Analysis, design and behavior of concrete face rockfill dams (CFRDs) 1.1. Numerical analyses of CFRDs

CFRDs are different from rockfill dams with clay or asphalt concrete cores because: 1) concrete

face is impervious and acted upon by the hydrostatic pressure, causing high compressive stresses

on the soils in the lower part of the transition zones. Therefore, the upstream slope stability

generally is ignored not only in static and seismic analyses with full reservoir, but also deep

drawdown of reservoir that it is inadmissible. As the upper part of this slope (usually with

H/V=1.4-1.5) with the under-laying transition zone is not subjected to hydrostatic pressure it is

much more sensitive to maximum seismic acceleration in the upper dam part that the less steep

(H/V=1.6-1.7) downstream slope of rockfill with much more shear strength.

Until recently it was considered useless to perform numerical analyses of CFRDs and

promoters of these dams claimed that their design was result of only experience and empirics.

A number of incidents affected several recent high CFRDs, which has enlighted the interest of

numerical models to keep control on extrapolation towards higher dams. It has been shown that

not only stresses increase proportionally to the dam height, but even the dam stability. The valley

shape has been identified as an important factor, which induces bank-to-bank movements of

rockfill and very high compressive stresses in concrete face. Such problems are indeed quite

complex for numerical analyses, because:

• The problem is in general tridimensional (3D),

• The response of rockfill to loads requires non-linear constitutive laws with rather large

displacements, including sliding movements along the rock abutments.

• The huge contrast between the large, deformable rockfill and the slender, rigid concrete

face creates numerical problems, all the more as sliding may occur along the contact surface

between both materials.

Fig. 1.1 gives an example of model mesh for CFRD,

where rockfill and concrete face are presented with

volume finite elements. In case of rock foundation it

can be omitted from the model due to its very low

compressibility, compared to the rest of the model.

Fig. 1.1. Finite element 3-D model of CFRD: 1- Left

dam end; 2 – Crest; 3 – Right crest end; 4 – Upstream

concrete face; 5 – Rock foundation shape.

In this context, Problem 10B “Analysis of CFRD including concrete face loading and

deformation” was proposed for the 10th

bench workshop, based on information of the 145 m high

Mohale CFRD in Lesotho. Four solutions were presented, with results under the form of

displacements and stresses in the fill during construction, stresses and joint openings in the

concrete face. Stresses consistent with the damages observed in the prototype were given by 2

solutions. The main reason for these damages was identified as a high compressibility of rockfill

under high stresses, due to the breakage of rock particles.

Recently many 140-200 m high CFRDs (Mohale dam in Lesotho, Barra Grande and Campos

Novos in Brazil, etc.) have serious problems with intense cracking of concrete face and large

opening of perimeter joints that’s results in dangerous seepage and subsequent high-cost repair.

It should be emphasized that three recent incidents, including the Mohale dam, show the need to

carefully evaluate and analyze every aspect of a project when extrapolating from precedent. This

should be based on good engineering judgment and complemented with detailed analysis tools.

1.2. Behavior of concrete face of CFRDs during first impounding of the reservoir

The hydrostatic water pressure is pressing the concrete face and underlying transition zones.

Thus, the shear resistance against sliding of the concrete face on these zones is also growing with

increasing water pressure. At the same time the water pressure prevents the separation of the

concrete face from the soil of underlying transition zone. Cracking and damage of concrete face

is more likely to be expected in its upper part. At greater water depth local joint damage in the

concrete face due to compression and shear but also opening of vertical joints must be expected,

leading to increased leakage.

Untill recently the trend in CFRD design, based on the intuition of specialists, was to pay

great care on the placing of rockfill materials just below the concrete slabs with which these

dams are provided, and to accept much less care in the downstream area (thicker layers, lower

quality of rock, etc.). Some of these dams have shown many damages on slabs and high leakage,

due to excessive and uneven deformability of rockfill zones.

Accurate models with non-linear properties of rockfill have shown the adverse effect of

excessive compressibility of the downstream shell on the deformations imposed to the concrete

face (Anthiniac & al., 2002). The influence of excessive downstream slopes has also been put

into evidence. It is still difficult to obtain realistic rockfill properties from laboratory tests, due to

the size of finite elements and samples. Research is underway to understand the plastification

phenomenon at the scale of the block, whose objective is to provide an extrapolation law to

derive the behavior of large size rockfill from more manageable samples with only small blocks.

