Response,characteristics,of,plunge,pool,slabs,of,Xiaxiluodu,Hydropower,Station,to,flood,discharge,pulsating-pressure,under,valleydeformation,conditions

Jie Yun ,Qinwei Xi ,Xin Ji ,Yng Zhou ,Yu Hu

a National Institute of Natural Hazards,Ministry of Emergency Management,Beijing,100085,China

b State Key Laboratory of Hydroscience and Hydropower Engineering,Tsinghua University,Beijing,100084,China

c Xiluo du Power Plant,China Yangtze Power Co.,Ltd.,Zhaotong,Yunnan,657300,China

Keywords: Valley deformation Plunge pool Flood discharge pulsating pressure Finite element

ABSTRACT The key problem of the energy dissipation scheme of the arch dam body flood discharge and plunge pool below the dam is the stability problem of the plunge pool slab.As the protection structure of the underwater bed,the plunge pool slab bears the continuous impact of high-speed water flow.The hourly average dynamic water pressure on the slab is one of the main loads directly affecting the stability of the slab and is the main factor causing its erosion destruction.After the impoundment of the Xiluodu Hydropower Station,the measuring line of valley width in the plunge pool area has been continuously shrinking.By 2020,the cumulative shrinking value is about 80 mm.In light of the general background condition of valley shrinkage,daily inspection,annual detailed inspection,underwater inspection and drainage inspection of the plunge pool found that the plunge pool has experienced different degrees of damage,which greatly influences the long-term safety stability of the plunge pool.In this paper,the prototype observation data of flood discharge is used as the input load of pulsatingpressure,and the stress and displacement distribution of the plunge pool structure under the vibration load of flood discharge is analyzed under the condition that the stress and strain state of the plunge pool is changed under the influence of valley displacement.The results show that the stress,strain,and displacement distribution of the plunge pool are mainly caused by valley deformation,the vibration caused by flood discharge is little in influence,and the impact effect of deep hole flood discharge tongue on the plunge pool slab is weak.

Xiluodu Hydropower Station,located on the mainstream of Jinsha River at the junction of Leibo County,Sichuan Province and Yongshan County,Yunnan Province,is one of the main power sources of the middle line of China"s West-to-East Power Transmission Project.It is a superlarge hydropower station with comprehensive benefits such as flood control,sand control and improvement of downstream navigation conditions.The power station junction is composed of the dam,flood discharge structure,water diversion power generation structure and regulating structure,and is featured by a"high arch dam,high head,large discharge and narrow valley".The flood discharge and energy dissipation facilities of Xiluodu Hydropower Station are composed of 7 surface holes and 8 deep holes in the dam body,plunge pools behind the dam (using the layout of "layered outflow,midair collision and energy dissipation of plunge pools") and 2 "dropped outlet" type spillway tunnels with compression-free tunnels in each bank (Wang,2003).After the flood discharge water is injected into the plunge pool,huge impact pressure is generated,which may lead to buckling failure of the plunge pool slab.Therefore,it is of great significance to study the response characteristics of the plunge pool slab to the flood discharge pulsating-pressure (Lian et al.,2001;Wang et al.,2011).

Valley deformation refers to the larger horizontal deformation phenomenon of reservoir banks in the upstream and downstream of the dam caused by reservoir filling under specific geological conditions.After the impoundment of the Xiluodu Hydropower Station,the measuring line of valley width in the plunge pool area has been continuously shrinking (He et al.,2018;Yang et al.,2018).Recently,after analyzing the valley width measuring line of the plunge pool area,the transverse direction and downstream direction displacement of the plunge pool area,and the transverse direction displacement of the plunge pool slab area,it is found that:

(1) After impoundment,the valley width measuring line of the plunge pool area has a continuous shrinkage phenomenon,and the valley shrinkage displacement is evenly distributed along the elevation.The rate of valley width shrinkage has decreased to some extent since June 2015,and the current cumulative shrinkage value is about 80 mm.

(2) The plunge pool bank slope presents a deformation trend from the left and right banks to the valley,and it is predicted that it will continue to deform at a low rate.The accumulative deformation from the left bank to the valley is 35 mm,and that from the right bank to the valley is 60 mm.

(3) The slops on both banks of the plunge pool show the upstream deformation.Compared to the right bank,the left bank slope presents the trend of strong upstream deformation,but at present,the upstream deformation is in the“plateau”that has been kept for more than four years.It can be seen that the upstream deformation of slope has stabilised.Currently,upstream cumulative deformation on the left bank is 30 mm,and upstream cumulative deformation on the right bank is 15 mm.

