Analysis of Chinese dams

Politecnico di Milano

School of Civil, Environmental and Management Engineering

Master of Science in Civil Engineering for Risk Mitigation

Analysis of Chinese Dams

Supervisor: Prof. Gabriella Bolzon

Master Graduation Thesis by: Ge Yijun

Student ID number: 872231

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Table of Content

Abstract ... 7

Sommario ... 8

Chapter 1 Introduction ... 9

Chapter 2 General Information about Dams in China ... 12

2.1 Main Use of Dams in China ... 12

2.2 Main Problems of Dams in China ... 14

2.3 Characteristics of Dams ... 16

2.3.1 Gravity dam ... 16

2.3.2 Arch Dam ... 18

2.3.3 Embankment Dam ... 19

2.4 Dams Distribution in China ... 22

2.4.1 Gravity Dam ... 24

2.4.2 Arch Dam ... 31

2.4.3 Embankment Dam ... 36

2.5 Representative Dams in China ... 43

2.5.1 Concrete Gravity Dam ... 43

2.5.2 Concrete Arch Dam ... 46

2.5.3 Rock-fill Dam ... 49

Chapter 3. Stress Analysis of a Concrete Gravity Dam ... 52

3.1 Analysis of Concrete Gravity Dams According to Chinese Codes ... 52

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3.1.2 Stress Analysis ... 55

3.2 Application Case ... 60

3.2.1 Geometry and Loading Combination ... 60

3.2.2 Stresses Distribution according to Chinese Codes ... 71

3.2.3 Finite Element Analysis ... 79

3.2.4 Numerical Results ... 91

3.2.5 Comparison ... 97

Chapter 4 Conclusion... 100

References ... 102

Appendix A ... 103

A.1 Gravity Dams ... 103

1. Concrete Gravity Dam ... 103

2. Masonry Gravity Dam ... 156

A.2 Arch Dam ... 161

1. single-arch Dam ... 161

2. Double-curvature Dam ... 166

3. Multiple-arch Dam ... 200

A.3 Embankment Dam ... 202

1.Rock-fill Dams ... 202

2.Concrete-face Rock-fill Dams ... 210

3.Earth-fill Dams ... 226

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B.1 Load Results Tables ... 263

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List of Figures

Figure 1.1 Mianhuatan concrete gravity dam ………9

Figure 1.2 Tiantangshan concrete arch dam………10

Figure 1.3 Dashahe earth-fill dam ………10

Figure 2.1 China Provinces Map………22

Figure 2.2 China water system Map……… 23

Figure 2.3 China Mountain Range Map……… 23

Figure 2.4 Gravity dam categories pie chart ……… 29

Figure 2.5 Distribution of gravity dams in survey ……… 30

Figure 2.6 Arch dam categories pie chart……… 34

Figure 2.7 Distribution of arch dams in survey ………35

Figure 2.8 Embankment categories pie chart………42

Figure 2.9 Distribution of embankment dams in survey………43

Figure 2.10 The Three Gorges dam………44

Figure 2.11 Ertan Concrete Double Curvature Arch Dam………47

Figure 2.12 Xiaolangdi dam ………49

Figure 3.1 Sketch for stress calculation of solid gravity dams………57

Figure 3.2 Dam section profile………61

Figure 3.3 Dam cross section profile ……… 62

Figure 3.4 Lift pressure on section 1 ………68

Figure 3.5 Lift pressure on section 2 ………68

Figure 3.6 Lift pressure on section 3 ………69

Figure 3.7 Lift pressure on section 4 ………69

Figure 3.8 Simplified wave pressure calculation diagram ………70

Figure 3.9 𝜎𝑥 Distribution diagram………75

Figure 3.10 𝜎𝑦 Distribution diagram………76

Figure 3.11 𝜏𝑥𝑦 Distribution diagram………76

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Figure 3.13 𝜎𝑥 Distribution diagram under earthquake………78

Figure 3.14 𝜏𝑥𝑦 Distribution diagram under earthquake ………78

Figure 3.15 𝜎𝑥 diagram of rough and fine meshes………80

Figure 3.16 𝜎𝑦 diagram of rough and fine meshes………81

Figure 3.17 𝜏𝑥𝑦 diagram of rough and fine meshes………81

Figure 3.18 New model with foundation………82

Figure 3.19 Final model with smoother geometry ………83

Figure 3.20 Water levels and silt level for analysis model………84

Figure 3.21 Surface loads distribution on dam ………89

Figure 3.22 Deformed configuration of gravity dam………91

Figure 3.23 𝜎𝑥 diagram of gravity dam ………92

Figure 3.24 𝜎𝑦 diagram of gravity dam ………92

Figure 3.25 𝜏𝑥𝑦 diagram of gravity dam………93

Figure 3.26 𝜎𝑥 Distribution on sections comparison between Partial Amplified Method and Finite Element Method ………97

Figure 3.27 𝜎𝑦 Distribution on sections comparison between Partial Amplified Method and Finite Element Method ………98

Figure 3.28 𝜏𝑥𝑦 Distribution on sections comparison between Partial Amplified Method and Finite Element Method ………99

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List of Tables

Table 2.1 Gravity dams’ distribution in Provinces………24

Table 2.2 Arch dams’ distribution in Provinces ………31

Table 2.3 Embankment dams’ distribution in provinces ………36

Table 3.1 Loading combinations for concrete gravity dam………54

Table 3.2 Hydrostatic nodal forces on upstream surface ………86

Table 3.3 Hydrostatic nodal forces on downstream surface………87

Table 3.4 Uplift nodal forces on base surface ………88

Table3.5 Silt nodal forces on upstream surface………90

Table 3.6 Stress results of section 1………94

Table 3.7 Stress results of section 2………95

Table 3.8 Stress results of section 3………96

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Abstract

As a Country with a vast land area and a rich river water system, China has an

astonishing number of dams built and under construction, which can provide

huge economic and living benefits to human beings. However, the collapse of a

dam can cause catastrophic damage to the people who lives in the downstream.

The structural safety of dams is ensured by the design rules provided by National

Standards, which are based on more or less sophisticated interpretation models

of the mechanical response of these large infrastructures.

This work illustrates the three common categories of Chinese dams and their

distribution in different provinces. The stress analysis of concrete gravity dam

according to Chinese codes is summarized. The results of this methodology are

compared with finite element analyses in a specific application. Computations are

performed by 2D models implemented in a Matlab code developed and provided

by Professor Cocchetti at the Politecnico di Milano.

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Sommario

La Cina è un Paese estremamente vasto, con un ricco sistema fluviale e un numero

sorprendente di dighe, costruite e in costruzione, che possono fornire enormi

benefici economici e migliorare le condizioni di vita degli esseri umani. Tuttavia, il

crollo di una diga può causare danni enormi alle persone che vivono ai suoi piedi.

La sicurezza strutturale delle dighe viene comunque garantita dalle regole di

progettazione previste dalle norme nazionali, che si basano su modelli di

interpretazione più o meno sofisticati della risposta meccanica di queste

importanti infrastrutture.

Questo lavoro illustra le tre categorie comuni di dighe in Cina e la loro

distribuzione in diverse province. Viene inoltre introdotta l'analisi dello stato

tensionale delle dighe a gravità in calcestruzzo secondo la normativa cinese. I

risultati di questa metodologia vengono confrontati con l'output di analisi degli

elementi finiti in una specifica applicazione. I calcoli sono eseguiti su modelli 2D

implementati in un codice Matlab sviluppato e fornito dal Professor Cocchetti al

Politecnico di Milano.

Parole chiave: dighe, categorie, distribuzioni, analisi dello stress, standard cinesi,

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Chapter 1 Introduction

Dams are water retaining structures that intercept the flow of river channels to

raise the water level or regulate the flow. They form reservoirs, raise water levels,

regulate runoff, and concentrate water heads for flood control, water supply,

irrigation, hydroelectric power generation, and improvement of shipping and

other large rivers. Man-made dams are typically classified as Arch dams, Gravity

dams and Embankment dams according to their structures.