One of the difficulties brought by non-linear process in FE analyses is the need to check the

process convergence. Non-linear software generally use only a global convergence criterion,

based on the proportion of unbalanced energy relative to the total deformation energy. This

criterion as proved to fail in some specific cases, e.g. opening of joints in a concrete slab of a

CFRD. The reason is that even a small unbalanced local force may prevent a whole structure

from collapsing (this is the “zipper” effect). Only the engineer can detect such critical cases, and

it is therefore necessary that all software with non- linear capabilities propose means to detect

(and visualize) the amount of local unbalanced forces, at different steps of the analysis.

1.3. General seismic resistance of CFRD

The following failure modes due to seismic actions are considered for CFRDs:

(1) sliding of shallow materials along planar surfaces;

(2) wedge failure or deep-seated rotational failure (Seed et al., 1985);

(3) vulnerability of perimetric joints (Wieland, 2008) as the joint (protected with filters) is a

critical element and washing out of foundation soil is to be prevented in leakage case;

(4) cracking of concrete face due to high compressibility of the upstream transition zones. Use

in these zones well graded and compacted fine and coarse-grained soil of low compressibility

and their compaction can minimize cracking of concrete face;

5) long-term settlements of well compacted rockfill is in the range of 0.1-0.2 % of the dam

height. Strong ground shaking can produce its settlements in the range of about 0.5-1.0 m.

For assessment of the seismic performance of concrete face, the analysis of the effect of the

cross-canyon earthquake component is to be made to receive realistic values of dynamic stresses

in the concrete face and its response to these forces. The behavior of the rigid concrete face for

in-plane motions is very different from that of the rockfill in CFRD, thus the rockfill motion in

crest direction will be restrained by the concrete face. Therefore, for cross-canyon vibration, the

rigid concrete face attracts seismic forces from the dam. Hence, very high stresses may develop

in the face. Shear failure and/or spalling of concrete may occur in the highly stressed joints.

The recent case of CFRD serious damage and concrete face intense cracking was registered in

156 m high Zipingpu CFRD (China), which was designed for peak ground acceleration of 0,26g.

The dam was subjected to very strong ground shaking of Wenchuan earthquake (magnitude 8.0)

in May 12, 2008. The seismic intensity at the dam site in the range of 9-10 (Chinese seismic

scale) was beyond the value accepted in the design. During the earthquake the reservoir level

was low that was the main cause of the crest dam damage and concrete face cracking. On the

crest the recorded peak accelerations were over 2g; however, as the concrete crest behaved

differently from the dam body and since the concrete part also separated from the rockfill the

dynamic behavior of the concrete dam crest was quite different from that of the rockfill.

After the earthquake the maximum settlement at the dam crest was 735 mm and the horizontal

downstream deflection was 180 mm. The cross-canyon deformation of both abutments was 102

mm. Due to the reservoir low level at earthquake, it is difficult to estimate what the dam

behavior, the concrete face and waterproofing system would have been if the reservoir were full.

1.4. General recommendations for dynamic analysis of CFRDs

3D dynamic response of the system “dam-foundation-reservoir” affects the values of joint

opening of concrete face, the condition of the dam contact with abutments, behavior of control

gallery and overall picture of displacement and stress fields.

1. The boundaries of computational domain of dam foundation are appointed from the

condition of their sufficient remoteness so, that their effects on dam behavior would not be

significant. Justification the length of dam foundation in dynamic problem is complicated by the

need to eliminate the possibility of wave reflection from boundaries of computational domain.

Modern programs, such as FLAC, ADINA and Abaques allow on boundaries of the selected

computational domain to apply conditions of passing or absorption of seismic waves.

2. Degree of reliability of the results of dynamic analyses significantly depends on the

likelihood of estimated conditions on contact elements of the system. On contacts of the face

slab with transition zone should be placed one-sided links (contact works only in compression)

taking into account friction between concrete face and transition zones. FLAC, ADINA and

Abaques programs allow to realize these conditions.