(4) Before the large-scale impoundment in May 2013,the left bank of the plunge pool first rose and then fell,and the right bank of the plunge pool was manifested as subsidence;after impoundment,the left bank of the plunge pool continued to rise and tended to be stable after July 2015.The right bank of the plunge pool showed a subsiding -uplifting -subsiding change and tended to be stable after May 2016.Up to now,the uplift of the left bank of the plunge pool has reached about 20 mm,and the settlement of the right bank has reached about 15 mm.

(5) There is no obvious overall interlayer dislocation phenomenon in the plunge pool area.

In the overall background of valley shrinkage,daily patrol inspection,annual detailed inspection,an underwater inspection of the plunge pool,and emptying inspection all revealed different degrees of destruction to the plunge pool,and defects are mainly manifested as concrete crack development of sidewalls of galleries such as transverse gallery climbing section,longitudinal gallery of plunge pool bottom and auxiliary weir gallery,posing certain influence on the safe operation of the plunge pool of Xiluodu Hydropower Station.

Considering that valley displacement can change the stress and strain state of the plunge pool and has greater impact on long-term safety and stability of the plunge pool (Wang,2013),this paper will carry out simulation analysis and research on structural stability of the plunge pool of Xiluodu Hydropower Station in light of the actual operation situation of Xiluodu Hydropower Station using the finite element numerical calculation method,analyze the response characteristics of the plunge pool slab of Xiluodu Hydropower Station to the flood discharge pulsating-pressure under the condition of valley deformation (Zhao et al.,2020),and control measures were put forward for the safe operation of the plunge pool of Xiluodu Hydropower Station,and put forward control measures for safe operation of the plunge pool of Xiluodu Hydropower Station,propose safety strategy suggestions for key parts and local defective areas to guide the operation,maintenance and repair of the plunge pool.It provides a practical reference for safety evaluation of similar engineering problems in the future,scientific scheduling,and safe operation.

2.1.Finite element model

This paper adopts ABAQUS finite element analysis software (Dassault,2012),and the model grid adopts the form of solid modeling.The grid model is mainly based on a hexahedral mesh,including the dam,plunge pool,auxiliary weir,and other major structures.In the plunge pool,slope concrete partition,structural joints,galleries,and other characteristics are considered and the total number of units is 218294.In addition,49 545 damping units and 49 545 spring units are used to simulate a semi-infinite space base (Liu et al.,2005,2006),as shown in Figs.1– 3.

Fig.1.Overall three-dimensional finite element model of plunge pool.

Fig.2.Local three-dimensional finite element model of plunge pool.

Fig.3.Finite element model of the plunge pool and its internal grid perspective.

2.2.Material parameters

The calculation model in this paper takes into account the concrete partition of plunge pool slope protection,and the thermodynamic parameters of concrete are selected according to the specifications.The material parameters are shown in Table 1.Fig.4 is the material partition layout of the plunge pool section.

Table 1 Material parameters.

2.3.Loading condition

In this paper,the vibration response of the plunge pool slab during flood discharge is analyzed by combining 3-D model with the data from prototype observation.Because there is no obvious overall layer dislocation in the plunge pool area,this calculation does not consider the dislocation of weak rock strata.Through the sorting and analysis of the monitoring data of the temperature field of the plunge pool,it is found that the temperature process is relatively stable after the plunge pool impoundment.The temperature of the bedrock in the slope is stable at about 20°C,and the temperature under the slab is stable at about 25°C,with little fluctuation.Therefore,the temperature field is no longer considered in this calculation.

Fig.4.Material partition layout of plunge pool section.

Fig.5.Loading condition.

The loads considered in the analysis include: valley deformation;the dead weight of the plunge pool and the auxiliary weir should be considered as a whole;hydrostatic pressure of reservoir water;when the water stop is intact,the slab is in a normal vibration state,and the force received is mainly the pulsating-pressure load on the upper surface of the plate,as shown in Fig.5.In this calculation,the pulsating-pressure load is the hydrodynamic prototype observation data of the plunge pool,specifically the pulsating-pressure data of each measuring point of the plunge pool slab and slope when the No.3 deep hole was opened for flood discharge on September 22,2019.Fig.6 shows the layout of measuring points for the plunge pool pulsating-pressure load,and Fig.7 only shows the pulsating-pressure data curves of F1-F4 measuring points.In specific calculations,pulsating-pressure data of all measuring points are distributed on the surface of the plunge pool through interpolation calculation.