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Figure 1.2 Tiantangshan concrete arch dam

Figure 1.3 Dashahe earth-fill dam

These three types of dams have distinctive structural characteristics and

distribution situation in China. A number of dams are studied according to their

categories in order to known the difference. These dams are classified in to

sub-categories on the basis of the construction material and geometry layout, which

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Chapter 2. Also, in this chapter, the distribution of dams is shown by considering

the regional difference among provinces.

In Chapter 3, it is mainly focus on the stress analysis of concrete gravity dam. An

analytical calculation example of stress analysis of concrete gravity dam by using

partial amplified method according to Chinse standards is presented. In the end,

the analytical result with the results obtained from Finite Element Method (2D

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Chapter 2 General Information about

Dams in China

The most commonly used dams in China are: concrete gravity dam, concrete arch

dam and earth-fill dam.

China is the country with the largest number of dams in the world. In addition to

the Nu River and Yarlung Tsangpo River, dams have been built on the main stream

or tributaries of almost all major and minor rivers, totaling more than 86,000,

including almost all modern types in the world. The main types of existing dams

in China are: concrete gravity dam, concrete arch dam and earth-fill dam. Recently,

it tends to build high dams to fasten the hydropower development process.

2.1 Main Use of Dams in China

1). Power generation and economic profits.

Hydropower is a renewable and clean energy source compared with thermal

power. In China, the “West-to-East Power Transmission” project can inject 7.7 to

14.2% of the annual growth rate of the western national economic output, which

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2). Flood control and reduction of flood peaks

Nowadays, the total storage capacity of all reservoirs in China is almost one-sixth

of the annual average runoff of rivers in the country. This means that when the

flood reaches, 300 million people, hundreds of large and medium-sized cities, 500

million acres of arable land, and transportation infrastructure Facilities can be

protected by dams.

3). Increase the amount of adjustable water resources

Nearly four-fifths of China's reservoirs are used for irrigation, and the irrigated

area of the reservoir accounts for one-third of the country's irrigated area. With

the development of the national economy and the adjustment of the industrial

structure, the proportion of urban residents and industrial water use has increased.

More than 100 large and medium-sized cities in the country have been relying

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2.2 Main Problems of Dams in China

From the late 1950s to the 1970s, the number of dams increased dramatically.

Many small dams were constructed under the condition of “four unclear” (water

volume, drainage area, storage capacity, unknown geological conditions) and the

processes of survey, design, construction were mixing conducted at the same time.

Today, people in China need to continue to make large sums of money for the

reinforcement of a quarter of large and medium-sized dams and two-fifths of

small dams.

2). Dam accidents due to flood

In the past 20 years, the Chinese economy has entered the fast lane. China's dam

engineering technology has advanced by leaps and bounds, and many high dams

have been built. Due to the large volume of flood peaks in China, the

concentration of floods, and the large changes in flood peak flow, the flood

discharge structures of the dam account for a large proportion, which creates

difficulties for dam layout and construction diversion. According to statistics, dam

accidents owing to flood control standards for dams or floods exceeding the

standards accounted for approximately 37% to 51% of the total number of dam

accidents. In addition, the geological conditions in various parts of China are very

different, and the seismic requirements during the dam construction are also very

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3). Special high dam construction technical problems.

Many of the dams under construction in China are the highest, the most

complicated and the hardest in history. How to ensure safety and how to be

technically reliable will be a prominent issue. Such as high-pressure water splitting,

bearing capacity of the foundation and determining the basic mechanics of the

dam.

4). Seismic problems

China is located between the two major seismic zones in the world, on the one

hand, the collapse of a dam caused by earthquake can cause catastrophic damage

to the people who lives in the downstream. On the other hand, Reservoir water

may also induce earthquakes. As a result, a dam should have high strength and

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2.3 Characteristics of Dams

2.3.1 Gravity dam

In a gravity dam, the force that holds the dam in place against the push from the

water is Earth's gravity pulling down on the mass of the dam. The water presses

laterally (downstream) on the dam, tending to overturn the dam by rotating about

its toe (a point at the bottom downstream side of the dam). The dam's weight

counteracts that force, tending to rotate the dam the other way about its toe. The

designer ensures that the dam is heavy enough that the dam's weight wins that

contest. For this type of dam, it is essential to have an impervious foundation with

high bearing strength. The shape that prevents tension in the upstream face also

eliminates a balancing compression stress in the downstream face, providing

additional economy.

When situated on a suitable site, a gravity dam can prove to be a better alternative

to other types of dams. When built on a carefully studied foundation, the gravity

dam probably represents the best developed example of dam building. Since the

fear of flood is a strong motivator in many regions, gravity dams are being built

in some instances where an arch dam would have been more economical.

Gravity dams are classified as "solid" or "hollow" and are generally made of either

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the hollow dam is frequently more economical to construct.

Advantages

1. Gravity dams are relatively safe and reliable, good durability, and have strong

resistance to leakage, flooding, earthquake and war damage;

2. Gravity dams need Simple design and construction techniques, easy to

mechanized construction;

3. Gravity dams are adaptable to different terrains and geological conditions.

They can be built in any shape of valley, and the requirements for foundation

conditions are relatively low.

4. Drainage and discharge holes can be arranged in gravity dams to solve

problems such as power generation, flood discharge and construction diversion.

Disadvantages

1. The stress of the dam body is low and the material strength cannot be fully

exerted.

2. The dam body is large in volume and consumes much cement.

3. The temperature stress and contraction stress of the concrete in the

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2.3.2 Arch Dam

In the arch dam, stability is obtained by a combination of arch and gravity action.

If the upstream face is vertical the entire weight of the dam must be carried to the

foundation by gravity, while the distribution of the normal hydrostatic pressure

between vertical cantilever and arch action will depend upon the stiffness of the

dam in a vertical and horizontal direction. When the upstream face is sloped the

distribution is more complicated. For this type of dam, firm reliable supports at

the abutments (either buttress or canyon side wall) are more important. The most

desirable place for an arch dam is a narrow canyon with steep side walls

composed of sound rock. The safety of an arch dam is dependent on the strength

of the side wall abutments, hence not only should the arch be well seated on the

side walls but also the character of the rock should be carefully inspected.

There are three types of arch dam, one is single-arch dam which is divided into

the constant-angle and the constant-radius dam. Another type is the

double-curvature or thin-shell dam. The appearance is similar to a single-arch dam but

with a distinct vertical curvature to it as well lending it the vague appearance of a

concave lens as viewed from downstream. The multiple-arch dam is the third type

which consists of a number of single-arch dams with concrete buttresses as the

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Advantage

1. Arch dams have the beneficial joint effect of arches and beams;

2. The loads on the arched beams can be mutually adjusted, so they can

withstand overload;

3. Arch dam body can drain;

4. Arch dams present good seismic performance;

5. Arch is a thrust structure, to withstand the axial pressure, is conducive to the

use of ramming and mortar masonry material compressive strength.

Disadvantage

1. The stability mainly depends on the reaction force of the arches at both sides

of the strait, so the requirements for the foundation are high;

2. No permanent expansion joints in arch dams;

3. The geometric shape of arch dams is complex, and the construction is difficult.

2.3.3 Embankment Dam

Embankment dams are made from compacted earth, and have two main types,

rock-fill and earth-fill dams. Embankment dams rely on their weight to hold back

the force of water, like gravity dams made from concrete.

Rock-fill dams are embankments of compacted free-draining granular earth with

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particles, hence the term "rock-fill". The impervious zone may be on the upstream

face and made of masonry, concrete, plastic membrane, steel sheet piles, timber

or other material. The impervious zone may also be within the embankment in

which case it is referred to as a core. Rock-fill dams are resistant to damage from

earthquakes. A concrete-face rock-fill dam (CFRD) is a rock-fill dam with concrete

slabs on its upstream face. This design provides the concrete slab as an impervious

wall to prevent leakage and also a structure without concern for uplift pressure.

