagging effect;Typhoon;Seepage pressure;Mutation factor;Piezometric level

1.Introduction

China is located in the western Pacific Ocean region,which is significantly influenced by typhoons.On average,eight to nine typhoons or gales make landfall in China each year(Xiao et al.,2011).Typhoons and storms after landfall cause heavy rainfall,floods,and other catastrophes,which seriously threaten lives and property(Tang et al.,2011).The factors of hazards,especially the impacts of heavy rainfall and storm surges during a typhoon,appear as sudden impact loads(Feng and Luo,2009).For an earth rock dam and its foundation,the sharp rise of the reservoir water level caused by heavy rainfall during a typhoon is equivalent to a sudden loading and unloading process(Lin and Jeng,2000).The location of the phreatic line in an earth rock dam directly impacts its side slope stability.Therefore,it must be measured during the safety monitoring of the earth rock dam(Chigira et al.,2013).

Li et al.(2003)established an element-free method(EFM) with a free surface based on the moving least square method, which requires only the information at element nodes,and successfully analyzed the steady seepage and transient seepage in a uniform earth dam.Chen et al.(2010)simulated the fracture or drainage segment in a rock mass using a special sub-element with de finite seepage characteristics and deduced the governing equation for the composite element using the variational principle.Kazemzadeh-Parsi and Daneshmand(2012)proposed a new non-boundary- fitted finite element method,the smoothed fixed grid finite element method(SFGFEM),to solve the uncon fined seepage problem in domains with arbitrary geometry and continuously varied permeability.Through transformation of the area integral into the line integral around edges of smoothing cells, the gradient smoothing technique was used to obtain the element matrix,and the phreatic surface was computed through the iterative process under nonlinear boundary conditions.Jiang et al.(2010)established a three-dimensional numerical manifold method for uncon fined seepage analysis using a tetrahedral mathematical mesh.The element conductivity matrix and global simultaneous equations for uncon fined seepage analysis were derived by constructing hydraulic potential functions of the manifold element. Hashemi and Hatam(2011)conducted numerical simulation of two-dimensional transient seepage using the radial basis function-based differential quadrature(RBF-DQ)method. Compared with the analytical finite element method and existing numerical solutions from the literature,the RBF-DQ method was able to produce more accurate results for seepage analysis.Cho(2012)assumed that the hydraulic conductivity was different for different layers of an embankment,and that the hydraulic conductivity in a layer was uncorrelated with that in other layers.Two-dimensional random fields were generated using the Karhunen-Lo`eve expansion in a manner consistent with a speci fied marginal distribution function and an autocorrelation function.A series of seepage analyses of embankment foundation systems was performed using random fields generated to study the effects of uncertainty due to the spatial heterogeneity of the hydraulic conductivity on the seepage flow.Ahmed(2009)considered the hydraulic conductivity of earth dams a spatially random field following a lognormal distribution and conducted corresponding uncon fined seepage analysis.Results showed that the seepage discharge obtained from the stochastic solution was lower than that obtained from the analytical solution,and the free surface was observed to emerge at a point lower than the location obtained from the analytical solution.Most of the dam seepage analyses described in the literature were conducted under normal operating conditions.However,in recent years frequent extreme weather conditions have presented severe challenges to the safe operation of dams worldwide (Hossain et al.,2010;Lubchenco and Karl,2012;Xiang et al., 2012).Development of an accurate seepage safety monitoring model for an earth rock dam during a high-impact typhoon will signi ficantly bene fit real-time security control of earth rock dam seepage behaviors(Gu and Wu,2006).

In this study,seepage safety analysis of an earth rock dam under the influence of a high-impact typhoon was conducted, and the seepage pressure in the dam body during the typhoon was quantified by establishing a statistical theoretical model based on the particle swarm optimization(PSO)algorithm. The traditional statistical model of the piezometric level in earth rock dams can be divided into four parts:the upstream water level component,the rainfall component,the temperature component,and the time effect component.The piezometric level was assumed to be linearly correlated with the upstream water level and rainfall(Fu et al.,2011).However, an analysis based on monitoring data indicated that when a reservoir encountered heavy rainfall and the potential historical extreme reservoir water level under the influence of a typhoon,the correlation between the piezometric level and environmental variables exhibited obvious nonlinearities,and the piezometric level increased sharply during the typhoon.It was found that using the traditional statistical model to fit the piezometric level would produce an underfitting problem (Hashemi and Hatam,2011).The cause of this phenomenon can be explained from two aspects:when a reservoir reaches a new higher water level after impoundment,the material of the earth rock dam body exhibits collapsibility and rheidity because of water immersion,producing new seepage channels and leading to an increase in the piezometric level;some originally inactive seepage channels at the bottom of the reservoir begin to leak,further increasing the piezometric level.For these reasons,a mutation factor was introduced in this study to simulate the nonlinear variation of the piezometric level under the influence of the typhoon.To verify the model,the earth rock dam of the Siminghu Reservoir in Zhejiang Province was used as a case study.The present model was used to fit the piezometric level in the dam during Typhoon Fitow in 2013.The effectiveness of the present model was verified by comparing its results with those of the traditional statistical model.

