Journal of Rock Mechanics and Geotechnical Engineering. 2011, 3 (2): 186–192

Stress-strain analysis of Aikou rockfill dam with asphalt-concrete core Chaoyang Fang, Zhenzhen Liu State Key Laboratory of Water Resources and Hydropower Engineering Sciences, Wuhan University, Wuhan, 430072, China

Received 13 December 2010; received in revised form 4 March 2011; accepted 24 March 2011

Abstract: Aikou rockfill dam with asphalt-concrete core is situated in a karst area in Chongqing City, China. In order to study

the operative conditions of the rockfill dam, especially those of the asphalt-concrete core, the Duncan model is adopted to

compute the stress and strain of both the rockfill dam and the asphalt-concrete core after karst grouting and other treatments.

The results indicate that the complicated stress and deformation of both the dam body and the core are within reasonable

ranges. It is shown that structure design and foundation treatment of the dam are feasible and can be used as a reference for

other similar projects. Key words: asphalt-concrete core; rockfill dam; Aikou reservoir; stress and deformation

1 Introduction

Aikou rockfill dam with asphalt-concrete core is located on the Pingjiang River, about 1.7 km away from Aikou Town in Xiushan County, Chongqing City, and about 0.6 km downstream of the estuary of the Liangqiao River merging with the Cenlong River.

Some data related to the reservoir, the dam and the core are listed in Table 1. Table 1 Data related to the reservoir, the dam and the core. m

Normal water level

Safety check flood level

Elevation of dam top

Elevation of the wave wall

Maximumdam height

Crest width

544.45 548.90 549.20 550.30 80.20 10

Maximum base width Crest length

Maximum height of core

Top core width

Core width at elevation of 481.0 m

238.28 217.0 70 0.6 1.2

The core width expands to 3.0 m from the elevation

of 481.0 m to the top of the grouting gallery, following the ratio of 1:0.3. Copper seals are set to ensure the connection between the concrete and the asphalt- concrete core.

From upstream to downstream of the river, the dam body is arranged as follows: upstream main rockfill, transition layer, roller-compacted asphalt-concrete core, Doi: 10.3724/SP.J.1235.2011.00186 Corresponding author. Tel: +86-18986162669; E-mail: 404741985@qq.com

cushion layer, transition layer, and downstream main rockfill. The maximal cross-sectional profile of the dam is shown in Fig.1.

The main stratum of the dam foundation is composed of dolomite 3 of Houba group of Cambrian system, limestone with dolomite of Moda group; Ordovician system 1tO in dam left abutment, limestone 1hO , and a small amount of dolomite limestone. Here, 3m , 1

1tO , 31tO and 1hO are karst

layers, 3h is normally a weak karst layer, and 21tO

and 1dO are water-resistant layers. Karst is also strongly developed at the fault. The descriptions of the rocks corresponding to different strata are shown in Table 2.

Karst is developed in the whole dam site. On the left bank, a karst system of w3K and w2K is developed, which is duct-like and relatively isolated. The dam foundation is located on the layer 1

3m , a strongly developed karst layer, where the minimal straight rate of limestone cavern is 5.08% and the maximum is 50%. On the right bank, the abutment is mainly located on an ancient streambed, where karst layers 3m and

3h are fully developed, and w12K , w51K and w103 systems exist. The elevation of karst layer in the dam right abutment and dam right bed can reach 330–370 m.

The hydraulic conductivity of rock mass is moderate on the left bank, but it is very strong on the riverbed. Among the total tested sections, 38.9% have a value of

Chaoyang Fang et al. / J Rock Mech Geotech Eng. 2011, 3 (2): 186–192 187

Fig.1 Cross-section of the dam body.

Table 2 Rocks corresponding to different strata.

Stratum Description

11tO Muddy band limestone with dark gray crude crystal

21tO Black gray dolomitic shale

31tO Dark gray limestone with dolomite

1dO Siltstone with shale and purple shale with marl

3h Light gray to gray microcrystal dolomite

3m Light gray to gray dense limestone and dolomitic limestone and dolomite

q > 10 Lu. The hydraulic conductivity of rock mass on the right bank is the strongest, with 67.2% having a value of q > 10 Lu, and 29.4% having a value of q < 5 Lu.

