Experimental Study on Cracking, Reinforcement, and Overall Stability of the Xiaowan Super-High Arch Dam

ORIGINAL PAPER

Experimental Study on Cracking, Reinforcement, and OverallStability of the Xiaowan Super-High Arch Dam

Peng Lin • Weiyuan Zhou • Hongyuan Liu

Received: 17 November 2013 / Accepted: 11 April 2014

� Springer-Verlag Wien 2014

Abstract The Xiaowan super-high arch dam has faced

challenging construction problems. Here, we provide a

scientifically-based reference for applying geomechanical

model testing to support the nonlinear design of super-high

arch dams. We applied experimental similarity theory and

techniques. Based on four 3D geomechanical model tests,

the dam stress characteristics, deformation distribution, and

the safety factors of the dam foundation were identified and

compared. We also analyzed cracking characteristics of the

up- and downstream dam surfaces and induced joints in the

dam heel, the rock mass failure process of the dam-foun-

dation interface, and the abutments. We propose founda-

tion reinforcement measures for weak rock masses,

alteration zones, and other faults in the abutments based on

the 3D and plane tests each at a different elevation. The

results show that all dam deformations remained normal

with no yielding or tensile cracking under a normal water

load. The reinforced rock mass increased the crack initial

safety in the dam heel and toe by *20 %. The minimum

crack initial safety factor (K1) of the dam heel was 1.4. The

induced joint in the dam heel contributed to a reduction in

tensile stress at the upstream dam heel, improving K1.

Compared with similar projects following reinforcement

measures, the abutment stiffness and overall stability of the

Xiaowan arch dam satisfy operational requirements. Four

years of monitoring operations show that key areas near the

dam remained normal and the dam foundation is func-

tioning well. Our results may also be applicable to the

design and construction of similar projects worldwide.

Keywords Xiaowan super-high arch dam �Geomechanical model � Overall safety factor �Cracking � Reinforcement

1 Introduction

Geomechanical model tests can be used to simulate both

the engineering structural features and the influence of

geological defects, such as weathered rock, bedding joints,

and faults, on overall engineering stability. They are also

an important way of evaluating dam foundation stability in

hydraulic engineering (Fumagalli 1979; Zhou et al. 2008a)

and excavations, slope stability (Zhou et al. 2008c; Zhu

et al. 2011), and mining engineering (Heuer and Hendron,

1971; Li et al. 2005, 2011; Wong et al. 2006; Li and Liu

2013). With the development of high-performance com-

puters, three-dimensional (3D) numerical simulations are

now applied widely to analyze the integrity and stability of

high arch dams (Pan 2004; Lin et al. 2004, 2011) and

underground tunnels (Liu et al. 2009; Barla et al. 2012; Lin

et al. 2013b). Dams, however, are always associated with

complex foundations involving steep slopes, weathered

rock masses, and intersecting joints and faults. Geome-

chanical model experiments are still necessary to analyze

the overall stability and reinforcement measures for super-

high arch dams (Zhou et al. 2008a, b; Lin et al. 2011).

P. Lin (&)

State Key Laboratory of Hydroscience and Engineering,

Tsinghua University, Beijing 100084, China

e-mail: [email protected]

W. Zhou

Department of Hydraulic Engineering, Tsinghua University,

Beijing 100084, China


H. Liu

School of Engineering and ICT, The University of Tasmania,

Hobart, Australia


123

Rock Mech Rock Eng

DOI 10.1007/s00603-014-0593-x

Based on similarity theory, geomechanical model tests can

accurately represent the spatial relationships of geological

structures at dam abutments and engineering structures

when simulating the influence of construction procedures,

and can reveal failure scenarios more directly. It is easier

for engineers to understand the stress characteristics,

deformation trends, and overall stability of the dam foun-

dation. Such physical model simulations, in conjunction

with or complementing numerical models, are effective in

optimizing the design of dams, subsidiary structures and

foundation reinforcement.

Early geomechanical model tests designed to analyze

the failure of arch dams were performed in the 1950s (Li

1958; Jerome 1960). In the 1970s and 1980s, dam model

tests were widely conducted in, for example, the United

States, Germany, Yugoslavia, Sweden, Switzerland, Rus-

sia, Japan, and Italy (Fumagalli 1979; Chow and Yang

1984; Chen et al. 1984). These countries have now passed

their peak period of dam construction and, with the

development of numerical simulations, few geomechanical

tests have been conducted in the past 30 years. In the late

1950s, some R&D institutions in China began research into

geomechanical model testing (Li 1958, 2004; Zhou et al.

2008a). Starting in 1956, the Tsinghua University of Bei-

jing has performed model tests on dam foundations and on

the abutment stability of most of the high dams in China.

The overall stability results and safety coefficients were

compiled into the official design criteria for concrete arch

dams in China (the PSCG of PRC 2007). A series of high

arch dam 3D model tests have also been carried out by a

research group led by Prof. Zhou (Zhou et al. 2008a).

In recent years, a series of super-high arch dams, such as

the Xiaowan (height 294.5 m), Xiluodu (height 285.5 m),

Jinping I (height 305 m), and Laxiwa (height 251 m) dams,

have been constructed in China. Along with an increase in

the height and complexity of arch dams, the geological

foundation at the dam sites has also proved more complex.

Some of these issues (Lin et al. 2011, 2013a) include the

mechanical parameters themselves and the strength models

required to deal with problems of jointed rocks cracking in

the dam heel and toe, reinforcement measures for atypical

faults, weak rock masses and alteration zones, grouting for

the dam-foundation interface, and anchorage force damage

and nonlinear evaluation of the overall stability. To solve

these key problems, advanced testing methods and tech-

niques of scale model experiments have achieved impor-

tant results through 3D experimental tracking studies

(Zhou et al. 2008a, c). For example, Jiang et al. (2002)

carried out overloading tests on the overall stability of the

Goupitan high arch dam (height 232 m) using a 3D geo-

mechanical model. A deep sliding stability assessment of

the monolith of the Three Gorges Dam foundation was

made in 2003 (Liu et al. 2003) using physical model tests.

The stability of the slopes (Zhang et al. 1994) and of the

Xiaowan dam was analyzed using strength reduction based

on rupture model tests (Fei et al. 2010).

The Xiaowan high dam (Fig. 1) is an arch dam on the

Meigong River in Nanjian County, Yunnan Province,

southwest China. The dam is a concrete double curvature

arch with a maximum height of 294.5 m, and a dam crest

length of 905 m. It is the highest arch dam in operation in

the world and the related hydroelectric power station is the

third largest one in China, after the Three Gorges and the

Xiluodu dam projects (Wang et al. 2007; Lin et al. 2012).

The primary purpose of the Xiaowan hydroelectric power

station is to generate 4,200 MW of hydroelectric power.

The complex geo-conditions of the Xiaowan arch dam led

to dam rock mass relaxation and destressing as excavation

unloaded the pre-existing high-ground stresses (Wu et al.

2009; Fei et al. 2010). It is therefore important to study the

reinforcement solutions, stability, and safety of the dam

with the aid of geomechanical model tests. Dam abutment

reinforcement was tested in a systematic fashion in the pre-

feasibility and feasibility studies and during the project

tendering and construction processes.