In addition, the CFRD design is flexible for topography, faster to construct and less

costly than earth-fill dams.

Earth-fill dams, also called earthen dams, rolled-earth dams or simply earth dams,

are constructed as a simple embankment of well compacted earth. A

homogeneous rolled-earth dam is entirely constructed of one type of material

but may contain a drain layer to collect seep water. A zoned-earth dam has

distinct parts or zones of dissimilar material, typically a locally plentiful shell with

a watertight clay core. Because earthen dams can be constructed from materials

found on-site or nearby, they can be very cost-effective in regions where the cost

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Advantages

(1) Embankment dams can obtain materials locally, save important building

materials such as steel, cement and wood, and reduce the long-distance

transportation of dam materials.

(2) The structure of embankment dam is simple, easy to maintain and increase,

expansion.

(3) The dam body is a rock-slug granular structure that has good performance in

adapting to deformation and therefore has low requirements for the foundation.

(4) The construction technology is simple and the number of working procedures

is small, which facilitates the rapid construction of combined machinery.

Disadvantages

(1) The dam body cannot overflow, and the construction diversion is not as

convenient as the concrete dam.

(2) The filling of viscous soil materials is greatly affected by the climate and other

conditions, affecting the construction period.

(3) The dam body needs regular maintenance, which increases the operation and

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2.4 Dams Distribution in China

A survey of different types of existing dams and their distribution in varies

Provinces of China has been conducted, which could be found in Appendix A. The

following maps are useful to understand the distribution of different types of dams

in China.

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Figure 2.2 China water system Map

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2.4.1 Gravity Dam

Table 2.1 Gravity dams’ distribution in Provinces

Type Province Name Heigh

t [m] Lengt h [m] Storag e capacit y [10 ⁶ m³] Anhui Yuetan 36.6 214 157 Chongqing Yingpan 80 147 320 Fujian Chitan 78 253 87 Dayan 17.7 219 Dongzhang 38 201 185 Gongchuan 25 113 27.86 Hongkou 130 340 449 Jinshan 39.5 134 55 Jintan 24.7 292.1 1.68 Liangqian 21 246.7 17.95 Jitou 46.5 150 89 Kongtou 26.5 282.8 6 33.1

25 Concret e gravity dam Solid concrete gravity dam Mianhuatan 111 308.5 2035 Mowu 32.9 265.5 5 29.6 Nanyi 96.8 193.4 158 Shanzai 65.6 273.6 172.3 Xiayang 12 80 2.2 Yongxi 34 198 690 Yongkou 32 260 5.04 Guangdon g Changhu 66 181 155 Feilaixia 52.3 2952 17,550 Nangao 78 240 78.7 Guangxi Zhuang Autonomo us Region Bailongtan 28 384 340 Baise 130 720 5,660 Jinjitan 42.7 337.4 230.9 Rongdi 41 89 14.4 Gansu Bapanxia 33 396 49 Daxia 70 241 90 Liujiaxia 147 204 5,700 Yanguoxia 57.2 321 220 Guizhou Suofengying 115 188 201.2 Silin 117 326.5 1,205

26 Wujiangdu 165 368 2,300 Hainan Daguang 57 719 1,710 Hebei Panjiakou 107 1,039 19,500 Taolinkou 74.5 500 709 Hubei Gaobazhou 57 419.5 430 Hanjianggush an 49 640 109 Huanglongtan 107 371 11,625 Lushui 97 345 706 Suojinshan 55 124 11.14 Three Gorges 181 2,309 39,300 Hunan Guanyinjiao 25 200 20 Jiangya 131 325 1,740 Tielu 71 246.3 32.83 Wanmipo 64.5 237 125 Wuqiangxi 85.83 724.4 4,200 Zaoshi 88 351 783 Jiangxi Laohushao 55 627 804 Luowan 47.2 181.8 77 Wanan 68 1104 2,216 Liaoning Baishi 49.3 513 1,645

27 Shenwo 50.3 532 791 Qinghai Geermu 42.8 102 10 Sichuan Baozhusi 132 524.4 8 2,550 Gongzui 85 447 310 Guanyinyan 159 838 2,072 Tongkou 33 278 36 Wudu 120 361 572 Xiaotiandu 39 152 127 Yingliangbao 38 68 5 Shanxi Ankang 125 541.5 2,585 Majiabian 55 207.5 12 Tianqiao 42 752 67 Taiwan Wushantou 56 1,273 1,030 Tibet (Xizang) Zangmu 116 389.5 866 Yunnan Ahai 130 396 806 Dachaoshan 115 480 940 Gelantan 113 466 409 Gongguoqiao 105 356 49 Huangdeng 203 464 1,500

28 Lidi 74 356.4 71 Longkaikou 116 768 507 Manwan 132 418 920 Tuoba 158 500 1,040 Wunonglong 137.5 247.1 36 Zhejiang Anmin 46.6 132 3.32 Baozishi 23.5 88 53 Changzhao 68 211 189 Fenshuijiang 34.7 268.5 193 Huaguangtan 36.5 134 3 Jiaokou 67.4 286 120 Shuitaozhuan g 60 262.9 29 Tingxia 76.5 317 150 Hollow concrete gravity dam Guangdon g Baipenzhu 66.2 240 385 Fengshuba 95 400 1,940 Hainan Niululing 90.5 341.2 778 Zhejiang Changtan 71 210 172 Fujian Fengtou 60 348 177 Liangba 48.5 84 6

29 Masonry gravity dam Guanxi Zhuang Autonomo us Region Junshan 69 220 25 Hainan Tuoxing 69 370 144 Hebei Zhuzhuang 95 544 416 Hunan Shuifumiao 54 242.5 370 Liaoning Yingnahe 28 296 30.36

It is obviously that the most widely used type of gravity dams in China is solid

concrete gravity dams, and the height of these dams in the survey varies in a wide

range.

Figure 2.4 Gravity dam categories pie chart

Gravity dams in survey

concrete gravity dam (solid) concrete gravity dam (hollow) masonry gravity dam

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According to the following graph, the majority of gravity dams are in the south

part of China. That may due to the water system distribution in China, the southern

area has more large rivers and flat terrain. And gravity dams are suitable for

reservoirs and river courses with good geological conditions, a wide area, and a

large water surface. These conditions could be satisfied in southern provinces.

Figure 2.5 Distribution of gravity dams in survey

0 2 4 6 8 10 12 14 16 18 20 N u b er o f gra vity d ams in surv ey Provinces

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2.4.2 Arch Dam

Table 2.2 Arch dams’ distribution in Provinces

Type Province Name Height

[m] Top arch length [m] Storage capacity [10⁶m³] Single-arch dam Anhui Xianghongdian 87.5 367.5 2,360 Chongqing Pengshui 116.5 325.5 518 Fujian Meihua 22 64.35 0.116 Hebei Wenquanbao 48 187.9 2 Hubei Geheyan 151 665.45 3,120 Qinghai Longyangxia 178 396 24,700 Sichuan Shapai 132 250.25 18 Double-curvature dam Chongqing Tengzigou 117 339.47 193 Fujian Liujiangong 81 113 70.9 Wangkeng 58 134 1.5 Anrenxi 66.5 202 26 Shuangkoudu 81 177 19.18 Gansu Longshou 80 140.84 132 Guangdong Bamei 53 142.8 2.4