The karst at the dam base is strongly, asymmetrically and unevenly developed. The karst straight rate of the foundation at the depth of 0–40 m is 0%–78%, averaging 21.15%. The karst cave is filled with mud, sand and gravel with an average filling rate of more than 77%. The largest cave is up to 12.92 m in diameter. Therefore, local collapsing of dam foundation probably exists.

In order to prevent collapsing, and to ensure the stability of the dam foundation, two reinforcement

measures are adopted. First, karst caves were dug up in the depth of 3–5 m underground, and then they were backfilled with concrete C15. Second, consolidation grouting was employed. The grouting holes were gradually deepened and thickened by using the so-called three-sequence-aperture method. The distance between the aperture pitches of sequence I is 12 m, and the depth of the aperture pitches varies from 36 m in the dam’s foundation to 13 m at the dam’s toe, heel and abutment. Similarly, the distance between the aperture pitches of sequence II is 6 m, and the depth varies from 21 to 13 m; the distance between the aperture pitches of sequence III is 3 m, and the depth is 13 m.

During construction, if there appeared any karst cave with the diameter more than 12 m at the bottom of the apertures of sequence I, the nearby apertures of sequences II and III would be deepened to the depth of sequence I. If the diameter of a karst cave at the bottom of the apertures of sequence II was more than 8 m, the around apertures of sequence I would be deepened to the depth of sequence II [1, 2].

Based on these measures, it is indicated that the stability of the dam base can be ensured [3]. In this paper, the deformation and safety of the dam body and the asphalt-concrete core are studied [4].

C20 reinforced concrete wave wall

557.70 m

554.70 m

550.25 m (check flood level)

544.45 m (normal pool level)

548.63 m (design flood level) 550.50 m

548.00 m

C15 precast concrete block slope (150 mm)

Crushed stone (200 mm)

3 m 525.00 m

M7.5 grouted rubble drainage ditch

499.00 m

Blast backfill Original ground level

Main rockfill zone (3B) 500.00 m

Dam axis

Transition layer (2.7–3.0 m) Asphalt-concrete core wall (0.6–1.2 m) Cushion layer (4.4–4.7 m) Transition layer (3.0 m)

Asphalt-concrete core centerline

Main rockfill zone (3B)

C20 precast concrete block slope (150 mm) Crushed stone (200 mm)

505.15 m (dead water level)

502.15 m (sand accretion elevation) 501.50 m

Blast backfill

466.00 m

478.00 m

470.50 m

Gallery Curtain grouting Host rock boundary

al4Q al

4Q

al4Q

13m

13m

13m

10 m

2.5 m

188 Chaoyang Fang et al. / J Rock Mech Geotech Eng. 2011, 3 (2): 186–192

2 Computational methods and parameters

Since asphalt-concrete is a hybrid material with multi-phase and multi-component characteristics, its compacted structural and physico-mechanical properties are not only correlated with the material quality and the physical characteristics of the adoptive minerals, but also related to the physico-chemical characteristics of the minerals. Triaxial tests of asphalt- concrete have been conducted at Tongji University. Experimental results show that, when the lateral pressure reaches 0.6–1.2 MPa, the stress-strain relationship of asphalt-concrete can be described approximately with hyperbola. Thus, it is reasonable to use the Duncan model to describe the stress-strain relationship of high rockfill dam with asphalt-concrete core [5, 6].

Many studies have been carried out about rockfill dams with the asphalt-concrete core. The results show that with the Duncan model, the stress and deformation analyses of dams are close to the actual ones, which demonstrates the application of the Duncan model [7–10]. The physico-mechanical parameters of the materials used by Zhang et al. [7] are shown in Table 3, where K, n, G, F and D are the experimental parameters.

Table 3 Physico-mechanical parameters used in the analysis of

rockfill dam with asphalt-concrete core [7].