In this paper, we first explain the basic theory and the

geomechanical model testing simulations, and describe the

preparation of the modeling materials, the model scale, and

the geo-condition abutments, as well as the bed foundation

modeling of five different 3D and plane tests of the

Xiaowan arch dam. Based on the experimental results, we

identify and compare the dam stress characteristics,

deformation distribution, and the overall safety factors of

the dam foundation. The dam cracking, abutment failure

process, reinforcement schedule, and the dam overall sta-

bility are analyzed and studied. It should be noted that the

Xiaowan arch dam has encountered basic problems never

before seen in dam construction processes. The test results

provide a scientific basis for optimizing the design and can

also be used globally as an important reference for the safe

design of dams in general.

2 Test Design of the Xiaowan Arch Dam

2.1 Basic Similarity Theory and Simulation

Technology

2.1.1 Similarity Principles

Geomechanical model testing of high arch dams involves

taking into account some basic theories and methods,

including similarity principles, dimensional measurements

and loadings, and measuring and loading principles. The

principle of similarity in model tests means that the phys-

ical features of the model should be similar to the prototype

P. Lin et al.

123

in that the model material, shape and loadings must follow

certain rules.

For a linear elastic model, similarity is obtained from the

theory of elasticity. Each point inside the model must

follow the equilibrium, compatibility, and geometrical

equations. The points on the model surface should satisfy

the boundary conditions. The physical entities ratio of

prototype (p) to model (m) is called the similarity constant

(C). For a model subjected to damaging forces, the stress

and strain should be the same as in the prototype in the

elastic range and beyond it until the point of failure. In the

post-elastic phase, the residual strains should be the same

as e0p ¼ e0

m, where e0 is the residual strain. In some situa-

tions, the effect of time should also be considered. The

similarity criteria for a linear elastic model and a damage

test model are shown in Table 1.

2.1.2 Dam Safety Factors

The safety evaluation methods for high arch dams consist

mainly of (1) overloading, (2) strength reduction, and (3)

comprehensive tests.

Overloading tests assume that the mechanical founda-

tion rock mass parameters remain constant while the water

pressure is increased until the dam and the foundation fail.

The ratio of failure load to the normal load is called the

overloading safety factor. Overloading tests include the

excess normal water level (rectangular load) and the excess

volume-weight of normal water (triangular load), as illus-

trated in Fig. 2. Kc, the coefficient of excess water density,

is defined as:

Kc ¼DPc þ P0

P0

¼ Dcþ c0

c0

¼ cc0

; ð1Þ

where DPc is the triangular load, p0 is the normal water

load, c is the excess water density, c0 is the original water

density, and Dc is the difference between c and c0.

Fig. 1 Xiaowan arch dam in

operation

Table 1 Model test linear elastic and damage similarity criteria

Test type Similarity

criteria

Similarity criteria of concrete

dam under self-weight

and water pressure

Linear elastic

model

(1) Cr=CXCL ¼ 1 (1) Cc ¼ Cp

(2) Cl ¼ 1 (2) Cr ¼ CcCL

(3) CeCE=Cd ¼ 1 (3) Ce ¼ CcCL=CE

(4) CeCL=Cd ¼ 1 (4) Cd ¼ CcC2L=CE

(5) C �r=Cr ¼ 1

Damage model (1) Cr=CXCL ¼ 1

(2) Cu ¼ 1

(3) Ce ¼ 1

(4) CE=Cr ¼ 1

(5) Cd=CL ¼ 1

(6) Cd =Cr ¼ 1

(7) Cs=CtR ¼ 1

(8) CcR=Ct

R ¼ 1

(9) Cr=CtR ¼ 1

(10) Cf ¼ 1

(11) C0e ¼ 1

(12) Cce ¼ 1

(13) Cte ¼ 1

Experimental Study on Cracking, Reinforcement, and Overall Stability

123

In this study, the volume-weight of normal water

method is employed to analyze the dam cracking and

failure process. Three safety factors are defined to evaluate

the overall stability of the dam and the foundation as

follows:

1. Kc ¼ K1 represents the dam onset of cracking safety

factor; a crack is initiated at K1 p0, generally at the dam

heel.

2. Kc ¼ K2 represents the onset of structural nonlinear

behavior safety factor. At the nonlinear phase, the dam

displacement shows large deformations and nonlinear

behavior. The cracks in the dam propagate quickly and

multiple cracks coalesce.

3. Kc ¼ K3 represents the maximum loading safety factor

of the dam-foundation system. At K3 p0, the dam

foundation fails and the undertaking capacity is lost.

Strength reduction tests involve varying the coefficient

of friction f and the cohesion c of the jointed abutment rock

mass or rock structural plane during testing. Kt is the shear

strength varying coefficient. The dam model fails when the

shear strength is lower than the shear strength coefficient of

the rock mass (Zhou et al. 2008a; Zhang et al. 1994). If

affected by underground water owing to flooding, the rock

mass strength may decrease.

Comprehensive tests combine the above two tests. Both

overloading and strength reduction of the abutment rock

mass during reservoir operation are assumed.

2.1.3 Simulation Technology

Geomechanical model simulation technology experiences

some key problems with combined load testing systems,

model material preparations, measuring instruments, and

test methods. A brief introduction to the topic is given

below.

In general, the loading is simulated by a combination of

water and sediment pressure, and the dam’s gravity. The

water pressure can be simulated with hydraulic jacks or by

a gas bag, which simulates the increase in water density c,

maintaining a triangular distributed load of the appropriate

height (Fig. 2b); the gas bag is kept in contact with the dam

surface during loading. The weight of the dam and its base

gravity are simulated with dead weights.

In the model, small blocks are used to simulate the rock

mass and the concrete dam structure, while the block

binder provides the strength. The small blocks are bonded

using various proportions of polyvinyl alcohol and water to

simulate different friction coefficient f and cohesion c val-

ues for the rock mass and dam concrete. As both the

material and model tests are performed at room tempera-

ture, the effect of temperature change on the strength of the

glue is not considered. Therefore, the selection of the

model materials is very important, where the main factors

include: (1) low cost, environmentally friendly materials,

stability, good workability before solidifying, and ease of

manufacture. (2) After machining the small blocks, to

assure credibility of the results, only very small tempera-

ture and humidity changes are permitted. (3) The chosen

material should have no creep characteristics. (4) The stress

versus strain relationship for the model material should be

identical to that of the prototype structure material both in

the elastic and the post-elastic ranges.

For the simulated reinforcement concrete plugs, the

replacement and cement grouting can be simulated by

changing the modeling material, if the simulated model on

the supporting systems relates to the abutments. The

working loads of the bolts and anchor cables are simulated

to carry scaled values of the real loads and are all manu-

factured to the appropriate scaled dimensions. In this study,

the scale ratio is 1:250. The main types of measurements

include displacement, strain, and cracking behavior. We

used the latest measuring methods that use instrument

miniaturization and automatic remote reading of instru-

ments to ensure high accuracy and reliability.

2.2 Xiaowan Geomechanical Model

2.2.1 Geo-Conditions of the Xiaowan Arch Dam

The Xiaowan arch dam is located on complex rock foun-

dations. The canyon is narrow with high, steep walls. The

foundation geological cross-section of the dam is shown in

Fig. 3. The dam rests on granite and dolomite. The rocks at

the dam site are Triassic granitic gneiss and amphibolite

gneiss, which are massive and dense. Rock masses with

28–35� bedding planes dip towards the river bed. Uniaxial

compression strength testing indicated strengths of

127–172 MPa. Geo-stress testing using discs from the drill

cores situated at a depth of 85 m at the dam site indicated

maximum principal stresses in the horizontal plane varying

from 22 to 35 MPa. This would imply a maximum of

44–57 MPa at the stress concentration zone in the valley

Fig. 2 Illustration of overloading tests

P. Lin et al.

123

floor. Such high stresses are commonly encountered in the

very strong rocks of the tectonically active regions of

southwest China where high mountains and gorges are

present (Wu et al. 2009).