To analyze the influence of valley deformation and pulsating-pressure on the stability of the plunge pool slab,three working conditions are set in this paper,respectively:

Working condition 1:The valley displacement(80 mm)is considered,and the static calculation of pulsating-pressure is not considered

Working condition 2:The valley displacement(80 mm)is considered,and the dynamic calculation of pulsating-pressure is not considered Working condition 3:The valley displacement is not considered,and the dynamic calculation of pulsating-pressure is not considered

3.1.Static calculation considering valley displacement (80 mm)

To compare and analyze the vibration response of the plunge pool during flood discharge,this section analyzes the stress and displacement distribution of the plunge pool,the auxiliary weir,and the dam under static load (valley shrinkage 80 mm).

Fig.8 is the nephogram of the maximum principal stress of the plunge pool.A local high tensile stress area appears near the dam.Fig.9 is the displacement nephogram of the plunge pool.It can be seen from the displacement and stress state distribution of the plunge pool:

(1) The transverse direction deformation distribution in the plunge pool area is the same as the downstream direction deformation distribution,and the transverse direction deformation is slightly smaller at the dam and the auxiliary weir.

(2) In the plunge pool area,there is a compressive stress concentration zone on both sides of the plunge pool slab and at the transition of slope protection,as well as at the transition of 360 horse road and upward slope protection,and the direction is consistent with the slope protection direction and extends to the top of the gallery.

(3) There is stress concentration on both sides of the sidewall of the downstream direction gallery and the sidewall along the valley of 355 galleries.The maximum tensile stress is about 4 Mpa,which exceeds the tensile strength of concrete in this area and has the risk of causing cracks.

Fig.6.Monitoring point arrangement of pulsating-pressure load of the plunge pool.

Fig.7.Pulsating-pressure data curves of F1～F4 measuring points.

(4) There is a tensile stress concentration zone on both sides of the side walls of the downstream direction gallery slope protection section of the plunge pool,and the tensile stress level of the two sides of the side walls is basically the same.The tensile stress concentration zone is consistent with the direction of the slope protection,and the maximum tensile stress is about 4 Mpa,which exceeds the tensile strength of the concrete in this area and has the risk of causing cracks.

Fig.8.Nephogram of the maximum principal stress of the plunge pool.

Fig.9.Displacement nephogram of the plunge pool.

3.2.Dynamic calculation considering valley displacement (80 mm)

The calculation in this section takes into account the valley displacement load and the pulsating-pressure load.The valley displacement load is the relative displacement of 80 mm on both sides,and the hydraulic pulsating-pressure load data is the prototype observation data of No.3 deep hole that opened in September 2019.

Fig.10 is the envelope diagram of the maximum principal stress of the plunge pool.A local high tensile stress area appears near the dam.Fig.11 Envelope diagram of displacement extremum of the plunge pool.By comparing the calculation results in Section 3.1 and 3.2,it can be found that the numerical value and the overall distribution of stress displace-ment in the plunge pool do not change much between the calculation results and the static calculation results without the application of pulsating-pressure load.This is because the application of valley displacement load leads to large stress and strain values of the plunge pool,so the influence of pulsating-pressure load on the plunge pool cannot be presented.In order to further analyze the influence of pulsating-pressure load on the plunge pool,the calculation and analysis of working condition 3 are carried out,that is,the valley displacement is not considered,and only the pulsating-pressure load is applied.

3.3.Dynamic calculation without considering valley displacement

In this calculation,only the pulsating-pressure load is considered.As in Section 3.2,the hydraulic pulsating-pressure load data is the prototype observation data of No.3 deep hole that opened in September 2019.

Fig.12 is the envelope diagram of the maximum principal stress of the plunge pool.A local high tensile stress area appears near the dam.Fig.13 is the envelope diagram of the displacement extremum of the plunge pool.According to the calculation results of working condition 3,the maximum principal stress (tensile stress) and minimum principal stress(compressive stress) of the plunge pool are～1 MPa and～2 MPa respectively under the action of pulsating-pressure load,both of which have not reached the ultimate load of concrete.

Fig.10.Envelope diagram of the maximum principal stress of the plunge pool.

Fig.11.Envelope diagram of displacement extremum of the plunge pool.