32 Quanshui 80 209 22 Tiantangshan 70 287 243 Guangxi Baotan 75 283.41 22.2 Kelin 58 150 2.115 Guizhou Dahuashui 134 287.56 123 Dongfeng 162 254 1,016 Goupitan 225 545 6,454 Hongyan 60 322 380 Puding 75 165.67 420 Shiyazi 134.5 273.14 321.5 Xiangbiling 135.5 459.6 263 Yushe 78.4 238.53 3.38 Zhaixiangkou 39.5 151.88 9.4 Hubei Dongping 135 285 334 Zhaolaihe 105 198.05 6.4 Hunan Dongjiang 157 438 5,670 Fengtan 112 488 1,730 Mantianxing 65 184.3 118 Ouyanghai 58 230.56 424 Jiangxi Gaodian 81.5 290 4 Shankouyan 99 287.94 105

33 Xiahuikeng 101 264.6 4 Qinghai Lijiaxia 155 414.39 1,650 Shanxi Hengshan 69 150 1 Linhekou 96.5 311 147 Shimen 88 254 1,098 Sichuan Baihetan 289 20,600 Dagangshan 210 635.47 742 Ertan 240 774.69 5,800 Jinping 305 552.23 7,760 Qinglong 16.5 102 0.234 Wudongde 270 325.67 2,600 Xiluodu 285.5 698.09 12,800 Yangfanggou 155 361.6 456 Yebatan 217 582.21 1,185 Taiwan Feicui 122.5 510 327 Yunnan Dayakou 92 299.56 250 Shimenkan 111 296.26 197 Xiaowan 294.5 922.74 15,132 Zhejiang Jinshuitan 102 350.6 1,393 Maozhu 34 187 2 Menxi 49.8 144 2

34 Tongkenggxi 48.8 58.72 0.28 Xiaan 64 274 135 Multiple-arch dam Anhui Foziling 75.9 510 500 Meishan 88 443.5 2,337 Fujian Waidu 15 200 0.69

The most common type of arch dams used in China is double-arch dams, and the

arch dams usually have large height around or over 100 m.

Figure 2.6 Arch dam categories pie chart

From the figure below, it is clear that those arch dams mainly distributing on the

southern part especially south-west part of China, such as Guizhou, Sichuan, and

Yunnan Province. These areas have abundant water resource and suitable Canyon

terrain at the same time, being suitable for constructing arch dams.

Arch dams in survey

35

Figure 2.7 Distribution of arch dams in survey

0 2 4 6 8 10 12 N n u m b ers o f d ams in s u rv ey Provinces

Arch Dams in Provinces

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2.4.3 Embankment Dam

Table 2.3 Embankment dams’ distribution in provinces

Type Province Name Height[m] Top arch

length[m] Storage capacity [10⁶m³] Rock-fill dam Chongqing Bashan 155 477 315,5 Shizitan 52 1,014 1,000 Henan Xiolangdi 160 1,677 12,650 Liaoning Zhenziling 36 644 210 Shanxi Jinpen 130 433 13.4 Sichuan Lianghekou 295 650 10,767 Shuiniujia 108 331.36 144 Tibet(Xizang) Malan 76.3 215 155 Yunnan Miaowei 139.8 576.68 660 Nuozhadu 261.5 608 23,700 Zhejiang Niutoushan 49.3 435 3,025 Conrete-face rock-fill Beijing Shisanling 70 464 401 Chongqing Liyutang 105 467 104 Fujian Jiemian 126 500.5 1,240

37 dam Qinshan 120 259.8 265 Guangdong Xuneng 60 144 2 Guangxi Dongba 105 467 297 Guizhou Sanbanxi 185.8 423.5 4,940 Heilongjian Nierji 40.55 1800 2,360 Hubei Doulingzi 88.5 338.5 484 Shuibuya 233 660 4,312 Jiangxi Dongjin 85.5 326 705 Nanche 60 191.5 123 Jilin Xiaoshan 85.9 290 107 Qinghai Gongboxia 132 429 630 Heiquan 123.5 438 172 Sichuan Daqiao 52 93 658 Tibet(Xizang) Pangduo 72.3 1052 1,174 Xinjiang Jilebulake 146 136 332 Jilintai 157 247.2 2,530 Wuluwati 138 365 340 Yunnan Huangjiaoshu 67.4 200.38 36 Liyuan 155 305 209 Sinanjiang 115 362.46 271 Zhejiang Sanchaxi 88.8 186 30

38 Shanxi 130.8 448 3.41 Tongbai 68.25 434 11 Yingchuan 87 250 37 Earth-fill dam Anhui Longhekou 33 320 820 Shaheji 27.4 720 211 Zhongxing 14 3,180 99 Beijing Chaohe 56 1,008 437 Tuolin 63.5 590.75 7,920 Fujian Dongzhen 58.6 367 282 Jiangkou 28.5 110 405 Shanmei 73 305 655 Guangdong Dashahe 19.8 201 157 Dashuiqiao 21 850 41 Gaozhou 43.2 320 11,500 Guangxi Zhuang Autonomous Region Chengbihe 70.4 425 11,300 Kelan 32.7 333 46 Laohutou 24 360 125 Wusijiang 30 220 128 Xianhu 47 296 127 Hainan Songtao 80 730 3,340 Hebei Angezhuang 49.4 1,281 309

39 Dongwushi 34 405 162 Koutou 30 596.6 106 Yunzhou 43 183.4 102 Henan Nanwan 38.3 816 8,800 Heilongjiang Hamatong 13.1 800 127 Huashuchuan 33.8 320 119 Hubei Datong 37.5 446 260 Fushui 46 941 1,665 Gaoguan 45 1,220 208 Huayanghe 33.5 522 123 Qingshan 59 383 448 Jiangxi Huinv 52 350 126 Panqiao 30 187 120 Shangyou 28 380 1.55 Sheshang 43.5 186.5 127 Youluokou 36 177 116 Jilin Liangjiashan 17.3 541 19 Taipingchi 8 3,200 201 Xingxingshao 33.2 510 203 Inner Mongolia Chaersen 40 1,712 1,253 Molimiao 11 6,420 192

40 Autonomous Region Liaoning Songshu 25.46 280 76.88 Zhuwei 19.5 340 155 Shandong Bailanghe 25 550 148 Bashan 33.6 1,780 529 Guangnan 7 8,000 114 Mahe 23 926 138 Rizhao 47 1,116 318 Taihe 48 760 166 Wangwu 28 761 149 Xiashan 21 2,750 1,405 Shanxi Fenhe 61.4 1,002 700 Shitouhe 114 590 147 Wenyuhe 55.5 740 26 Tianjin Yuqiao 24 2,222 1,559 Yunnan Dongfeng 47 450 9.035 Yuxi 42 450 8.931 Zhejiang Dongbaihu 95.5 535 116.4 Fushi 43.2 446 217

41

Hengjin 57.5 300 274

Laoshikan 36.9 560 117

Siminghu 16.85 600 122.27

Tongshanyuan 48.42 252 171

The most popular type of embankment dam in China is earth-fill dam with

relatively low height and large length. That may be a result of the lower cost and

easier construction of Embankment dams compared with others.

Figure 2.8 Embankment categories pie chart

The embankment dams are widely used in different provinces, similar to previous

situation, southern provinces still have more embankment dams than northern

provinces, which is mainly caused by the water system situation. Furthermore, the

overview of this distribution is more balanced compared with gravity dams and

arch dams.

Embankment dams in survey

42

Figure 2.9 Distribution of embankment dams in survey

0 2 4 6 8 10 12 N u mb er o f d ams in s u ve y Provinces

43

2.5 Representative Dams in China

2.5.1 Concrete Gravity Dam

The Three Gorges Dam is the largest concrete gravity dam which wins the World

Record of the World's Largest Water Conservancy Project by the World Record

Association. It is the largest hydropower station in the world and the largest

construction project ever built in China.