Several large faults (such as F7, F5, F11, F10, and F20),

geological altered rock zones (for example E1, E4, E5, E8,

and E9), and other small faults (f12 and f19) are found in

the river bed (Fig. 4a). These abutment defects have been

strengthened by reinforcement measures, such as replace-

ment with concrete plugs, reinforced bolts, or cement

grouting. The most challenging problems were found in the

river bed when high geo-stresses in the rocks were released

(Lin et al. 2011; Wu et al. 2009). This caused the excavated

river bed elevation to fall by 2.5 m, and the dam height to

increase from 292 m (design value) to 294.5 m. Addi-

tionally, large and deep stress-release zones occurred in the

dam foundations when inbuilt, high geo-stresses were

released by the excavation. Figure 4b shows the excavation

of the abutments in 2005. The excavations are important to

prevent the dam foundations from sliding. Another

important precaution to preventing cracking is the con-

struction of an induced joint in the upstream dam heel.

In this study, four 3D and one plane multi-elevation

geomechanical models were tested to investigate some key

problems. The objectives of the study included: (1)

investigating the influence of the main large faults (F7, F5,

F11, F10, F20), geological altered rock zones (E1, E4, E5,

E8, E9), and other small faults (f12 and f19) in the abut-

ment rock on the overall dam stability; (2) examining the

dam overloading stability capacity with the abutment

reinforcement; (3) deriving the crack growth characteristics

in the dam heel after setting an induced joint, and (4) the

Fig. 3 The foundation geological cross-section of Xiaowan arch dam

Fig. 4 Plane geo-map and snapshot of abutment excavation


123

influence of the excavation and the unloading of the

foundation stability.

2.2.2 Geomechanical Models

The different characteristics of the five models are shown

in Table 2. The first model test took place during the pre-

design study stage in 1995 and was intended to test the

natural foundation. The second test was conducted during

the bidding design study stage in 2000, with modeling of

the reinforced abutments and riverbed. The third test was

conducted during the construction design stage in 2008,

along with studies of the problems caused by the shallow

excavation of the relaxed rocks in the foundation and the

peripheral joints, and their influence on the integrity and

stability of the dam after reinforcement. The fourth test was

conducted during the construction design stage in 2009, to

study the cracking inside the dam caused by thermal stress,

and its influence on the integrity and stability of the dam.

The plane tests, conducted in 2004, were to assist with the

optimization analysis of the scheme to reinforce the fault

zones in both abutments. The geological rock resistance

conditions in the abutments are complex, and depend upon

the rock properties, geological structures, and a weak

structural plane. It was therefore necessary to take techni-

cal measures. The safety of the dam was studied under

natural conditions and after treatment at elevation levels

(ELs) of 1,245, 1,210, and 1,170 m.

Applying the similarity principles, the modeling mate-

rial chosen to represent the dam concrete was plaster. The

first step was to cast an oversized block, which was sub-

sequently machined to the final shape of the dam body. The

foundation model was constructed with thousands of small

spar gypsum blocks (5 9 5 9 10 cm), taking into account

the geological structure of the site. In addition, all the

structural mechanics parameters were simulated according

to the mechanical similarity principle (Table 3). Figure 5

shows the model design including the overall simulation

scale and the measurement instruments distributed on the

down- and upstream surfaces. A box-shaped test frame was

used to manufacture the final geomechanical model by

masonry that was made of plaster (Zhou et al. 2008a). The

displacement sensors and strain gauges were installed in

the downstream dam surface (Fig. 5a) and the overloading

system of jacks was installed in the upstream surface

(Fig. 5b). Fifty-eight hydraulic jacks were arranged in

seven horizontal lines to simulate the different levels of

water pressure (Fig. 5b). The load was first applied on the

bottom levels and then gradually extended to the upper

area. Multiple-stage and single loads were applied in the

elastic state, and then continuous loads followed until the

failure of the dam and abutment. The scale of the 3D model

to the prototype was 1:250.

The 3D model of the simulating prototype was 163 m

high, approximately 0.56H (H represents dam height) in

the upstream direction (Fig. 5c) and 780 m, approximately

2.65H in the downstream direction; 250 m, approximately

0.85H from the bottom of the dam to the bottom of the

foundation; and 550 m, approximately 1.87H in both

abutments. Figure 5d shows the distribution of the dis-

placement sensors and strain gauges on the downstream

surface. A total of 32 displacement sensors were installed

on the downstream surface for monitoring deformation

along and across the river. Additionally, 268 strain gauges

Table 2 Features of the Xiaowan geomechanical model types

Model type Dam geometrical characteristics Foundation simulation conditions

Model A: Year 1995

Original condition of foundation

Height 292 m, crest thickness and bottom of

crown cantilever are 12 and 72.9 m,

respectively

Natural foundation, including faults F7, F11, F5, F19, F23,

F10, F22, F27, F2, f12, f19 and alteration zones E1, E4,

E5, E8 (including f30)

Model B: Year 2000

Foundation reinforced

Same as Model A Based on Model A, reinforcement including concrete faults

replacement F11, F1, and alteration zones. Total 345 pre-

stressed anchorage cables and 940 anchorage cables

around the plunge pool

Model C: Year 2008

Dam with no cracks

Height 294.5 m, thickness in crest and

bottom of crown cantilever are 12 and

73.3 m, respectively.

Based on Model B, geological layers, weathering and

unloading rock layer areas affected by dam interface

excavation. Above EL 975 m, unloading rock layer:

0–7.5 and 7.5–20 m; Below EL 975 m, unloading rock

layer: 0–5, 5–10, 10–15 m. Fillets, peripheral joint, thrust

block, and concrete replacement and plug were installed

Model D: Year 2009

Dam has cracks

As Model C Based on Model C, total of 38 cracks from dam stage 13# to

30# were simulated

Model E: Year 2004

Abutment reinforcement plane

tests

Elevation level 1,170 m Based on Model A, abutment reinforcement transmission

blocks on the right, the long replacement concrete block

was 145 m long and 14 m wide. The short block was

55 m long and 8 m wide

P. Lin et al.

123

were installed on the down- and upstream surfaces for

monitoring the stress distribution under overloading con-

ditions. These monitoring instruments were connected to a

data logger, and a high-precision data acquisition system.

The loading process could be accurately adjusted in

response to feedback from the monitoring and data acqui-

sition system. A digital video monitor system was used to

observe the dam cracking process and foundation failure.

During testing, an auxiliary lighting and power system was

used to check for dam cracking and failure.

3 Dam Cracking Analysis

Based on the results of the four 3D geomechanical model

tests, the cracking characteristics of the up- and down-

stream surfaces of the dam, and the induced joint in the

dam heel, are analyzed below.

3.1 Analysis of the Dam Cracking Process

Figure 6 shows the cracking process and final damage

profile of the up- and downstream surfaces under different

states of overload in the four 3D model tests. Figure 7

shows the final cracking and failure of the up- and down-

stream dam surfaces. Table 4 shows the dam cracking

process analysis based on Fig. 6. Table 5 gives the main

experimental stress, the displacement results, and the

overall safety factors pertaining to the different models.