Material

Internal friction angle, (°)

Cohesion, c (kPa)

Failure ratio,

Rf K n G F D

Rockfill 45.4 0.046 0.81 644 0.37 0.41 0.08 1.44

Asphalt- concrete

26.9 0.24 0.72 273 0.28 0.48 0 0

Backfill 47.44 0.045 0.90 950 0.39 0.47 0.09 1.48

The tangent modulus tE of the Duncan model is

given by 2

t f i(1 )E R S E (1)

where fR is the failure ratio, S is the stress level, and

iE is the initial tangent modulus. The Mohr-Coulomb criterion can be written as

31 3 f

2 cos 2 sin( )

1 sin

c

(2)

The tangent Poisson’s ratio t is given by

3

at 2

lg

(1 )

g Fp

A

(3)

1 3

3 f 1 3a

a 3

(1 sin )( )1

2 cos 2 sin

nARKp

p c

(4)

According to geological data, the karst filling materials are mostly clayey soil with low-strength crushed stone.

The physico-mechanical parameters of materials employed in Aikou rockfill dam with asphalt-concrete core are shown in Table 4.

Table 4 Physico-mechanical parameters of materials of Aikou

rockfill dam with asphalt-concrete core.

Material

Unit weight,

(kN/m3)

Internal friction angle, (°)

Cohesion, c (kPa)

Failure ratio,

Rf K n G F D

Rockfill 21 35 0 0.8 1 000 0.3 0.37 0.1 11

Transition material

21.5 33 0 0.78 900 0.3 0.42 0.08 11

Asphalt- concrete

23.5 24 120 0.82 600 0.4 0.42 0.08 7

Cushion material

22 30 0 0.8 700 0.3 0.40 0.08 7

Backfill 20 35 0 0.75 500 0.4 0.38 0.15 2.7

3 Stress-strain analysis

3.1 Classification of calculated loads The deadweight of the dam body is the dominant

load during construction period. But in impoundment period, the load also includes the water pressure acting on the core and the buoyancy acting on the dam body.

In this paper, based on the construction schedule, the deadweight in construction period is divided into 10 levels, and the water pressure in water storage period is divided into 8 levels. In the whole process, the water level is considered to rise up to normal pool level and then drop to deadwater level and finally rise up again [9, 10]. 3.2 Analysis of computational results

For simplicity, the computational results of deformation and stress patterns of the dam after construction and under the condition of normal pool level are listed Figs.2–6.

The horizontal and vertical displacements of the asphalt-concrete core and the stresses under different calculation conditions are shown in Fig.7.

Chaoyang Fang et al. / J Rock Mech Geotech Eng. 2011, 3 (2): 186–192 189

(a) Vertical displacement.

(b) Horizontal displacement.

Fig.2 Displacement isolines of dam body after construction (unit: mm).

Fig.3 Stress level isolines of dam body after construction.

(a) Vertical displacement.

(b) Horizontal displacement.

Fig.4 Displacement contour lines of dam body under the condition of normal pool level (unit: mm).

501.5 m 495.5 m

489.7 m

▽ ▽

▽

550.5 m

4020

60

200220

240

525.0 m

499.0 m

▽

▽

▽ 180160140

1201001:2.0

1:2.0

550.5 m

499.0 m

Dam axis

501.5 m 1101009080 7060 50

4030 20

90 70

50

2010

20 100

10 30 525.0 m

495.5 m 1:2.0 1:2.0

525.0 m

501.5 m 495.5 m

550.5 m

499.0 m

489.7 m 0.3

0.2

0.5 0.4

0.4 0.5

0.6

0.7 0.6 0.7

0.3 0.2

0.1 0.2

0.4 0.5 0.3

1:2.0 1:2.0

550.5 m

525.0 m

499.0 m 495.5 m 489.7 m

544.44 m (normal pool level)

501.5 m

10

7050

3010

210

170 130

90 50

1:2.0 1:2.0

550.5 m

525.0 m

499.0 m

544.45 m (normal pool level)

Dam axis

501.5 m 495.5 m

260

240

220 200

180 160140

12010080 60

40

120 100

80 60 40

0 0

1:2.0 1:2.0

190 Chaoyang Fang et al. / J Rock Mech Geotech Eng. 2011, 3 (2): 186–192

Fig.5 The maximum principal stress isolines of dam body under the condition of normal pool level (unit: MPa).