3. An important issue is the choice of material models of the system “dam-foundation”.

Modern computers and software allow realizing in analyses different models of dam materials:

for concrete – elastic models, for soils – nonlinear elastic, elasto-plastic, plastic, etc. However,

there are great difficulties in selection of reliable dynamic parameters of materials of the system.

4. In dynamic (seismic) analysis the stress-strain state of the system from the static loads

(hydrostatic pressure of reservoir and dead weight of dam and face) should be considered as an

initial stress field (with zero displacements).

5. It is recommended to apply the seismic load (real and synthetic accelerograms) on the

lower boundary of the computational domain of foundation. It is permissible to apply the seismic

load directly to the bottom of the dam, if in the estimated accelerograms the dam influence on

them is already considered.

6. Modern computers and software allow taking into account in the dynamic analyses the loss

of energy due to internal friction by entering into the equations of motions the corresponding

damping coefficients.

7. With a full formulation of the problem (taking into account contact and material

nonlinearity of the system, with incorporating into computational domain the foundation) it is

required the solution by direct stepwise integration.

8. In the static analysis it is required the sizes of finite elements to be selected roughly so, that

in the zones of proposed changes of stress signs were at least five elements.

9. In the dynamic problems the sizes of elements must be no more than 1/5 of the length of

the shortest seismic wave. Researcher should choose, if program allows, a computational method

(explicit or implicit): from which the required step solution for its stability or accuracy depends

on. However, this solution step must be agreed with the step of the digitizing of accelerograms.

As a result of the studies carried out by varying design parameters of materials of the system a

researcher can get all necessary information the development to justify the dam and face slab. If

there is full information the development the dam structure is not a problem.

1.5. General design recommendations for seismic safety of high CFRDs

For the design of high CFRDs in highly seismic regions the following principal measures are

recommended, which can improve their seismic safety and behavior:

(1) downstream slope flattening in the upper part of CFRD (≈0.2H) to reduce its seismic shear

deformations;

(2) sufficient freeboard (accounting crest settlements and gravitational waves in the reservoir);

(3) wide crest (improves safety of the crest part of dam and increases resistance against

overtopping from gravitational waves);

(4) use of geogrid and other techniques to strengthen both slopes of crest part of CFRD;

(5) proper selection of dam materials and their zoning in dam body: well-compacted gravels

or crushed stones in the upstream transition zones and pebbles in the central dam part to decrease

their compressibility and deflection of concrete face during the reservoir impounding, solid

rockfill in the downstream slope with its maximum angles of inner friction under seismic loads;

(6) in gravel-fill CFRDs the upstream drainage zone with its horizontal part of coarse gravel

protected with filters should be provided to allow free draining of water leaking through the

cracked concrete face and further evacuating of water through gravel-fill without its piping;

(7) new effective method of decrease (up to 50-55%) of concrete face deflection by using

poor RCC zone instead of the upstream transition zone or by sluicing this zone with cement

mortar. This method was proposed in design of 275 m high Kambarata-1 CFRD in Kyrgyzstan

and 190 m high Sogamoso CFRD in Colombia;

(8) provision of bottom outlet to lower the reservoir if the concrete face or water-proofing

system is damaged;

(9) concrete face slabs with smaller width to decrease their non-uniform deformations near

steep abutments;

(10) arrangement of reinforcement of the concrete face to improve its load bearing capacity

in-plane and out-of-plane and its ductility;

(11) arrangement of proper joint system including horizontal joints and selection of the joint

width to account for the reversible nature of seismic response;

(12) water-proofing system of face slabs and plinth joint to account for static and seismic

movements of the joint.

References: Kreuser H. (2000). “The use of risk analysis to support dam safety decision and management”, General

Report to Q.76, 20th ICOLD Congress, Beijing, China.

Chen S.H., Wang J.S., Zhang J.L.,(1996).”Adaptive elasto-plastic FEM analysis for hydraulic

structures”. Journ. of Hydraulic Eng., 19 (2), 68-75.

Ghrib F., Leger P., Tinawi R., Lupien R. (1997). “Seismic safety evaluation of gravity dams”

Hydropower and Dams, Issue 2, pp. 126-138.

Fanelli M., Salvaneschi P. (1993). “A neural network approach to the definition of near-optimal arch

dam shape”. Dam Engineering, Vol. IV, Issue 2.

Carrere A., Colson M., Goguel B. (2002). “Modeling: a means of assisting interpretation of reading”.