Based on Figs. 6, 7 and Table 4, the dam cracking

analysis is summarized as follows:

1. Dam heel cracking occurred at 1.2 p0 (the minimum

loading) with the dam toe cracking at 2.5–3 p0. The

interface rock mass was reinforced and this increased

the safety factor for the initial cracking in the dam heel

and toe. The minimum dam heel safety factor for the

initial cracking K1 increased to 1.4.

2. Because the dam has a long arch, its cantilever effect is

stronger than that of the arch above EL 1,100 m. Most

of the cracks propagated along the cantilever direction

and fewer in the direction along the arch, more on the

right and less on the left. As the right-hand abutment

was still weak after reinforcement, the transverse

displacements were large, causing many vertical

tensile cracks and reducing the arching effect. The

right-hand cracks occurred along the cantilever section

across the dam from up- to downstream. Below EL

1,100 m, the shear cracks were perpendicular to the

dam-foundation interface, showing the effectiveness of

the arch.

3. Model D simulated 38 internal cracks caused by

incorrect temperature control during the concrete

pouring stage (Fig. 8). These cracks were observed at

monoliths 13–30 inside the dam at the final stage. Test

results show that the 38 internal cracks of the dam did

not propagate, and the dam remains linearly elastic

under normal water loading (p0). These temperature

cracks had a very small effect on the dam body

(Fig. 6g, h). These internal cracks begin to propagate

internally under a loading of 4.0 p0 and meet cracks in

the crown cantilever, affecting the cracking zone and

lowering the values of K2, K3, and the safety factor

down to 5.0 p0.

Table 3 Mechanical and

geomechanical model test

parameters of Xiaowan arch

dam

Material

property

Young’s modulus E (MPa) f c (MPa) Poisson’s

ratio lPrototype 9 103 Model Prototype Model Prototype Model 9 10-3

Dam concrete 22.4 89.6 1.4 1.4 1.6 6.4 0.22

I 25 100 1.5 1.5 2.2 8.8 0.22

II

II1 22 88 1.5 1.5 2 8 0.26

II2 20 80 1.4 1.4 1.8 7.2 0.27

II3 18 72 1.4 1.4 1.6 6.4

III

IIIa 14 56 1.2 1.2 1.2 4.8 0.28

IIIb1 10 40 1.15 1.15 1.0 4 0.29

IIIb2 6 24 1.1 1.1 0.7 2.8 0.3

IV

IVa 5 20 1.0 1.0 0.6 2.4 0.32

IVb 3 12 0.9 0.9 0.5 2 0.34

IVc 1.3 5.2 0.8 0.8 0.3 1.2 0.35

Va 1.0 4.0 0.5 0.5 0.15 0.6


123

4. The dam cracking zones are similar for Models D and

C, which were characterized by a stiff foundation and

nonconforming deformations between the dam and the

foundation. The internal cracks only propagated

locally within a local confined zone close to the

abutments.

(a) Downstream surface model (b) Upstream surface model

(c) Simulating scale (H represents dam height)

(d) Diagram showing displacement sensors and strain gauges distribution on the downstream surface

250

m,0

.85H

550 m, 1.87H

780m, 2.65H

163m,0.56H

550 m, 1.87H

Right abutment

Left abutment

Dam

Dam

Displacement Sensors

Dam

Jacks

Abutment

Anti-steel frame

Pad

Strain gauge

Displacement Sensorinstalled at crown cantilever

1Y

2Y

3Y

4Y

5Y

Fig. 5 3D geomechanical

model design of the Xiaowan

arch dam

P. Lin et al.

123

3.2 Cracking Analysis of the Induced Joint in Dam

Heel

Another key problem of the Xiaowan arch dam is that an

induced joint was set in the dam heel when large tensile

stresses occurred in the zone between EL 957.5 and

999.5 m (Fig. 9). Linear elastic numerical calculations

(Wang et al. 1998, 2007) showed that the dam heel would

have a higher tensile stress of about 5–7 MPa in the local

stress concentration zone under normal water loading, if no

joint had been created in the dam heel with the possibility

of generating dam heel cracking. The high tensile stress

value is only used as a reference for the dam design,

because the linear elastic numerical simulation in general

does not take into account rock joints at the dam heel,

where local stress concentration can easily form. The

results of two geomechanical model tests (Models A and

B) show that the cracking load at the Xiaowan dam heel is

not high (Table 5), approximately 1.6–1.8 MPa. The

physical Models A and B include the natural joints at the

dam heel, but not the peripheral (induced) joint. The

obtained tensile stress can affect the stability of the dam

heel according to the train gauge monitoring analysis. To

ensure the safety of the Xiaowan arch dam, an engineering

solution is needed to decrease the dam heel tensile stress

and improve the upstream stress distribution.

In dam projects worldwide, in addition to optimizing the

arch dam body to improve the stress state, peripheral joints

are built, generally in the dam heel or bottom seam, to

decrease the dam heel tensile stress. Examples of con-

structing the bottom and edge seam include the 86-m-high

Toules arch dam in Switzerland and the Hongrin arch dam

Fig. 6 Cracking process under different overload states for upstream and downstream dam surfaces (the number represents Kc, excess normal

water load times)


123

(125 m high), which is a double hyperbolic arch dam.

Dams with a bottom seam include the Verwoerd, LeRoux,

and Katze dams in South Africa and the Deji arch dam

(181 m high) in Taiwan. Other examples of peripheral

joints to improve the tensile stress distribution include the

272-m-high Inguri arch dam in Georgia (Ashikhmen and

Pronina 1995), and the 262-m-high Vajont arch dam in

Italy, among others. These arch dams have worked well so

far, with no cracking at the dam heel. The Toules arch dam

was the first to have a bottom seam installed and has been

working safely for 40 years (Hagin 2012). Although con-

structing an induced joint in a dam heel can improve the

tensile stress distribution state, it is bound to weaken the

overall stiffness of the arch dam, decreasing its capacity for

overloading. In addition, with different elevations of the

induced joints, seam depths, and the working behavior of

the contact surfaces between the pouring blocks, the stress

distributions and overload capacities will also be different.

In Model D, the induced (peripheral) joint in the bottom

of the crown cantilever was placed at a height of EL

957.5–999.5 m. Strain gauges were installed to monitor the

stress and strain changes at the induced fracture during the

failure tests (Fig. 9). Based on the experimental results, the

induced joint contributed effectively to reducing the tensile

stress in the upstream dam heel, thus improving the dam

safety factor K1 with respect to cracking. The internal joint

(a) Upstream surface (Model A) (b) Downstream surface(Model A)

(c) Upstream surface (Model B) (d) Downstream surface (Model B)

(e) Upstream surface (Model C) (f) Downstream surface (Model C)

(g) Upstream surface (Model D) (h) Downstream surface (Model D)

Dam crack

Foundation crack

Dam crack

Foundation crack

Foundation crack

Dam crack Dam crack

Foundation crack

Dam crack

Foundation crack

Dam crack

Foundation crack

Dam crack

Foundation crack

Dam crack

Anchor cable andbolt treatment




Fig. 7 Final failure image of

upstream and downstream dam

surfaces

P. Lin et al.

123

endpoints were installed inside the drainage gallery, pre-

venting the cracks from extending through the dam anti-

seepage curtain.

The effect and working condition can be seen from the

following test results:

1. The monitoring results at the internal measuring point

2 (Fig. 10) at a height of 957.5 m showed some tensile

stress around the induced joint. Positive strain indi-

cates tensile stress. Under an overload of 1.5 p0, the

induced joint opened (internal point 2, Fig. 10).