Fig.6 Stress level isolines of dam body under the condition of normal pool level.

(a)

(b)

(c)

Fig.7 Comparisons of horizontal and vertical displacements and stress level of core wall under different operative conditions.

The displacement during the special impounding process, in which the water level rises to the normal pool level and then drops to 520 m and finally rises again, is shown in Fig.8.

The computational results indicate that: (1) At all loads, the shear stress ratio (stress level)

between dam body and core is less than 1, which shows that the stress rupture does not happen. The maximum stress level is about 0.8 after dam construction and it appears near the upstream face of the dam. Because the deadwater level is comparatively low, it has a little influence on the stress level of the dam body. At water level of 520 m, the stress level of the upstream face of the dam increases, whereas the

478

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50 0 50 100 150 200 250 300 350 400

Horizontal displacement (mm)

Ele

vati

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m)

CompletionDeadwater levelWater level of 520 m Normal pool levelDesign water levelCheck water level

558

478

488

498

508

518

528

538

548

300 250 200 150 100 50 0 50 100

Vertical displacement (mm)

Ele

vati

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m)

Completion Deadwater level

Water level of 520 m Normal pool level

Design flood level

Check flood level

558

470

480

490

500

510

520

530

540

550

560

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Stress level

Ele

vati

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m)

Water level of 520 m Normal pool level Design flood level Check flood level

Completion

550.5 m

525.0 m

499.0 m

544.45 m (normal pool level)

Dam axis

501.5 m 0.6

0.8

1.0

1.2

0.2

0.4

0.6

495.5 m 1:2.0 1:2.0

550.5 m

525.0 m

499.0 m

544.45 m (normal pool level)

501.5 m 495.5 m

489.7 m

0.7

0.5

0.5 0.7

0.3

0.5

0.7

0.3 0.1

0.1

1:2.0 1:2.0

Chaoyang Fang et al. / J Rock Mech Geotech Eng. 2011, 3 (2): 186–192 191

(a)

(b)

Fig.8 Comparisons of horizontal and vertical displacements of the core under conditions that the water level drops from the normal water level to 520 m and then rises again.

safety level at the upstream dam decreases, and it is disadvantageous to the dam safety. But at the normal pool level, the high stress areas at the upstream dam are deviated from the dam axis. The stress level at the dam face decreases, and the safety level of the upstream slope increases. At the same time, there are a small number of elements with a stress level greater than 0.9, which occurs at the berm of the downstream slope. At the check flood level, there is little change in the stress level of the upstream slope, but the number of elements with greater stress levels increases below the berm of the downstream slope. From the stress level contours and their comparisons, we can see that the downstream slope protection benefits both the stability and the stress state of the downstream slope, especially those near the downstream dam face.

(2) The asphalt-concrete core has a relatively larger horizontal displacement. After dam construction, at the bottom of the core and 2/3 of the dam height, an upward displacement with a maximum value of 27.78 mm occurs. As the water level rises, the horizontal

displacement of the core gradually changes its direction to downstream and the maximum value occurs at the top of the dam. At the normal pool level, the maximum downward displacement at the dam top is 302.8 mm and the relative displacement at the bottom of the core is 269.0 mm. At the safety check flood level, the maximum downward displacement at the dam top is 379.4 mm and the relative displacement at the bottom of the core is 340 mm. The maximum settlement after completion of dam construction is 281 mm. At the normal pool level and the safety check flood level, those values are 206 and 198 mm, respectively. All of these happen at the height of 1/2–1/3 of the core. After impoundment, the top of the core wall is lifted in different states, reaching 100 mm in height at the safety check flood level. This indicates that the change of displacement in the core is very complex. The stress level is less than 0.65 under different conditions, so the core is safe. The change pattern of the shear strength is basically consistent with that of the core displacement. In order to cope with the complicated changes of stress and displacement, which may induce pore increasing in the asphalt-concrete and the material deformation limitation to be exceeded, high construction quality of the asphalt-concrete core must be ensured. At the same time, the tests on asphalt-concrete, cushion material and transition material are needed to control all materials’ moduli within a reasonable range, and to make sure that the deformation of the asphalt-concrete is acceptable.