Proc. 20th ICOLD Congress (Beijing), Q.78, R.63, Vol. 3.

Anthinianc P., Carrere A., Develay D. (2002). “The contribution of numerical analysis to the design of

CFRD”, Hydropower and Dams, Vol.9, Issue 4.

2. New structures of high concrete face rockfill dams (CFRDs)

Many high (more than 100 m) CFRDs have serious problems with intense cracking of concrete

faces and large openings of perimeter joints that results in dangerous seepage and subsequent

high cost repair (A. Marulanda, 2006). The new effective method to prevent or mitigate these

problems was proposed for 275 m high Kambarata-1 CFRD in Kyrgyzstan and 190 m high

Sogamoso CFRD in Colombia, both in very seismic regions.

2.1. Kambarata-1 CFRD (design variant, H=275 m, Kyrgyzstan) on rock foundation

• This dam was designed in the USSR as a rockfill dam built by the directional blasting of rock

banks of the dam site. At present, there is an urgent need for an independent international design

expertise of the dam due to its complex environmental and technological problems that include

the unpredictable results of the great explosion of rock banks of the dam site.

• Taking into account these problems a new design variant of 275 m high CFRD was developed

with the field-proven technology of its construction.

• Since the dam height is 40 m more than height (235 m) of Shubuya CFRD in China and dam is

located in a high seismic region of 9 grade per MSK-64 scale, the special measure was proposed

to reduce the concrete face deflections (normal to face): the 3-6 m thick upstream transition

gravel zone was replaced by roller compacted lean concrete (RCC) with low compressibility.

• 2D analysis of the stress-strain state by ADINA program with the elasto-plastic Mohr-Coulomb

model of rockfill and RCC zone with different schemes of dam construction and reservoir filling

showed that the concrete face maximum deflection can be reduced in two times comparing with

the upstream gravel zone that greatly increased the dam safety.

• The confined dam profile and high speed of its construction will provide a great technological,

economic and environmental advantages comparing with the old design of blasted rockfill dam.

Fig. 2.1. Longitudinal section and cross-section of Kambarata-1 CFRD (H=275 m)

Fig. 2.2. Structural details of Kambarata-1 CFRD (H=275 m)

A. Results of 2D static stress-strain analysis of the 275 m high Kambarata-1 CFRD

with the upstream transition gravel zone 2B under concrete face

Fig. 2.3. F.E. mesh for 3 stages of construction. Fig. 2.4. F.E. mesh for 5 stages of construction.

Results of 2D static analysis for 5 stages of dam construction (Fig. 2.5-2.8) showed that vertical

compressive stresses are distributed uniformly through the dam height, reaching 6 MPa in the

dam heel. In the upstream transition gravel zone under the concrete face there is a concentration

of the compressive stresses between 0.6 and 2.6 MPa.

Fig.2.5. Horizontal displacements, m. Fig. 2.6. Vertical displacements, m.

Fig. 2.7. Horizontal stresses, Pa. Fig. 2.8. Vertical stresses, Pa.

B. Results of 2D static stress-strain analysis of the 275 m high Kambarata-1 CFRD

with the upstream supporting zone of lean RCC under concrete face

Fig.2.9. Horizontal displacements, m. Fig. 2.10. Vertical displacements, m.

Fig. 2.11. Horizontal stresses, Pa. Fig. 2.12. Vertical stresses, Pa.

Conclusions

1. For dam construction in 5 stages the concrete face maximum deflection is equal to 120 cm,

which is 20% less than the same deflection for 3 stages.

2. Reduction of face deflection with RCC supporting zone is very effective: the face maximum

deflection is only 50 cm or 2.4 times less than face deflection with the gravel transition zone.

3. CFRD variant with lean RCC zone as a support for concrete face provides a great reduction

of the cost and time of dam construction compared with the rockfill blasted-type dam. Therefore,

CFRD variant is to be considered, as a principal one in the final design.

2.2. 190 m high CFRD Sogamoso (Colombia, under construction) on rock foundation

The 2D stress-strain state analysis of Sogamoso CFRD was made by ADINA program with

elasto-plastic model of dam materials with Mohr-Column criterion. The great influence of

consequence of dam construction and reservoir filling on stress-strain state of dam was received.