Figure 2.10 The Three Gorges dam

location: Yichang City, Hubei Province

Height: 181m

Length: 2,309m

Top width: 40m

44 Storage capacity: 39.3 billion cubic meters

Total dam concrete volume: 17 million cubic meters

Dam advantages:

1) Flood control and flood adjustment

When the Three Gorges Reservoir is in operation, it reserves a total of 22.15

billion cubic meters of flood protection capacity, and the flood regulation of

the reservoir can reduce the peak discharge to 27,000-33,000 cubic meters

per second, which is the highest in the world's water conservancy projects.

2) Hydroelectric power

The Three Gorges Hydropower Project installs 32 turbine generating units with

a capacity of 700,000 kilowatt-hours (including 6 hydroelectric generating

units for underground powerhouses) plus two 50-kilowatt-hour hydroelectric

generating units with a total installed capacity of 22.5 million kilowatts. With

an annual power generation of 100 billion kWh, it is the world's largest

hydropower station.

3) Improve shipping

The Three Gorges Reservoir returns water to Chongqing, a town in

southwestern China. It has improved its shipping mileage by 660 kilometers

and increased its one-way traffic capacity from 10 million tons to 50 million

tons. It is well-known that the Three Gorges Project is the most obvious first

45 4) Drought resistance

Once the downstream drought, the Three Gorges can increase the intensity of

water discharge to increase discharge flow so that drought can be effectively

alleviated.

Dam disadvantages:

1) The dam stopped the flow of sludge down the river, causing the estuary of the

Yangtze River, including the Shanghai area, to contract and the ocean’s salt water

pouring back into the interior. According to a report released this week by the

World Wildlife Federation, the flow of water through the dam is accelerating,

causing damage to the downstream flood embankment. Untreated sewage and

fertilizer residues are continuously discharged into dam reservoirs, causing the

proliferation of giant algae and threatening the downstream water supply. The

fluctuation of the water level in the reservoir is also considered to be the root

cause of the peculiar rat plague suffered by farmers in Hunan Province.

2) From the problems exposed by the Three Gorges Dam, it can be seen that, on

the one hand, China, a country that is rapidly moving toward industrialization, is

eager to get out of the shackles of nature, and on the other hand, the result of its

efforts is counterproductive. The opening of the Three Gorges Project coincided

with the review of the construction of dams by the ecological community abroad.

46 projects can only survive with state subsidies.

3) The impoundment of the dam and the adjustment of the water level during the

rainy season triggered landslides, which also seriously damaged the geological

structure of Miaohe Village and other areas.

4) Dam impoundment destroyed the water cycle, leading to continuous drought

in Yunnan and other places. Many rivers stopped flowing.

2.5.2 Concrete Arch Dam

Ertan Concrete Double Curvature Arch Dam

Ertan Hydropower Station has created and broken out many of the World Record

Associations in the world and China. The overflow double-curvature arch dams

height ranks first in Asia and third in the world for the same type of dam. The

underground caverns formed by the Tailwater surge chambers are the largest in

Asia. And the hydraulic pressure test of the unit scroll reaches 3.46 megapascals,

which is the highest in China.

The dam is a concrete double-curvature arch dam. To make the stress distribution

of the dam uniform, the abutment thrust is more biased toward the mountain

body, which is conducive to the stability of the dam body. The horizontal arch

circle is a secondary parabola and the upstream face of the arch crown beam is a

47

Figure 2.11 Ertan Concrete Double Curvature Arch Dam

Location: southwest Sichuan Province

Height:240m

Dam top arc length: 774.69 m

crown thickness: 11 m

Arch bottom thickness: 55.7 m

Maximum center angle of arch: 91.49 °

Storage capacity: 5.8 billion cubic meters

Dam concrete volume: 4 million cubic meters

The basic earthquake intensity in dam area is 7 degrees, design intensity is 8

48

Main design problem: temperature load, stress analysis, dam abutment stability

analysis.

Ertan dam site has good topography and geological conditions for the

construction of high concrete double arch dams. The preliminary design of the

double-curved arch dam arch bridge beam width 70.34m approved, the dam

concrete volume of 4.742 million cubic meters; after the optimal design, the final

use of the double-curved arch dam arch bottom beam maximum width reduced

to 55.74m, dam the concrete volume was reduced to 4.242 million cubic meters,

which saved 500,000 cubic meters of concrete compared to the initial design.

Ertan arch dam adopts a parabolic double curved arch dam, which reduces the

curvature of the arch near the bank and flattens it, so as to increase the angle

between the arch thrust and the bank slope and increase the abutment stability.

In order to make the stress distribution uniform, reduce the arch dam section, use

higher-order curves longitudinally, increase the longitudinal curvature, and

control the maximum backslope on the upstream side to 0.18. Due to the

incomplete symmetry of the terrain on both sides of the river, the left half arch

and the right half arches have different curvature radii. The radius of curvature of

49

2.5.3 Rock-fill Dam

The Xiaolangdi Water Control Project is a large-scale comprehensive water

conservancy project integrating drainage reduction, flood control, flood

prevention, water supply and irrigation, and power generation on the mainstream

of the Yellow River. It is a key project for the development and management of

the Yellow River. The dam is Clay diagonal wall rockfill dam with 518,500 cubic

meters of dam volume and the 1.2 meters deep and 80 meters deep concrete

impervious wall. Its filling capacity and concrete impervious wall are the highest

in China.

50

Location: Mengjin County, Luoyang City, Henan Province

Height: 160 m

Length: 1677m

Top width: 15m

Maximum bottom width: 864 m

Storage capacity: 12.65 billion cubic meters

The main project volume of the hub (including preparatory projects): 60.27 million

cubic meters of excavated earth and stone, 55.74 million cubic meters of earth

and stone, and 3.54 million cubic meters of concrete and reinforced concrete, and

32,600 tons of metal structures.

The upstream cofferdam is a part of the dam body. The concrete dam impervious

wall is used for the dam foundation. The project is initially designed as a slant wall

dam type, and the post-optimization is a diagonal core dam type. The main

difference is that the former is mainly based on horizontal impervious, and the

vertical impervious is supplemented; the latter is mainly vertical impervious, and

horizontal impervious is supplemented. The design of the dam has the following

characteristics:

1. Considering the seepage prevention effect of siltation in the reservoir area

reasonably, the dam foundation seepage prevention effect is more reliable;

2. The climbing of the inner covering improves the anti-sliding stability of the

51

area, but also does not affect the dam slope too much;

3. Reduced the number of earthworks filled in the upstream cofferdam and the

amount of basic treatment works, so that the relatively tight schedule after the

closure can be eased;

4. Compared with inclined-wall dams, the concrete seepage-proof wall has been

52

Chapter 3. Stress Analysis of a Concrete

Gravity Dam

3.1 Analysis of Concrete Gravity Dams According to Chinese

Codes

3.1.1 Load and Loading Combination

The loads acting on concrete gravity dam are classified into basic loads and special

loads:

3.1.1.1 Loads

Basic loads:

1) Dead loads: self-weight and the weight of the equipment on the dam.

2) Hydrostatic pressures on the upstream and downstream faces of the dam at

normal pool level or design flood level (selecting one of them as critical).

3) Uplift pressure.

4) Silt pressure.

5) Wave pressure at normal pool level or design fold level.

6) Ice pressure.

7) Earth pressure.

8) Hydrodynamic pressure at design flood level.

53 Special loads:

10) Hydrostatic pressures on the upstream and downstream faces of the dam at

maximum design flood level.

11) Uplift pressures at maximum design flood level.

12) Wave pressure at maximum design flood level.

13) Hydrodynamic pressure at maximum design flood level.

14) Earthquake loads.

15) Other infrequent loads.

3.1.1.2 Loading Combinations

The loading combinations used for the analysis of dam stability against sliding

and for the calculation of dam stresses are categorized into two cases, the usual

cases and unusual cases. Loading combinations shall be considered as per those

tabulated in the Table 3.1. Other adverse loading shall also be considered if

54

Table 3.1 Loading combinations for concrete gravity dam

Notes: 1. The most unfavorable loading combination shall be selected based on practicable possibility of simultaneous occurrence of various loads.