2. Under an overload of 3–5 p0, however, the induced

joint compressed up to a 6 p0 load, still in compres-

sional shear (Fig. 10). The fracture at a height of

998 m (internal monitoring point 1, Fig. 10) was in a

state of compression at all times.

3. The final cracking images at the dam heel and around

the induced joint are shown in Fig. 11. The drainage

gallery prevented cracks extending through the dam

anti-seepage curtain. The final cracking occurred at the

dam-foundation interface (Fig. 11b).

Table 4 Dam cracking process comparisons using four 3D test models

Model

type

Upstream surface cracking Downstream surface cracking

A The dam heel cracking occurred at 1.2 p0. Cracking occurred at

EL 1,020 m in left interface (see Fig. 6a). Under 2–3.5 p0, the

horizontal cracks propagated from abutment to arch crest, some

cracks propagated along the interface in both abutments. Some

vertical crack growth appeared along the beam direction

Cracks initiated at EL 1,020 m at both abutments under 2.5–3 p0

load. The main cracks propagated along the beam direction with

fewer along the arch, more on the right and less on the left.

Under a 2 p0 load, the horizontal cracks propagate from the

abutment to the arch crest at a 3.5 p0 load (see Fig. 6b). The

right cracks occurred along the beam section across the dam

from upstream to downstream. Overload increased, and

coalesced with horizontal cracks at the limitation load of 6.5 p0

B Upstream dam crack initiated from 1.25 p0 to 2.5 p0 (see

Fig. 6c).The tensile stress scale downstream of the dam was

large. The overall safety can meet the requirements of common

computation and safety factors, K3 was 6.5–7.0. As the right

abutment was still weak after reinforcement, the transverse

displacements were large, causing many vertical tensile cracks,

lowering the arch effect

Under a 2.5–3 p0 load, the downstream surface begins to crack in

the dam toe. Vertical cracks were found in the crown cantilever.

Some cracks along the dam interface propagate from the dam

bottom to the upper part. Under a 3–3.5 p0 load, a vertical crack

occurred in the upper direction (Fig. 6d). This crack paralleled

the first crack, initiated at the crest. At this loading step, the dam

had nonlinear mechanical deformations and many cracks

propagated and coalesced in the vertical direction of the

downstream right-hand surface (see Fig. 6d). Under limitation

loading of 6–6.5 p0, the expansion of cracks accelerated radially.

Dam structures deformed rapidly and approached the limitation

C Under normal water loading, fictitious cracks upstream are

compressed, here no cracking appeared in the dam and

abutment. Under a 1.4 p0 load, the dam heel and foundation

upstream began to rupture and the cracking depth was about

4.5 m under 1.9 p0 load (see Fig. 6e). Under a 4–5 p0 load, more

cracking, perpendicular to foundation interface occurred. It

propagated towards the foundation between EL 1,100 m and EL

1,170 m at the left abutment. Under a limitation load, 5 p0 to 7

p0, crack propagation accelerated and coalesced through

downstream cracks

Under a 3 p0 load, the dam downstream surface begins to crack

(see Fig. 6f). Under a 3.5–4 p0 load, the dam had nonlinear

deformations and cracks. A vertical tensile crack in the interface

continuously propagated at EL 1,050 m. Cracks from 1,070 m

turned at 1,130 m and formed horizontal cracks. Under a 4–5 p0

load, horizontal tensile cracks appeared and propagated along

EL 1,130 m. Around EL 1,090 m of the right abutment, new

tensile cracks initiated perpendicular to the foundation interface.

At EL 1,100-1,170 m of the left abutment, more cracks occurred

perpendicular to the foundation interface and propagated

towards the foundation. The lateral tensile crack appeared at

1,150 m elevation in the horizontal direction. Cracks also

occurred in some dam toe blocks. Under a 5–7 p0 load, cracks

coalesced horizontally. The overall dam structure deformed

rapidly

D The dam does not crack and stays elastically linear under normal

loads. Crack initiation begins at a loading of 1.4 p0, crack

growth with excess water loading occurs from 1.7 p0 to 3.0 p0

(see Fig. 6g). Under limitation loads of 5.5–6.0 p0, crack

propagation accelerates and coalesces through downstream

cracks

After a 3.5 p0 load, the dam started cracking. These cracks

propagated internally under a 4 p0 load, meeting cracks in the

crown cantilever (see Fig. 6h). Under a 4.0–5.0 p0 load,

cracking occurred. Downstream of the abutment surfaces, cracks

grew from surface cracks and propagated internally, and were

not coalesced with any dam internal cracks. Opened cross-

sections showed no internal crack propagation. As with the first

model of the dam, a limitation cracking state is likely. Similar

cracking zones occurred in the middle and along the edges of the

model


123

4 Reinforcement Foundation Analysis

4.1 Analysis of the Abutment Failure Process

Figure 12 shows the rock mass failure process at the dam-

foundation interface and abutments observed in the four 3D

model tests. The main analysis results are as follows:

1. Because of the foundation reinforcement, the founda-

tion deformations of Model B are clearly smaller than

those of Model A. Fault F11 was located in the right

abutment, with much higher strength because of the

change of body shape and concrete backfill. However,

the overall dam foundation safety factors are not

affected as a result of the altered zone. Since the dam

axis rotates 3� to the right abutment, fault F11 on the

right crosses over the dam at a height of 1,200 m and

the rock in the abutment becomes thicker. However,

the left abutment becomes closer to F11 and because of

the additional influence of the left-hand alteration zone

E8 (including f30) and the #4 ridge, the left abutment

rock mass ruptured earlier and more strongly than the

right abutment. The sides became ruptured surfaces

along the river bank and quickly slid downstream. A

particularly broken zone formed between fault F11 on

the left and the dam heel (Fig. 12b), which began to

crack at 2.5–3.0 times the normal water load. The dam

heel deformed noticeably under loads of between 3 p0

and 3.5 p0. Affected by alteration zone E8 (including

f30), the tangential deformation of the foundation was

caused mainly by the large tangential displacement of

the left abutment, in particular at the top.

2. Model C results show that deformations in both

abutments meet the regulatory requirements. Under

3.0 p0 loading, cracks appear on the downstream

surface at EL 1,160 m on the left and at EL 1,150 m

on the right (Fig. 12c). Under 4.0 p0 loading, cracks in

the foundation began to propagate and extend along

the left side of the abutment. Under 5 p0 loading, the

rock mass near the interface between the dam and the

foundation clearly moved and sheared at the height of

EL 1,160 m. Under 6 p0 loading, even though the

downstream foundation was reinforced by anchors, the

downstream foundation surfaces were heavily sheared,

especially in the river bed foundation. The anchorage

zone on both abutments collapsed at 6.5 p0. The left

side deformed linearly before 3 p0 and non-linearly

after 4 p0. In the right abutment, linear deformation

occurred up to 2 p0 with nonlinear deformation after

3 p0.

3. Model D, tested in 2009 to simulate the internal cracks

produced during the concrete pouring period, showed

that the abutments began cracking downstream under

3 p0 and 3.5 p0 loads. These cracks expanded from

outside to inside, and were not caused by internal

cracks (Fig. 12d). In the dam section, no internal

cracks propagated. Comparing these tests, the crack

distributions are similar. Internal cracks begin to grow

between 4.0 p0 and 6.0 p0 loads. The growing internal

cracks meet the external ones, resulting in a 20 %

lower maximum load with respect to dams with no

temperature cracks. After 4.0 p0 loading, the internal

cracks begin to influence crack propagation, with

coalescence occurring in the arch crown zone. Con-

sidering the anchor and consolidation grouting to be

effective, the abutments have a much higher stiffness

and fewer cracks in the abutment (Fig. 12d).