The new effective method of decrease (40-55%) of deflection of concrete face by inclusion of

6-3 m thick RCC supporting zone (instead of upstream transition zone of gravel, 2B) under the

concrete face was proposed for this dam.

Fig. 2.13. Cross-section of Sogamoso CFRD (190 m) with upstream RCC coffer-dam (h=36 m)

Table 1. Design parameters of Mohr-Coulomb elasto-plastic model for dam materials

Parameters Zone 3А Zone 2B

(RCC)

RCC

coffer dam

Zone 3D Zone3B Zone 3C

Deformation modulus,

MPa

50 500 500 20 40 30

Poison’s coefficient 0,3 0,2 0,2 0,33 0.32 0.33

Dry density, t/m3 2,0 2,35 2,35 1,93 2.04 1.83

Angle of internal friction φ

(grades)

42 40 40 35 44 35

Cohesion, MPa - 0,1 0,1 - - -

Fig. 2.14. Five stages of dam construction considered in static analysis of stress-strain state

Fig. 2.15. Finite element mesh (846 super elements) in static dam analysis of stress-strain state

Fig. 2.16. Horizontal displacements (m) in Sogamoso CFRD with RCC support zone under concrete face

Fig. 2.17. Vertical displacements (m) in Sogamoso CFRD with RCC support zone under concrete face

Conclusions

1. For 5 stages of dam construction and reservoir filling the maximum deflection of concrete face with

underlying 2B transition gravel zone (3-6 m wide) can reach 180 cm.

2. In case of replacement of the transition zone 2B by RCC 3-6 m wide supporting zone the maximum

deflection of concrete face will be only 95 cm that greatly improve the dam safety.

3. Static and dynamic analyses of the heightening (from 43 to 82 m) of

concrete face gravel dam CFGD Limon (Peru)

3.1. Introduction

In June 2012 the Government of Lambayeque province (Peru) invited me as an international

consultant and member of ICOLD Committee on Dam Design to perform the expert validation

of design of the heightening of concrete face gravel dam (CFGD) Limon from 43 to 82 m. The

dam is one of the main element of project, called “Proyecto Especial Olmos–Tinajones (PEOT)”.

The hydraulic (transfer) scheme of Olmos multi-purpose project (mainly for hydropower and

irrigation purposes) includes the TransAndes water-transfer 26 km long tunnel now completed.

The 82 m high Limon CFGD is located on the right bank of the Huancabamba river in the

remote region of Andes with a very high seismicity (North-East of Peru, 980 km from Lima).

In the first PEOT project, developed by Hydroproject Institute (Moscow) in 1982, the variant

of 82 m high Limon rockfill dam with clay core was adopted as one-stage dam construction. But

later due to the political and financial problems in Peru the project implementation was delayed

for nearly 20 years and was resumed as a two-stage construction by BOT scheme, proposed by

Odebrecht construction company (Brazil). The company changed the Soviet design of one-stage

82 m high Limon traditional rockfill dam in favor of two-stage CFGD (43 and 82 m high).

3.2. Seepage analysis Limon CFGD (H=82 m) and its alluvial (40 m deep) foundation

In the figure 3.1a is presented the geometry of dam with zones of materials and its 40 m deep

alluvial strata of foundation in channel section 10-10' and their permeability coefficients. In the

figure 3.1b is presented the finite element mesh of dam and its foundation in channel section 10.

Fig. 3.1a. Zoning and permeability of soils of CFGD Limon H=82 m and its foundation in channel section

Fig. 3.1b. Finite element mesh of CFGD Limon H=82 m and (40 m deep) foundation in channel section

Fig. 3.2a. Equipotential lines of the total seepage heads in rock foundation below the concrete diaphragm

The results of the equipotential lines of total seepage heads in the rock foundation below the

plastic concrete diaphragm are presented in the figure 3.2a, verifying the significant reduction of

the total seepage heads by the effect of the plastic concrete diaphragm in the dam foundation.

Also, in the figure 3.2b is verified the significant reduction of the seepage pressure heads in the

rock foundation mainly due to the plastic concrete diaphragm.