According to the statistical analysis of the hydraulic prototype observation and monitoring results of the plunge pool,the prototype observation data of pulsating-pressure includes two parts,one is the hydro-static pressure,about 450 kPa,the other is the pulsating-pressure caused by flood discharge,about 10.4 kpa–14.8 kpa.Therefore,there is no obvious impact pressure on the plunge pool slab under flood discharge conditions,and the pulsating-pressure range is not large.Compared with the influence of valley deformation on the stress and strain state of the plunge pool slab,the impact effect of the deep hole flood discharge tongue on the plunge pool slab is weak.

All the concrete constitutive models used in the above analysis are isotropic,and the concrete in the actual plunge pool has certain reinforcement.Therefore,it is necessary to analyze the influence of concrete reinforcement of the plunge pool on the working behavior of the plunge pool.The strain of the plunge pool is mainly in the transverse and vertical directions,while the strain in the downstream direction is small.Therefore,the stress state of the plunge pool can be simplified as the plane strain problem.The following is an analysis of the influence of concrete reinforcement on the working behavior of the plunge pool based on the two-dimensional model.As the plunge pool is approximately an axisymmetric model,the established two-dimensional model of the plunge pool is half of the actual model,as shown in Fig.14.The model takes into account the concrete partition,structural joints,galleries and other features of the plunge poolside slope,as well as the concrete reinforcement and bedrock anchor bar of the plunge pool.The number of total units is 8 495 (see Fig.15).

Fig.12.Envelope diagram of maximum principal stress of plunge pool.

Fig.13.Envelope diagram of displacement extremum of the plunge pool.

The anchor bars use beam units (able to withstand tensile force,shear force and bending moment),and the concrete reinforcement of plunge pools uses bar units (able to withstand tensile force only),which have defined embedding relationship with the concrete bedrock.There are some construction joints in the construction process of the concrete for slope protection in the plunge pool,and structural joints are set up at the top of the gallery.These reserved joints are treated with water stops during the construction of slope protection.However,slope deformation and other factors lead to the dislocation of the structural joints at the top of the gallery,and the epoxy sealing joints filled inside are detached.To simulate this kind of structural joints,the contact treatment is adopted in this calculation model.Because both sides of the structural joint are reinforced concrete,coupled with the water stop and epoxy joint sealing treatment in the joint,the friction coefficient of 0.75 is used to calculate the contact friction.

Fig.14.Two-dimensional grid model of plunge pool.

Fig.15.Nephogram of maximum principal stress of plunge pool,reinforcement and anchor bar.

As shown in Fig.15,calculation results show that the reinforcement concrete of the plunge pool did not produce significant tensile stress,namely,under the loading of valley deformation,the concrete reinforcement of the plunge pool was not stressed,concrete reinforcement of the plunge pool did not generate obvious influence on concrete behavior of the plunge pool,indicating that the isotropic constitutive model of concrete used in the foregoing analysis is reasonable.

In this paper,the static response and dynamic response of the plunge pool are analyzed respectively for the vibration response of the plunge pool and related areas under the condition of flood discharge.The main conclusions are as follows:

(1) Considering the valley deformation,the local stress of the plunge pool and the auxiliary weir in the static calculation results exceeds the ultimate strength of concrete;compared with the dynamic calculation results of flood discharge considering the pulsatingpressure and the static calculation results without considering the pulsating-pressure,there are no significant differences in the stress,strain and displacement distribution of the plunge pool.The main reason is that the stress,strain,and displacement distribution of the plunge pool are mainly caused by the valley deformation under the condition of the valley deformation,and the vibration caused by flood discharge has little influence.

(2) In the static state without considering the valley deformation,the maximum principal stress and minimum principal stress of the plunge pool and the auxiliary weir do not exceed the ultimate strength of concrete.The dynamic calculation results without considering the valley deformation also show that the stress state of the plunge pool does not exceed the ultimate strength of concrete.

(3) The prototype observation data of the pulsating-pressure include hydrostatic pressure and the pulsating-pressure caused by flood discharge.The calculation shows that the pulsating-pressure caused by flood discharge is about 10 kPa,and the pulsatingpressure range is not large,and the impact effect of the deep-hole flood discharge tongue on the plunge pool slab is weak.

Conflict of interest

The authors do not have any possible conflicts of interest.

Acknowledgement

The comments from the editor and anonymous reviewers are very appreciated.This manuscript benefited greatly from their insightful reviews.This work was supported by the National Institute of Natural Hazards,Ministry of Emergency Management of China (No.ZDJ2020-08).

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