2. Dams to be constructed in stages shall have their corresponding loading combination calculated for each stage. 3. Loading combination during construction period shall be exam as an unusual load case

4. If, according to geology or other conditions, the drainage system in the dam is susceptible to blocking and needs to be repaired during operation, loading combination with drains inoperative shall be considered, as an unusual case. 5. For earthquake condition, if ice pressure in winter is considered, wave pressure shall be excluded.

Dead load Hydros tatic pressur Uplift pressur e Silt press ure Wave press ure Ice pressur e Earthq uake load Hydr odyn amic Earth pressure Other loads (1) Normal pool level 1) 2) 3) 4) 5) _ _ _ 7) 9)

The earth pressure, depending on whether

there is earth fill against the dam face

(the same below) (2) Design

flood level 1) 2) 3) 4) 5) _ _ 8) 7) 9)

(3) Freezing 1) 2) 3) 4) _ 6) _ _ 7) 9)

The hydrostatic and uplift pressures shall be calculated with the

corresponding reservior water level in

winter (1) Maximum design flood level 1) 10) 11) 4) 12) _ _ 13) 7) 15) (2) Earthquake 1) 2) 3) 4) 5) _ 14) _ 7) 15)

The hydrostatic and wave pressures shall be calculated with the

normal pool level, which may be other water level if justified Usual Unusual Remarks Loads Loading combinatio ns Load case

55

3.1.2 Stress Analysis

According to “Design Standard for concrete Gravity Dams” (SL319 - 2005),

Stresses to be computed for concrete gravity dams mainly include stresses in the

selected horizontal planes, localized stresses in the weakened parts of the dam,

stresses at the individual locations of the dam, stresses within the dam foundation

(if required) and stresses which may include some or all of the above-mentioned

items, or any other added item, depending on the project size and the dam

structure.

The cross section of a concrete gravity dam shall be determined based on the

gravity method and the rigid-body limit equilibrium method, and also by the finite

element method as a supplementary method. The stresses on the upstream and

downstream faces of a solid gravity dam are calculated by the equations using

gravity method.

3.1.2.1 Vertical Normal Stresses at Upstream and Downstream Faces

1. Vertical normal stress at upstream face (refer to Figure 3.1):

𝜎_𝑦𝑢 ₌∑ 𝑊

𝑇 + 6 ∑ 𝑀

𝑇2

Where 𝑇− horizontal distance from upstream edge to downstream edge of computational plane, m;

Σ𝑊− resultant vertical force above computational plane including uplift pressure (the same as below), positive in downward direction. For a solid gravity dam, a

56

unit length of dam body along the axis is selected for calculation (the same as

below);

Σ𝑀− resultant moment of all the vertical and horizontal forces above computational plane about center of gravity of section, positive for moment

procedures compression at the upstream face.

2. Vertical normal stress at downstream face:

𝜎_𝑦𝑑 =∑ 𝑊 𝑇 −

6 ∑ 𝑀 𝑇2

3.1.2.2 Shear Stresses at Upstream and Downstream Faces

1. Shear stresses at upstream face: 𝜏𝑢 _{= (𝑃 − 𝑃}

𝑢𝑢− 𝜎𝑦𝑢)𝑚1

Where 𝑚1− slope of upstream face;

𝑃− hydrostatic pressure at the upstream face of computational plane (sediment pressure also to be included, if any);

𝑃𝑢𝑢− uplift pressure at upstream face of computational plane.

2. Shear stress at downstream

𝜏𝑑 _{= (𝜎}

𝑦𝑑− 𝑃′+ 𝑃𝑢𝑑)𝑚2

Where 𝑚2− slope of downstream face;

𝑃′− hydrostatic pressure at the downstream face of computational section (sediment pressure included, if any);

57

Figure 3.1 Sketch for stress calculation of solid gravity dams

3.1.2.3 Horizontal Normal Stresses at Upstream and Downstream Faces

1. Horizontal normal stress at upstream face:

𝜎𝑥𝑢 = (𝑃 − 𝑃𝑢𝑢) − (𝑃 − 𝑃𝑢𝑢− 𝜎𝑦𝑢)𝑚12

Horizontal normal stress at downstream face:

𝜎_𝑥𝑢 _{= (𝑃 − 𝑃}

58

3.1.2.4 Principal Stresses at Upstream and Downstream Faces

1. Principal stresses at upstream face:

𝜎₁𝑑 = (1 + 𝑚₂2)𝜎𝑦𝑑− 𝑚22(𝑃 − 𝑃𝑢𝑑)

𝜎₂𝑢 = 𝑃 − 𝑃_𝑢𝑢

3. Principal stresses at downstream face:

𝜎₁𝑑 = (1 + 𝑚₁2)𝜎_𝑦𝑢_{− 𝑚}

12(𝑃 − 𝑃𝑢𝑢)

𝜎₂𝑢𝑑 = 𝑃 − 𝑃_𝑢𝑢

All the above equations are applicable to the load combination with uplift

pressure included. If the uplift effect is not included, P𝑢𝑢 and p𝑢𝑑 in all the

equations shall be taken as zero for calculation of stresses at the upstream and

downstream face. If seismic loading has to be considered, the calculations shall

conform to the relevant specifications of “Specification on Seismic Design of

Hydraulic Structures” (SL 203).

The vertical stresses on the dam-foundation interface shall be calculated

according to the equation below:

The vertical stresses on the dam-foundation interface shall be calculated

59 𝜎_𝑦 =∑ 𝑊

𝐴 + ∑ 𝑀𝑥

𝐽

Where σ𝑦− vertical stresses on the dam-foundation interface, kPa;

Σ𝑊− summation of all normal forces (including uplift, the same as below) acting on the dam-foundation interface of one dam monolith or one unit length of dam

monolith, kN;

Σ𝑀− summation of moments of all forces about the centroid axis of the dam-foundation interface under consideration, kN∙m;

𝐴− area of the dam-foundation interface of one dam monolith or one unit length of dam monolith,𝑚2;

𝑥− horizontal distance from the centroid axis of the interface to the point under consideration, m;

𝐽− moment of inertia of the interface of one dam monolith or one-unit length of dam monolith about its centroid axis,𝑚4_.

The allowable stress of the concrete shall be determined by dividing the ultimate

strength by a corresponding safety factor. The safety factor for determining the

allowable concrete compressive stress shall not be smaller than 4.0 for usual

loading combination and 3.5 for unusual loading combination (exclude

earthquake load). When the concrete in local areas is required to resist tensile

stresses, the safety factor for determining the allowable concrete tensile stresses

60

3.2 Application Case

The general information of the application case is taken from a thesis work in

Chinese from Internet resource which can be found from:

http://www.docin.com/p-234060840.html

3.2.1 Geometry and Loading Combination

3.2.1.1 Geometry Layout

The basic data of this design is derived from the existing water conservancy

projects in the southwest region of China. The site is located in the H River. The H

River is the middle and upper reaches of the W River system. The basin is

subtropical climate zone, and the climate is mild and rainy. The annual average

temperature of the dam site is 20.1C°, and the average annual humidity is 80%.

The average annual precipitation in the dam area is 1343.5mm. The runoff is

mainly formed by precipitation. The average annual runoff is 1610𝑚3_{/s, and the}

average annual runoff is 50.8 billion𝑚3_{. The interannual variation is relatively}

stable, with an annual coefficient of variation of 0.24. The H flood is mainly caused

by heavy rain. The dam site belongs to a relatively stable block and belongs to the

weak-shock environment. The basic seismic intensity of the dam site and the

earthquake-induced intensity of the reservoir are all 7 degrees. The valley of the

dam site is a relatively flat "V" shaped valley with an aspect ratio of 3.5 and stratum

61

The elevation of the dam base is 190m and the normal pool level elevation and

maximum design flood level elevation of the upstream are 376.73 m and 379.83

m. While those of the downstream are 225.5 m and 260.4 m respectively. There

is a maintenance drainage gallery inside the dam. The distance from the upstream

wall to the upstream dam surface is 28 meters, and the distance from the

downstream to the dam toe is 8 meters.