Fig.3.2b. Equipotential lines of seepage pressure heads in rock foundation below the concrete diaphragm

Table 3.1 shows the unit seepage flows in the dam foundation for construction stages of H=43

m and H=82 m in sections 8-8' (in right abutment) and 10-10' (channel section) below the

concrete diaphragm, in the central dam axis and below the dam toe. The relationship of unit

seepage flows in section 8-8' shows that seepage flow in the foundation of the dam H=82 m

would be more than twice the seepage flow in the foundation of the dam H=43 m.

Table 3.1. Unit seepage flows in the dam foundation for construction stages of H=43 m and H=82 m

Dam Section

Unit seepage flows (m3/s/m)

Below concrete

diaphragm

In axis of dam

cross-section

Below toe of

downstream slope

I Stage

H = 43 m

8 - 8' 1.373 x 10-3

1.37 x 10-3

0.744 x 10-3

10 - 10' 1.495 x 10-3

1.38 x 10-3

0.652 x 10-3

II Stage

H = 82 m

8 - 8' 2.865 x10-3

2.759 x 10-3

1.904 x 10-5

10 - 10' 3.163 x 10-3

2.791 x 10-3

0.536 x 10-3

Relation

QH82/QH43

8 - 8' 2.09 2.01 2.56

10 - 10' 2.12 2.02 0.82

3.3. Seismic (dynamic) analysis of 82 m high Limon CFGD under MCE action (Amax=0.57g)

The main results of dynamic nonlinear analysis of stress-strain state of Limon CFGD (H=82 m,

variant 2 with additional downstream rockfill zone) with full reservoir under Maximum Credible

Earthquake (MCE) action of the Mar-Chile Earthquake accelerogram are given in fig. 3.3-3.15.

Another MCE of the Lima-Peru Earthquake accelerogram was considered also in the dynamic

analysis, but its action was less dangerous than that of the Mar-Chile Earthquake accelerogram.

In fig. 3.3 the accelerogram of Mar-Chile Earthquake normalized to the maximum acceleration

of Amax=0.57g is shown. The Mar-Chile Earthquake with the return period T=5000 years and

Amax=0.57g corresponds to the recommendations of ICOLD Bulletin 148 (2010) and was much

more dangerous than adopted in previous (2009) brazilian design: Amax=0.39g, T≈1000 years.

The static and dynamic analyses of stress-strain state of Limon CFGD (H=43 and 82 m) were

made by FLAC software (USA), which was estimated in the ICOLD Congress (Canada, 2003) as

one of the best software for dynamic analyses of large rockfill dams including CFRDs. The finite

element model of Limon CFGD (H=43 and 82 m) with its foundation is shown in the fig. 3.4.

Fig. 3.3. Accelerogram of Mar-Chile Fig. 3.4. The finite element model of Limon CFGD

Earthquake normalized to Amax=0.57g (H=43 and 82 m) with its foundation

Parameters of the elasto-plastic model with Mohr-Coulomb criterion for dam materials and

foundation soils in static analyses of Limon CFGD (H=43 and 82 m) are given in the table 3.2.

Table 3.2. Parameters of Mohr-Coulomb model in static analyses of Limon CFGD (H=43 and 82 m)

Numbers and names of

zones of dam materials

and foundation soils

Material

or soils

Dry density

and void ratio

Parameters of deformation Parameters of shear

strength of materials

γdr, t/m3 n E

(MPa)

Angle of

dilatancy (0)

ν C (MPa) ψ(0)

1-st stage dam (H=43 m)

1, 3. Foundation Alluvium 2,15 0,2 108 0 0,30 0 42

2. Diaphragm Concrete 2,25 0 320 0 0,40 0,4 30

4. Plint slab Concrete 2,5 0 20000 0 0,17 1,0 60

5. Embankment zone Gravels and

pebbles

2,2 0,15 168 0 0,30 0 46,5

6. Transition zone Gravels 2,15 0,2 150 100 0,33 0 42

7. Transition zone Sand 2,1 0,25 100 100 0,33 0 40

8. Concrete face Concrete 2,5 0 20000 0 0,17 1,0 60

2-nd stage dam (H=82 m)