4.2 Reinforcement Analysis with Plane Tests

In Sect. 4.1, the reinforcement effects were evaluated based

on the four 3D tests. A series of demonstration plane model

tests was also carried out before the installation of the

proposed abutment reinforcement measures. The main

purpose of these plane experiments was to study the

abutment foundation performance and failure modes at EL

1,170 m and EL 1,245 m, and to identify the relationship

between the replacement blocks and the reinforcement,

which works to increase the main weak structural plane as

the load changes. In this study, only the foundation rein-

forcement requirement and the influence on the overall

safety are discussed by comparing the results of the rein-

forced design and the original plane test at EL 1,170 m.

For the EL 1,170 m plane model tests the actual simu-

lations are as follows. The model scale is fixed at 1:500.

The model simulates a prototype of 175 m length,

approximately 0.6H in the upstream direction, and 725 m,

approximately 2.5H, in the downstream direction. Both

abutments are 830 m in total width (right abutment 430 m

and left abutment 400 m). The model scale was chosen to

ensure that the main faults and altered zones were simu-

lated (Table 2). The model bottom was kept smooth using

wax and two sides were constrained by a steel frame. The

two plane test results are shown in Fig. 13 for the natural

and reinforced foundations.

Figure 13a shows the final cracking and failure results

of the natural foundation at EL 1,170 m. The left abutment

joints and cracks became dislocations under 2–3 p0 load-

ing, eventually leading to a large sliding mass with E8,

F11, f19, and F20 (Fig. 13a). The two abutment founda-

tions were damaged by both cracking and sliding. The

damage zones are approximately 50–60 m from the dam-

foundation interface. The right abutment failure developed

along fault F11 and the alteration zone E1 at less than

1.8 p0 loading, and propagated, forming a composite

P. Lin et al.

123

sliding mass at fault f11 under 2 p0 loading. The right

sliding zone included E1, F11, E4, E5, and f11, and most of

the cracking occurred around the boundary of E4 and E5.

Therefore, improving the stiffness of the zones where the

cracking and sliding occurred is essential for the Xiaowan

dam. Apart from reinforcing, replacement with a concrete

pedestal should also be considered.

Figure 13b shows cracking and failure of the reinforced

foundation at EL 1,170 m. Under 2.4 p0 loading, both

upstream abutments showed transverse cracks, which

Table 5 Comparison of stresses, displacements and safety factors using four 3D test models

Model

type

Max.

longitudinal

Disp. (mm)

Max.

transverse

Disp.

(mm)

Displacement

distribution

characteristics

Tensile

stress at

dam

heel/

MPa

Max.

compressive

stress in

downstream

surface/MPa

Stress distribution

characteristics

K1 K2 K3

A 205 24 Greater on left arch

than on right arch

1.8 13.4 High stress

concentration at local

zone

1.2 3.0 5.0

B 192 19 Greater on the left

arch. A similar

deformity is found

on both abutments

1.6 12.8 Stress on the

downstream surface

changes steeply,

giving a weak

foundation and arch

effect.

1.3–2.5 3.0 6.5–7.0

C 179 20 Displacement in the

lower part of dam is

greater on the left

arch. Reinforcement

of the left abutment

strengthens the

stiffness

0.95 12 Tensile stress at the dam

heel decreases due to

the peripheral joint

1.4–2.0 2.9–3.5 6.5

D 181 18 Dam deformation is

symmetric. Under

overloading

conditions, dam

crack deformation

increases due to the

decrease of stiffness

1.12 12.5 Compressive stress on

the downstream

surface concentrates

on the two sides.

Upstream surface

tensile stress

distribution has a more

average

1.4–1.7 2.7–3.0 5.5–6.0

Table 6 3D geomechanical model tests of safety factors for different typical high arch dams

Dam Operation

date

Dam height

(m)

Arc length

(m)

Bottom

thickness

(m)

Ratio of

thickness

to height

Ratio of

arc

to height

K1 K2 K3

Ertan 2000 240 775 55.7 0.23 3.16 2 4 11–12

Jinping I (natural foundation) 2014 305 698.1 72 0.24 2.29 1.5–2 3–4 5–6

Jinping I (foundation

reinforcement)

305 552.2 63 0.21 1.81 2.5 4–5 7.5

Xiaowan (Model A) 2010 292 937.3 72.9 0.25 3.21 1.2 3 5

Xiaowan (Model B) 292 937.3 72.9 0.25 3.21 1.3–2.5 3 6.5–7

Xiaowan (Model C) 294.5 892.8 72.9 0.25 3.03 1.4–2 2.9–3.5 6.5

Xiaowan (Model D) 294.5 892.8 72.9 0.25 3.03 1.4–1.7 2.7–3.0 5.5–6

Goupitan 2011 232.5 552.6 50.3 0.22 2.38 2.4 4.4 8.6

Laxiwa 2011 250 545 49 0.20 2.18 2.18 3.5–4 7–8

Xiluodu (824 dam body) 2014 278 710 69 0.25 2.55 1.8 5 6.5–8

Xiluodu (03 dam body) 278 650 62 0.22 2.34 1.8–2 4.5 7–8.5

Xiluodu (03 dam body) 285.5 681.5 60 0.22 2.45 2 4.5 8.5

Dagangshan 2015 210 622.4 52 0.25 2.97 2 4.5 9.5


123

eventually formed a tensile area upstream of the arch-side.

A compression and shear zone occurred in the right

abutment near the foundation surface under 3–5 p0 load-

ing. The main fracture on the edge of E4 (close to the

river) formed a partial sliding zone under 5 p0 loading.

The shear sliding zone in the right abutment was limited

to a range of 60 m near the arch-side, which is a key

reinforced area. The analysis also showed that the force

transfer was effective in both abutments within 50 m. A

tensile cracking zone formed in the left abutment along

the joints and E8.

In summary, the experiment illustrates that the length of

the transmission blocks should be kept at approximately

50 m. The shear fracture zone in the right abutment is the

key area governing the behavior of the alteration zone and

abutments. To overcome the influence of the faults on the

stability of the Xiaowan arch, we recommend that a foot

pad and anchors are combined downstream of the arch-side

near the river to accurately determine the safe range of E1,

E4, E5, and E8. Replacing the altered zones, faults, and

anchors in the IIIb and IVb reinforcement zones can

improve the stability of the abutment. These recommen-

dations were adopted by the designer and are reflected in

Models C and D. Figure 14a, b show a classic anchor cable

and bolt treatment section of the abutment downstream. A

current image of the reinforced left abutment can be seen in

Fig. 1.

Fig. 8 Distribution of internal

temperature cracks in the

Xiaowan arch dam

Vertical cross-section of dam heel

A-A cross-section

Internal strain gauges 3 Internal strain gauges 1

Internal strain gauges 2

Internal strain gauges 2 isinstalled at induced joints arch

crown 957.5

(a)

(b)

Fig. 9 Set of induced joint in

the upstream dam surface and

internal strain gauges for

monitoring cracking around the

induced joint

0

1

2

3

4

5

6

7

-600 -400 -200 0 200 400Tim

es o

f o

ver

no

rmal

wat

er lo

ad(p

0)

Strain

internal monitoring point 1

internal monitoring point 2

Fig. 10 Relationship between strain and the excess normal water

load time for upstream induced joint (monitoring point shown in

Fig. 9)

P. Lin et al.

123

5 Analysis of the Overall Stability of the Xiaowan Arch

Dam

5.1 Results of the 3D Model Test

Based on the four 3D rupture model test results, compar-

ative analyses were done on the displacement, stress dis-

tribution characteristics and overall stability of the dam.