(3) The stress level and displacement near the bottom of the core and the interface of the grouting gallery are both small, and their changes are comparatively mild and slow. This shows that the structural shape and geometrical size adopted in the design can guarantee the safety of the core.

(4) It can be observed from the isolines of the maximum principal stress ( 1 ) that, at the same elevation, the maximum principal stress of the asphalt-concrete core is smaller than that of the transition-cushion material on both sides, and the settlement of the core is larger than that in the fillings on both sides of the core, which indicates the occurrence of “arch effect”. On the other hand, the differences of maximum principal stress and settlement between the core and the transition-cushion material on both sides are small, which indicates that “arch effect” is not very obvious, and the transition and cushion layers play an important role. It can also be seen from

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300 250 200 150 100 50 0 50 100 150

Vertical displacement (mm)

Ele

vati

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m)

520 m water level Normal pool level Check flood level Falling from normal pool level to water level of 520 m Rising to normal pool level againRising to check flood level again

558

478

488

498

508

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0 50 100 150 200 250 300 350 400

Horizontal displacement (mm)

Ele

vati

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m) Water level of 520 m

Normal pool level

Check flood level

Rising to normal pool level again

Rising to check flood level again

558

Falling from normal pool level to water level of 520 m

192 Chaoyang Fang et al. / J Rock Mech Geotech Eng. 2011, 3 (2): 186–192

the physico-mechanical parameters of the rockfill that the deformation moduli of the cushion and transition materials should be compatible with that of the asphalt-concrete.

(5) At the normal pool level, the normal stress of the core in the vertical direction and the hydraulic pressure at corresponding elevations are shown in Fig.9. It can be seen that the hydraulic pressure at any point of the core is less than the normal stress. Therefore, no hydraulic fracturing occurs.

Fig.9 Normal stress and hydraulic pressure of the core at various elevations.

(6) The isolines of the stress level at different

heights and under different conditions show that after impounding, the stress level in the middle and upper core decreases. In other words, the impounding is advantage for the upper part of the core. But in the lower part of the core, the stress level is always relatively higher.

(7) Unloading and reloading cycles will reduce the horizontal displacement and increase the settlement slightly. It implies that the water level fluctuation has a little impact on the displacement of dam body, which may be partly due to the little wetting deformation of the rockfill materials.

(8) Unloading and reloading cycles have an impact on the stress level, especially on the stress level of the upstream dam face at the elevation of 535 m (about 2/3 of the dam height), where the stress level of a few individual elements approaches 1. However, considering the actual adoption of precast concrete block revetment, as long as the precast blocks are mutually closely dogged, the cushion layer and the project quality are ensured, no failure of these units happens. 4 Conclusions

By applying the schemes proposed in this paper to the karst base in Aikou dam project, the stress, displacement and stability of the dam foundation can

meet the engineering requirements. Especially after the foundation treatment, the displacement of the dam foundation is clearly reduced, which is well beneficial to the functioning of the asphalt-concrete core.

After the foundation treatment, no shear damage occurs in the dam body or the asphalt-concrete core under various loads, which shows that the design of the dam structure is feasible. Due to the complex deformation characteristics in the asphalt-concrete core, further tests are needed.

The scheme of structural design and karst- foundation treatment of Aikou rockfill dam with asphalt-concrete core can provide a reference for other similar projects.

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470

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500

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520

530

540

550

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Stress (MPa)

Ele

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m)

Normal stress Hydraulic pressure