2.Basic theories

2.1.Construction of piezometric level statistical model

An analysis of measured data shows that the seepage pressure in an earth rock dam body is primarily influenced by factors such as the upstream water level,rainfall,the ambient temperature,and the time-varying characteristics of the dam materials(Wu,2006).In addition,in order to simulate the uprush feature of the seepage pressure under the influence of a typhoon,a mutation factor is introduced into the model.The novel statistical model of the piezometric level in an earth rock dam is thus as follows:

wherePis the dam body piezometric level,PHis the upstream water level component,PRis the rainfall component,PTis the temperature component,Pθis the time effect component,andPEis the mutation factor caused by the typhoon.solution in the space,and a particle adjusts its own fly path based on its and its partners'flying experiences.It is assumed that within ann-dimensional search space,there is a group withmparticles.In this group,the position of theith particle in then-dimensional search space is expressed as anndimensional vector,representing a potential solution.Letbe the current position of particlei;be the current flying speed of particlei;be the best position of particlei;andbe the optimum position of the group. The fitness value can be calculated by substitutinginto the target function,and the quality ofis judged by its fitness value.The speed and position of each particle are iterated using the following equations:

where the subscriptjrepresents thejth dimensionirepresents theith particlerepresents thet′th iteration;wis the inertia weight;are random numbers in the range ofare the acceleration constants,ranging from 0 to 2.The constantadjusts the fly step size toward the optimum position of a particle,andadjusts the fly step size toward the optimum position of the group.To reduce the possibility of particles leaving the search space during the evolution process,is usually confined within a certain range,i.e.,If the search space is to be restricted withinthen.In the case when the position and speed of a particle exceed the allowable regions,they are assigned to be the boundary values.

Using the multiple correlation coefficient of the statistical model as the fitness value to search for the lagging time and affecting time,the PSO-based algorithm was developed and steps are as follows:

Step 1:Parameter setting.With the acceleration constants set atc1=c2=1,the number of particles set at 20,the maximum number of iterations set at 100,the range of search space set at［0，60］,and the range of speed set at［-5，5］,the calculation equation for the inertia weight of thet′th iteration is as follows:

Step 2:Initialization of the initial position vector X0and initial speed vector V0of the particle group.

Step 3:Judgment of whether to introduce a mutation factor.If the reservoir water level exceeds the historical extreme valueHmax,or the daily rainfall exceeds the historical extreme valueRmax,the mutation factor is introduced, and the corresponding historical extreme water level or rainfall is updated.

Step 4:Calculation of the fitness value.Continuous integration in Eqs.(2)and(3)is converted into discrete integration,with 2-3 times of the affecting time as the interval of integration.With respect to the particle group X=（x1，x2，…，x20）,stepwise regression analysis of the recorded piezometric level is conducted,and the multiple correlation coefficientRis calculated,which is the local fitness valueFlof the particle group.

Step 5:Assessment of the local fitness value.The obtained local fitness valueFlwas compared with the global optimum fitness valueFg;ifFl＞Fg,the historical global optimum fitness valueFgis replaced with the current local fitness valueFl.

Step 6:Re-calculation of the speed and position of each particle according to Eqs.(7)and(8).

Step 7:If the accuracy is satisfied,or the maximum number of iterations is reached,the current optimum results are saved, and the calculation is completed.Otherwise,the process returns to Step 3.