Table 5 shows the main experimental stress, displacement

results and overall safety factors. Considering that the

Xiaowan arch dam has been operating for approximately

four years, Models C and D are compared. Figure 15

shows the up- and downstream dam surface stress distri-

bution characteristics under a normal water load. Similarly,

Fig. 16 shows the relationship between the crown cantile-

ver displacement along the river and overloading factor Kc

for the downstream surface. Displacement sensors 1Y, 2Y,

3Y, 4Y, and 5Y were installed at EL 1,240 m, EL 1,170 m,

EL 1,090 m, EL 1,010 m, and EL 960 m, respectively

(Fig. 5d).

Based on the test results (Table 5), the largest dam dis-

placements along the river are between 179 and 205 mm

under normal water loading. The deformations and stiffness

for both the abutments are symmetrically distributed, given

the overall foundation reinforcement. Figure 16 shows that

the displacement of the crown cantilever above EL 1,170 m

is much larger than that at the lower position (Fig. 16a, b).

In Model C, when the overloading factor Kc is greater than

2.9, the cantilever displacement is greater than 600 mm and

the dam structure shows a nonlinear response. Model D

shows nonlinear states at Kc = K2 [ 2.7. When Kc is

greater than 5.5, the displacement along the river on the

cantilever increases sharply, and the dam fails at 6.5 p0 in

Model C and 6.0 p0 in Model D.

Under normal water loading, the stress distribution on

both the up- and downstream surfaces exhibits the expected

behavior of a double curvature arch dam. The highest

compressive stresses are between 10 and 13 MPa on the

downstream surface and 1.0 and 1.9 MPa tensile stresses

were observed on the upstream surface. The test results

show that the tensile stress on the upstream surface is a

little higher than that on the downstream surface. After

foundation reinforcement optimization, the tensile stress at

the dam heel decreased by approximately 48 and 38 % in

Models C and D, respectively (Table 5; Fig. 15).

Based on the experimental results, the factor of safety

against the onset of dam cracking is not high. The lowest

K1 is under 1.5, the safety factor against the onset of

nonlinear behavior, K2, is approximately 3.0 and the factor

of safety for the maximum load, K3, is no more than 7.0.

For Model B, which allows for different reinforcement

measures and geological conditions, such as weathering

and altered zones in both abutments, the strength of the

rock foundation is weak. The tensile stress in the dam heel

upstream is large and the tensile stress parallel to the

downstream bank is also high, particularly in the tensile

zone below EL 1,050 m on the left abutment. The safety

factor for crack onset has a lower value of 1.25–2.5 for the

upstream surface and 2.5–3.0 for the downstream surface.

After reinforcement, the dam longitudinal displacement is

shown to be smaller. Although the stability requirements of

dam abutments under a normal water load are satisfied, the

final overloading safety factor is the same as for the rein-

forced test of Model A, K3 = 6.5–7.

Model C contains geological features, including faults

f19, f17, f12, and f34 on the left bank, ruptured rocks

caused by released stresses owing to high ground removal,

and no reinforcement of f19 in the left abutment below EL

1,160 m. Therefore, the cracks in the left abutment and the

downstream foundation are more prevalent than those that

appear in Model B. The shallow unloaded part of the

foundation somehow affects the dam deformation. Cracks

propagate along the river, starting from upstream tension

cracks and turning into compression shear cracks, and

some cracks coalesce. The safety factor, however, becomes

acceptable after the reinforcement measures. An anchorage

block at the downstream toe of the dam keeps the rock

mass intact and the anchoring proves effective. The

installation of measures to induce controlled fracturing

helps improve K1, which contributes to restricting the size

of the upstream tensile area. The overall stability safety

parameters, therefore, are K2 [ 2.9 p0 and K3 [ 6.5 p0.

Cracking in the dam heel

(b)

(a)

Cracking around the induced joint adjacent to the inspection tunnel

Inspector tunnel of induced joint

Induced joint

Cracking along dam and foundation interface

Induced joint

Fig. 11 Cracking in the dam heel and induced joint


123

Fig. 12 Failure of abutments

for four 3D model tests (red line

indicates cracking) (color figure

online)

P. Lin et al.

123

Mel D simulated the 38 internal temperature flaws

existing within the Xiaowan dam. We analyzed the

influence of the internal cracking on dam stability, in

particular the induced joint and elastic deformations of

the dam under conditions of overloading. The results

show that under normal water loading, the internal

cracks have only a small effect on the stress distribution.

In general, shear compression cracks are formed. Fol-

lowing a load of 3.0 p0, cracking occurs in the local

zones of the dam. Overall, cracks then spread and

eventually coalesce at the cantilevered crown at loading

of up to 5 p0, thus lowering K2, K3, and the overall

safety factor. As a result, K1 = 1.4–1.7, K2 = 2.7–3.0,

and K3 = 5.5–6.0.

In summary, after a series of reinforcement measures,

including foundation reinforcement, installation of an

induced joint, construction of a fillet at the dam toe and

high-strength anchoring and grouting, the integrity and

stability of the Xiaowan arch dam can satisfy the opera-

tional requirements (the PSCG of PRC 2007).

Fig. 13 Cracking and failure of

the natural and reinforcement

foundation at EL 1,170 m

(F large faults, f small fault,

E altered rock zones)


123

5.2 Comparison with Other Super-High Arch Dams

In recent years, geomechanical model tests have been

widely used for the analysis of structural failure and

abutment stability of high dams, with many advances in

this field (Zhou et al. 2008a; Lin et al. 2011; Jiang et al.

2002; Zhang et al. 1994). So far, no specific rules or criteria

have emerged for the evaluation of the results of design

specification tests. How to interpret and evaluate model

dam test results is still an engineering question of concern.

The Department of Hydraulic Engineering at Tsinghua

University has summarized the overload safety coefficients

that apply to many super-high arch dams in China (Zhou

et al. 2008; Lin et al. 2011). These have been adopted in the

various engineering specification documents. The safety

coefficients include K1 (onset of cracking safety factor), K2

(onset of structural nonlinear behavior safety factor), and

K3 (dam-foundation maximum loading safety factor), as

shown in Table 6. These values are often compared with

numerical simulation results when checking proposed

designs. Based on Table 6 and comparing the results with

those of similar projects, the overall stability of the Xiao-

wan arch dam satisfies the operational requirements (the

PSCG of PRC 2007).

5.3 Comparison with Numerical Simulation and Site

Monitoring Results

Some numerical simulation studies have also been carried

out. In this paper, we present a simple comparative analysis

with the numerical and experimental results of Model D.