The water retaining structure is a roller compacted concrete gravity dam. The

maximum height of the gravity dam is 190m, the top width of dam is 16m and

the bottom width of dam base is 145.22 m. The upstream slope n=0.2 while

downstream slope m=0.7. The concrete has a specific weight 24 kN/𝑚3_{, an elastic}

modulus 𝐸𝑐 = 30000 N/ 𝑚𝑚2 and a Poisson coefficient 𝑣𝑐 = 0.16. The

foundation is made up of sandstone which has the unit weight of 23.6 kN/𝑚3_{, an}

elastic modulus E = 6.74× 1010 _N/𝑚𝑚2 _{and a Poisson coefficient 𝑣= 0.25.}

62

3.2.1.2 Divided Load Calculation

3.2.1.2.1 Determination of the Calculation Section

The four cross sections with a height of 0m, 100m, 130m, and 163.87m

respectively are to be calculated by using EXCEL for the applied load and stress.

Figure 3.3 Dam cross section profile (unit: m)

3.2.1.2.2 Loads and Load Combinations

The maximum dam height is selected for calculation, and various loads are

63 1. Self-weight

The standard value of the self-weight of a hydraulic structure can be determined

according to the structural design dimensions and the material weight of the

structure. In this pivot calculation, the material unit weight is 24.0 kN/m3_.

2. Hydrostatic Pressure

The hydrostatic pressure acting perpendicularly on the surface of a building

should be calculated as follows:

𝑝_𝑤𝑟 = 𝛾_𝑤𝐻

Where 𝑝𝑤𝑟- Hydrostatic pressure at the point of calculation, kN/𝑚2;

H - The head of water at the calculation point, m, determined by the difference

between the calculated water level and the calculated point;

𝛾_𝑤 – The unit weight of water, kN/𝑚3_{; this pivot calculation uses 9.81 kN/𝑚}3_.

3. Hydrodynamic Pressure Calculation

The representative value of the average pressure of the gradual flow can be

calculated by calculating or experimentally obtaining the surface line according to

the flow conditions under the corresponding design conditions: 𝑝𝑡𝑟 = 𝜌𝑤𝑔ℎ𝑐𝑜𝑠𝜃

Where 𝑝𝑡𝑟 - Mean pressure representative value at point of calculation on the

flow surface, N/𝑚2_;

𝜌_𝑤- Water density;

g- Gravity acceleration, 𝑚/𝑠2_;

64

θ - The angle between the bottom surface of the structure and the horizontal plane.

The pressure of the hydrodynamic pressure on the underside of the anti-arc

section of the discharge structure such as overflow dam is approximately evenly

distributed, and its representative value can be calculated as follows: 𝑝_𝑐𝑟 = 𝑞𝜌_𝑤𝑣/𝑅

Where 𝑝_𝑐𝑟 - Water centrifugal pressure representative value;

q- Single-width traffic on anti-arc section under corresponding design conditions,

𝑚3/(s· m);

v- Average cross-section velocity at the lowest point of the anti-arc, m/s;

R-radius of anti-arc.

The horizontal and vertical force representative values of the centrifugal force on

the anti-arc segment of a spillway building such as an overflow dam can be

calculated as follows:

𝑃_𝑥= 𝑞𝜌_𝑤𝑣(𝑐𝑜𝑠𝜑₂− 𝑐𝑜𝑠𝜑₁) 𝑃_𝑦 = 𝑞𝜌_𝑤𝑣(𝑠𝑖𝑛𝜑₂+ 𝑠𝑖𝑛𝜑₁)

Where 𝑃_𝑥 - The representative value of horizontal component force of the

centrifugal force on the unit width;

𝑃𝑦- The representative value of vertical component force of the centrifugal force

on the unit width;

𝜑₁- Dam downstream slope angle;

65 4. Earthquake Load

1) Earthquake inertia force

The pseudo-static method is used to calculate the effect of seismic action. The

horizontal seismic inertia force representative value acting on the mass point i

along the height of the building is calculated as follows: 𝐹_𝑖 = 𝑎_ℎ𝜉𝐺_𝐸𝑖𝛼_𝑖/𝑔

Where 𝐹𝑖- The representative value of horizontal seismic inertia force acting on

mass i;

𝑎ℎ- Horizontal design earthquake acceleration representative value;

𝜉 - The effect reduction factor of earthquake action is generally taken as 0.25;

𝐺_𝐸𝑖 - The standard value of gravity acting on mass i;

𝛼_𝑖- The dynamic distribution coefficient of mass i.

𝛼_𝑖 = 1.4 (1 + 4(ℎ𝑖 ⁄ H) 4 1 + 4 ∑ 𝐺_𝐺𝐸𝑖 𝐸 𝑛 𝑗=1 (ℎ𝑗⁄ )𝐻 4

Where n- The sum of calculated dam masses;

H - The height of dam;

ℎ𝑖, ℎ𝑗 - The height of the mass i, j respectively;

𝐺𝐸 - The standard value of total gravity effect of buildings that generates

earthquake inertia force.

2) Earthquake dynamic water pressure

During the earthquake, due to the vibration of the reservoir and the ground

caused by the vibration of the ground and dam body, additional ground motion

66

earthquake, the representative value of the ground motion water pressure at

vertical water depth h is represented by the following formula: 𝑝_𝑤(ℎ) = 𝑎_ℎ𝜉𝜓(ℎ)𝜌_𝑤𝐻₁

Where 𝑝𝑤(ℎ)- The representative value of earthquake water pressure acting on

the depth of the vertical face of the facing dam;

𝜓(ℎ)- The distribution coefficient of the ground motion pressure at depth h,

according to the specification SL203-97 look-up table 6.1.9;

𝐻₁- water depth;

𝜉- The effect reduction factor of earthquake action is taken as 0.25;

𝜌_𝑤- Water body mass density standard value.

The total ground water pressure per unit width along the axis of the dam is: 𝐹0 = 0.65𝑎ℎ𝜉𝜌𝐻12

Its effect point is located 0.54𝐻1below the water level.

5. Silt Pressure

The standard values of horizontal silt pressure acting on dams, sluice gates, and

other retaining structures of fixed length can be calculated as follows:

𝑃_𝑆𝐾 =1 2𝛾𝑆𝑏ℎ𝑠

2_𝑡𝑔2_{(45° −}𝜑𝑠

2) Where 𝑃𝑆𝐾- Silt pressure standard value, kN/m;

𝛾_𝑆𝑏- Floating unit weight of silt, kN/𝑚3_;

ℎ𝑠- Siltation thickness before retaining structure, m;

67

The pressure of siltation in the vertical direction is calculated according to the

floating weight of silt sand and the area of sedimentation.

6. Lift Pressure

The specification states that concrete dams should be calculated based on the

vertical distribution of forces acting on the technical sectional area.

This hub calculation uses the calculation of the floating force and the infiltration

pressure distribution. The calculated cross section of the dam lift pressure as

follows:

When the dam foundation is provided with an anti-seepage curtain and an

upstream main drainage hole, and there is a downstream auxiliary drainage hole

and drainage system. The head of the lift pressure on the dam above the

calculated cross sections is H1. The centerline of the primary and secondary

drainage holes is α1H1, α2H2, and the downstream is H2, and the segments are

68

Figure 3.4 Lift pressure on section 1

69

Figure 3.6 Lift pressure on section 3

Figure 3.7 Lift pressure on section 4

The lift pressure coefficient 𝛼1 before the main drainage hole is 0.2.

Residual lift pressure coefficient 𝛼₂ is 0.5 and 𝛼₃ is 0.2.