3.Case study

3.1.Project introduction

The Siminghu Reservoir is located upstream of the Yaohe River in the Yongjiang Basin,in Zhejiang Province of China. The catchment area above the dam site is 103.1 km2,and the total reservoir capacity is 1.23×108m3with a normal water level of 16.28 m,a 100-year design flood water level of 17.88 m,and a dead water level of 6.28 m.The dam is an earth rock dam with a clay slope wall,used as the seepage control measure through combination with composite geomembrane. The dam crest height is 21.13 m,and the crest length and width are 600 m and 5.5 m,respectively.The upstream slope ratio is 1:3.7,and the downstream slope is divided into two sections,with slope ratios of 1:2.2 and 1:2.5,respectively.For monitoring the dam seepage safety conditions,63 piezometers were installed in the dam body(mainly in five seepage monitoring cross-sections along the dam axial line at 0+105.00 m,0+210.00 m,0+265.00 m,0+385.00 m,and 0+480.00 m)and abutments.The piezometer arrangement in a typical cross-section(0+105.00 m)is shown in Fig.1.Two sets of piezometers were installed under geomembrane,two sets of piezometers were installed in the dam body,and another two sets of piezometers were installed in the dam foundation.The horizontal layout of the monitoring devices under geomembrane in the dam is shown in Fig.2.By excluding the damaged piezometers during the operation,the remaining piezometers under the concrete slab were analyzed.

Fig.1.Arrangement of dam seepage pressure measuring points in 0+105.00 m cross-section.

Fig.2.Horizontal layout of monitoring points under composite geomembrane.

3.2.Typhoon Fitow and rainfall process

The 23rd tropical storm in 2013,Typhoon Fitow,originated over the Paci fic Ocean,east of the Philippines,at 20:00 on September 30,2013.When it formed,the center was located at latitude 12°35′N and longitude 136°40′E,the wind speed near the center was level 8(18 m/s),and the lowest pressure at the center was 1000 hPa.The tropical storm evolved into a severe tropical storm over the northwestern Paci fic Ocean at 17:00 on October 1,then strengthened until it was a typhoon before the dawn of October 3,and further intensi fied into a severe typhoon on the afternoon of October 4.However,because the eyewall was not closed,the typhoon's development was stagnated.The typhoon made landfall in Shacheng Town,in Fuding City of Fujian Province,at 01:15 on October 7.The maximum wind speed near the center at landfall reached level 14(42 m/s),and the lowest pressure at the center was 955 hPa.The typhoon first weakened at03:00 on October7,then gradually weakened into a severe tropical storm at 04:00,a tropical storm at 05:00,and finally a tropical depression at 09:00.The development of Typhoon Fitow is shown in Fig.3.Typhoon Fitow threatened the safe operation of hydraulic structures in this area.

The landfall of Typhoon Fitow caused the Yongjiang Basin to suffer the highest rainfall in the historical hydrological record(Li et al.,2003).The rainfall process in the Siminghu Reservoir region from October 5 to 9,2013 is shown in Fig.4. It is clear that the reservoir region experienced intermittent heavy rains to severely heavy rains from October 5 to October 9.The rainfall was concentrated on October 6 and October 9, with the areal rainfall of these two days reaching 507.2 mm, while the four-day accumulated rainfall was 565.2 mm.The total rainfall caused the reservoir water level to approach the 100-year design flood water level.

Fig.3.Development of Typhoon Fitow.

3.3.Quantitative analysis of piezometric level in earth rock dam during Typhoon Fitow

Fig.5 shows the reservoir water level and piezometric level at the typical measuring points under the composite geomembrane during Typhoon Fitow.The reservoir water level rose continuously from October 5 and reached 17.59 m on October 8,2013,the highest reservoir water level recorded since the construction of the reservoir.Under the impact of the typhoon,the piezometric level at each monitoring point rose significantly,except for the SW2-2 and SW3-1 measuring

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Received 2 September 2016;accepted 29 December 2016

Available online 9 March 2017

This work was supported by the National Natural Science Foundation of China(Grants No.51179108 and 51679151),the Special Fund for the Public Welfare Industry of the Ministry of Water Resources of China(Grant No. 201501033),the National Key Research and Development Program(Grant No. 2016YFC0401603),and the Program Sponsored for Scientific Innovation Research of College Graduates in Jiangsu Province(Grant No.KYZZ15_ 0140).

*Corresponding author.

E-mail address:yxiang@nhri.cn(Yan Xiang).

Peer review under responsibility of Hohai University.

http://dx.doi.org/10.1016/j.wse.2017.03.005

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?2017 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http:// creativecommons.org/licenses/by-nc-nd/4.0/).