Figure 17 shows the main numerical results, including

the dam displacements along the river, the maximum dam

stress, and the dam safety factors under normal water

loading. Note that the deformations and stiffness for both

the abutments, following the reinforcement measures, are

Horizontal cross section(EL 1028m)

Vertical cross section (0+125.00)

(a)

(b)

Fig. 14 A classic anchor cable

and bolt treatment section of

downstream abutment

P. Lin et al.

123

Upstream surface (Model C)

Downstream surface (Model C)

Upstream surface (Model D)

Downstream surface (Model D)

Left right

Right Left

1245

1210

1170

1130

1190

1050

1010

975

960

950.5

-5.4-30

-13.2-46.3

-15.1-33.2

-10.2-25.1

-4.2-22

-5.4-30

-3.4-12

-5.4-30

-5.4-30

-5.4-30

-5.4-30

-5.4-30

-2-10.6

-2-10.6

-3.6-13.2

-3.6-13.2 -5.3

-15.1

-5.3

-15.1

-5.1

-16.6

-5.1

-16.6

-4.2

-14.4

-4.2

-14.4

-2

-93.9 -4

4.0

5.1

8.0-5.6

-5

9.5

-3

10.2

-4

7.2

-3

4.7

1.2-10

-2.8 -41.8

-3.6 -48.2

-4.5 -36.6

-2.8 -41.8

-7.2-57.2

-7.8 -40.5-35.6

-6.8 -47.4

-4.0 -54.2 -5.0-44.8

-3.3

-30.8-6.8

-45.8

-12.8

-78.4

-6.0

-88.8

-5.0

-95.2 4.4

-83.6

2.5

-95

2

-112.2

6.2

-120.8

4

-108.5

2.0

-104

2.0

-104

6.3

-74.2

3.0

-1.0

-87.8

-82.8

-2.2

-50.5

1245

1210

1170

1130

1190

1050

1010

975

960

950.5

Right Left

Left right

(a)

(b)

(c)

(d)

Fig. 15 Stress distribution

characteristics of Model C and

Model D (unit: kg/cm2)


123

symmetrically distributed, with reasonably good agreement

between the numerical and physical results (Table 5).

Figure 17a shows that the greatest crown cantilever

displacement is approximately 194.17 mm at EL 1,245 m

and the maximum transverse displacement is 21.5 mm at

EL 1,010 m on the left side of the dam. Under normal

water loading, The dam heel principal tensile stress is

approximately 0.9 MPa and the compression stress at EL

1,030 m of downstream surface is approximately 10.3 Pa

(Fig. 17b, c). With the increase in water loading to 3.5 p0,

the tensile stress gradually increases to more than 1.5 MPa.

The dam point safety factors are between 1.2 and 2.0

(Fig. 17d).

To date, the dam (Model D) has been operating for four

years. Field monitoring results show little change in the

horizontal displacement of the foundation. On September

7, 2013, the reservoir water level was at 1,228.96 m. The

maximum cumulative radial displacement (along the river)

is 94.75 mm (EL 1,174 m) and the maximum cumulative

tangential displacement (across the river) is 12.57 mm (EL

1,190 m). When the water level increased, the pressure at

the induced joints became high, reducing the compression

stress, and some surface sliding occurred. The monitoring

of the dam cracking showed that the internal cracks

remained largely stable. Both abutments have remained

stable, and there have been no abnormal deformations and

seepage pressures during the operational period of the dam.

The monitoring results of the dam displacement, stress, and

seepage indicated no anomalies at the key areas near the

dam, and showed that overall the dam is working properly

and in accordance with the designers’ expectations.

The difference in the maximum cumulative radial dis-

placement between the field monitoring and numerical and

experimental results is approximately 50 %. The main

reason for this relates to the assumed values of the geo-

mechanical parameters. In general, the design parameters

used in China for rock mass and concrete are conservative

compared with the actual parameters (Luo et al. 2014). The

feedback analysis shows that the actual parameter values

are higher by nearly 40–50 % compared with the design

values. Furthermore, after impounding, the dam reservoir

basin can withstand the weight of the water, the dam heel

vertical deformation, and the effect of the dam hung

upside-down increases. In numerical and physical analysis

their role is often ignored.

6 Conclusions

The Xiaowan arch dam has faced challenging construction

problems. In this paper, we studied the test results of four

3D geomechanical models and a series of plane models.

The displacements, distribution of stresses, overall safety

factors, cracking, and the failure processes of the dam

foundations were analyzed. The main conclusions are as

follows.

1. This work provides a scientifically-based reference for

geomechanical model testing that can serve as a

guideline for nonlinear design of super-high arch

dams. The key problems that affect the construction

processes and the safety factors of the Xiaowan arch

dam have been analyzed. The model studied cracking,

its spread and distribution, and the effects of various

types of abutment reinforcement measures and foun-

dation design alternatives.

2. Based on the results of four 3D model tests, under

normal loading conditions all deformations were

normal without any yielding or tensile cracking. The

first cracking occurred at the heel of the dam at 1.2

times the normal water load. Cracking at the dam toe

occurred downstream at 2.5–3 times the normal water

load. When the rock mass was reinforced, the dam heel

safety factor K1 increased to 1.4. The crack propaga-

tion safety factor of the dam was 2.5–3.0 p0 for the up-

and downstream surfaces, respectively. Nonlinear

deformation of the dam also occurred at 2.5–3.0 p0

/ mmδ(a) Model C

(b) Model D

0

1

2

3

4

5

6

7

0

1

2

3

4

5

6

7

0 500 1000 1500 2000 2500 3000

0 500 1000 1500 2000 2500 3000

1Y EL.1240m

2Y EL.1170m

3Y EL.1090m

4Y EL.1010m

5Y EL.960m

1Y EL.1240m

2Y EL.1170m

3Y EL.1090m

4Y EL.1010m

5Y EL.960m

Kγ

Kγ

/ mmδ

Fig. 16 Relationship between the crown cantilever displacement

along the river and the overloading factor Kc

P. Lin et al.

123

Fig. 17 The main results of

numerical simulation on Model

D under normal water loading

Table 1. Model test linear

elastic and damage similarity

criteria


123

load p0. Therefore, the safety factor against the onset

of structural nonlinear behavior, K2, is approximately

2.5–3.0. After reinforcement, the dam longitudinal

displacement became smaller. Although the stability

requirement of the dam abutments under a normal

water load was satisfied, the final overloading safety

factor was the same as for the reinforced test of Model

A, K3 = 6.5–7.

3. An artificially-induced (peripheral) joint at the bottom

of the crown cantilever contributed to a reduction of

the tensile stress in the upstream dam heel, thus

improving the margin of safety against cracking, K1.

The fracture ends were designed to occur inside the

drainage gallery to prevent the cracks extending

through the curtain.

4. The series of 3D and plane model tests on abutment

failure were very important in allowing recommenda-

tions to be made concerning the detailed and complex

reinforcement measures needed at faults in various

weak and localized zones (E1, E4, E5, and E8), and for

IIIb and IVb type rock mass. Comparing the perfor-

mance of similar high-arch dams in China, after taking

reinforcement measures (including foundation rein-

forcement, setting an induced joint in the dam heel and

a fillet at the toe, and providing high-strength anchor-

ing and grouting for the abutments), it is evident that

complex reinforcement measures are effective in

increasing the abutment stiffness and the overall

stability of the Xiaowan arch dam. The overall stability

of the dam can satisfy the operational margin of the

safety requirements. The field monitoring results over

the four years of operation show nothing abnormal in

the key areas near the dam, indicating that the dam is

working properly.

Acknowledgments This research work was supported by National

Natural Science Foundation of China (No. 11272178), the National

Basic Research Program of China (973 Program) Grant No.

2011CB013503, and the Tsinghua University Initiative Scientific

Research Program. The authors are very grateful to Prof. Yang RQ and

Shen DL, and the Kunming Hydroelectric Investigation and Design

Institute, China Hydropower Engineering Consulting Group Co. for

support this study. The authors are also very grateful to Prof .Giovanni

Barla, Anson Elaine and two reviewers for their critical recommen-

dations which helped the author to improve this paper significantly.

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Documents

Experimental Study on Cracking, Reinforcement, and Overall Stability of the Xiaowan Super-High Arch Dam