𝐻1- Water height of lift pressure on dam cross sections upstream;

70

T- The length of the dam calculated section in the upstream and downstream

directions;

H’- water head difference between cross sections upstream and downstream.

7. Wave Pressure

Wave pressure distribution as shown below:

Figure 3.8 Simplified wave pressure calculation diagram

The standard value of wave pressure per unit length is calculated as follows:

𝑃_𝑤𝑘 = 1

4𝛾𝑤𝐿𝑚(ℎ1%+ ℎ𝑧)

Where 𝑃𝑤𝑘- Wave length standard value per unit length on the water surface,

kN/m;

𝛾_𝑤- Unit weight of water, kN/𝑚3_;

𝐿_𝑚- Mean wave length, m;

71

Refer to hydraulic building load design specifications DL5077-1997:

Adopt the Hedi Reservoir formula: 𝑔ℎ_2% 𝑣₀2 = 0.00625𝑣0 1 6⁄ (𝑔𝐷 𝑣₀2) 1 3⁄ 𝑔𝐿𝑚 𝑣₀2 = 0.0386( 𝑔𝐷 𝑣₀2) 1 2⁄ ℎ_𝑧 =𝜋ℎ1% 2 𝐿_𝑚 𝑐𝑡ℎ 2𝜋𝐻 𝐿_𝑚

Where 𝐿𝑚- Mean wave length, m;

ℎ_2%- The height of wave with 2% cumulative frequency, m;

𝑣0- Calculated wind speed, 24 m/s;

D- Length of wind zone, m, D=2000 m;

g- Gravity acceleration, 9.81 𝑚/𝑠2_;

H – water depth.

All the calculated load results are presented in Appendix B.

3.2.2 Stresses Distribution according to Chinese Codes

3.2.2.1 Stresses Calculation

(1) Edge stress

Basic calculation formulas of dam surface stress according to solid gravity:

Upstream vertical normal stress:

𝜎_𝑦𝑢 ₌∑ 𝑊

𝑇 + 6 ∑ 𝑀

𝑇2

72 𝜎_𝑦𝑑 ₌∑ 𝑊

𝑇 − 6 ∑ 𝑀

𝑇2

Upstream shear stress:

𝜏𝑢 _{= (𝑝 − 𝑝}

𝑢𝑢 − 𝜎𝑦𝑢)𝑛

Downstream shear stress:

𝜏𝑑 = (𝜎_𝑦𝑑− 𝑝,+ 𝑝_𝑢𝑑)𝑚

Upstream horizontal normal stress:

𝜎𝑥𝑢 = (𝑝 − 𝑝𝑢𝑢) − (𝑝 − 𝑝𝑢𝑢− 𝜎𝑦𝑢)𝑛2

Downstream horizontal normal stress:

𝜎_𝑥𝑑 _{= (𝑝},_{− 𝑝}

𝑢𝑑) + (𝜎𝑦𝑑− 𝑝,+ 𝑝𝑢𝑑)𝑚2

Upstream principal stress:

𝜎₁𝑢 _{= (1 + 𝑛}2_)𝜎

𝑦𝑢− 𝑛2(𝑝 − 𝑝𝑢𝑢)

𝜎₂𝑢 = 𝑝 − 𝑝𝑢𝑢

Downstream principal stress:

𝜎₁𝑑 = (1 + 𝑚2)𝜎_𝑦𝑑 _{− 𝑚}2_(𝑝,_{− 𝑝} 𝑢𝑑)

𝜎₂𝑑 = 𝑝,_{− 𝑝} 𝑢𝑑;

Where T- The length of the dam calculated section in the upstream and

downstream directions;

n- Upstream dam slope, n=0.2;

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p, 𝑝, - Water pressure of calculated section on the upstream and downstream

faces (Silt pressure and Seismic dynamic water pressure should be taken into

account);

𝑝_𝑢𝑢_{, 𝑝}

𝑢𝑑- Uplift pressure of calculated section on the upstream and downstream

faces;

∑ 𝑊 – Sum of vertical forces on calculated section (Including self-weight, water

weight, silt weight and calculated uplift pressure). Downward is taken as positive

direction and solid gravity dam calculation is calculated per unit width.

∑ 𝑀 – Sum of moment of all vertical and horizontal forces to the centroid of

calculated section, which is positive if it produces compressive stress on the

upstream.

(2) Stresses of inner points

Partial amplification method is used:

1) Vertical stress; 𝜎_𝑦 = 𝑎 + 𝑏𝑥 a = 𝜎_𝑦𝑑 =∑ 𝑊 𝐴 − ∑ 𝑀𝑇𝑥𝑖 𝐽 b = 𝜎𝑦𝑢− 𝜎𝑦𝑑 = 12 ∑ 𝑀 𝑇2 2) Shear stress τ = 𝑎₁ + 𝑏𝑥 + 𝑐₁𝑥2 𝑎1 = 𝜏𝑑 𝑏₁ = −(6 ∑ 𝑃) 𝑇 + 2𝜏𝑢+ 4𝜏𝑑)/𝑇 𝑐1 = ( 6 ∑ 𝑃 𝑇 + 3𝜏𝑢+ 𝜏𝑑)/𝑇 2

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downstream side（Including presenting silt pressure and seismic dynamic water

pressure）; 𝜏_𝑑𝑑 = 𝑎₁+ 𝑏₁𝑙_𝑑+ 𝑐₁𝑙_𝑑2 𝜏_𝑢𝑢 _{= 𝑎} 1+ 𝑏1𝑙𝑢+ 𝑐1𝑙𝑢2 𝜏𝑚𝑢 = 𝐵𝜏𝑢𝑢/𝑏 𝜏𝑚𝑢𝑑 = 𝐵𝜏𝑑𝑑/𝑏

3) Horizontal normal stress

𝜎_𝑥 = 𝑎₃+ 𝑏₃𝑥 𝑎3 = 𝜎𝑥𝑑 𝑏₃ = (𝜎_𝑥𝑢− 𝜎_𝑥𝑑)/𝑇 𝜎_𝑥𝑑𝑑 = 𝑎₃+ 𝑏₃𝑙_𝑑 𝜎_𝑥𝑢𝑑 _{= 𝑎} 3+ 𝑏3𝑙𝑢 σ_𝑥𝑚𝑢 _{= 𝐵𝜎} 𝑥𝑢𝑢 /𝑏 σ𝑥𝑚𝑑 = 𝐵𝜎𝑥𝑑𝑢 /𝑏 4) Principle stress 𝜎₁ =𝜎𝑥+ 𝜎𝑦 2 + √((𝜎𝑦− 𝜎𝑥)/2)2+ 𝜏2 𝜎2 = 𝜎𝑥+ 𝜎𝑦 2 − √((𝜎𝑦− 𝜎𝑥)/2) 2_{+ 𝜏}2 φ = 0.5 × arctan (− 2τ 𝜎𝑦− 𝜎𝑥 )

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3.4.2.2 Stress Distribution Diagram

(1) 𝜎𝑦, 𝜎𝑥 and 𝜏𝑥𝑦 distribution under normal pool level condition:

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Figure 3.10 𝝈𝒚 Distribution diagram (unit: kPa)

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(2) 𝜎𝑦, 𝜎𝑥 and 𝜏𝑥𝑦 distribution at normal pool level under 7-degree earthquake:

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Figure 3.13 𝝈𝒙Distribution diagram under earthquake (unit: kPa)

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3.2.3 Finite Element Analysis

In this part, the gravity dam section will be analyzed as plane problem (2-D) by

using MATLAB codes. The MATLAB codes are provided by Professor Guiseppe

COCCHETTI.

The gravity dam is divided into a number of 4-nodes isoparametric elements

under plane strain conditions with thickness h=1m, and the base of dam is

constrained in the analysis.

Load combination under the normal pool level conditions:

1) Self-weight;

2) Hydrostatic pressure;

3) Uplift pressure;