9. Embankment zone Gravels 2,2 0,15 168 0 0,30 0 46,5

10. Embankment zone Gravels 2,2 0,15 168 0 0,30 0 46,5

11. Transition zone Gravels 2,15 0,2 150 100 0,33 0 42

12. Transition zone Sand 2,1 0,25 100 100 0,33 0 40

13. Concrete face Concrete 2,5 0 20000 0 0,17 1,0 60

14. Downstream zone

with 2 berms Pebbles 2,1 0,25 150 0 0,30 0 46,5

Fig.3.5. Scheme of CFGD Limon (H=42 and 82 m) Fig.3.6.Scheme of CFGD Limon (H=43 and 82 m) with

(adopted variant with d-s zone 14 with 2 berms) variable shear angles of gravel and pebble zones 10-11, 15-17

Table 3.3.Values of shear angles of gravel and pebble zones 10-11, 15-17 depending on normal stresses

Normal stresses, σn , MPa

0,2 0,5 0,8 1,0 ≥1,2

Shear angles (0) of gravel and pebble zones 46,5

0 46,3

0 42,0

0 41,1

0 40,0

0

Scheme of zoning of CFGD Limon (H=82 m) with variable shear angles of gravel and pebble

zones 10-11, 15-17 (Fig.3.6) was used in the pseudo-static analyses of the downstream slope

stability under action of the acceleration in dam foundation Ahor =2/3• Amax =2/3• 0.57g=0.38g.

Fig.3.7. Distribution of seismic accelerations through Fig.3.8.Factors of seismic (Fmin=1,19>Fperm=1,06) and static

the dam height (H=82 m) using shear wedge method stability (Fmin=1,69>Fperm=1,25) of downstream slope

The distribution of seismic accelerations through the dam height was received according to

Russian seismic design norms for dams (SNiP-2003) using the shear wedge method (Figure 3.7).

Figure 3.8 shows results of static (the most dangerous circular surface 2) and seismic (the most

dangerous circular surface 1) stability of downstream slope of Limon CFGD (H=82 m) taking

into account the variable shear angles of gravel and pebble zones 10-11, 15-17. This figure show

that the minimum factor of the downstream slope stability under action of seismic loads is more

that permissible as per design norms SNiP-2003 (Fmin=1,22>Fperm=1,06) and corresponds to the

deep circular sliding surface between the dam crest and upper alluvial layers of dam foundation.

The comparison of results of the seismic stability analysis of the downstream slope of Limon

CFGD (H=82 m) with additional pebble zone 14 with two berms (fig.3.5) with results of the

same analysis of the dam but without the additional zone show that the inclusion of this zone in

the downstream slope provide a significant increase of the minimum factor of the downstream

slope stability from 1.05 up to 1.22).

Below in figures 3.9-3.12 the main results of dynamic nonlinear analysis of stress-strain state

of Limon CFGD (H==43 and H=82 m, variant with the additional downstream pebble zone) with

full reservoir under action of MCE of the Mar-Chile Earthquake accelerogram are presented.

Parameters of Mohr-Coulomb model used in the dynamic nonlinear analysis of Limon CFGD

(H=43 and 82 m) are given in table 3.4.

Table 3.4. Parameters of Mohr-Coulomb model in dynamic analyses of Limon CFGD (H=43 and 82 m)

Note: (σm) – medium stress (effective) in kPa

Fig. A. Curves of reduction of the shear modulus G/Gmax and

initial coefficient of damping ξ,% of soils of the dam and

its foundation

Fig. 3.9. Zones of Limon CFGD (H=43 and 82 m) with the shear and tension stress state of soils

under action of SMC of the Mar-Chile Earthquake accelerogram with Amax=0.57g

Numbers and

names of zones of

dam materials and

foundation soils

Material

or soils

Dry density

and void

ratio

Dynamic modulus of

elasticity

Edyn

,, MPa

Shear modulus

Gmax (MPa)

Initial

coefficient of damping ξ, %

Reduction of

parameters

Gmax and ξ γdr,

t/m3

n

1-st stage dam (H=43 m)

1, 3. Foundation Alluvium 2,15 0,2 1300 Gmax=35(σm)0,5

5 see Fig. A

2. Diaphragm Concrete 2,25 0 1600 G= Edyn

/ [2(1+ν)] 3 --

4. Plint slab Concrete 2,5 0 20000 G= Edyn

/ [2(1+ν)] 2 --

5. Embankment

zone

Gravels and

pebbles

2,2 0,15 2000 Gmax=40(σm)

0,5

5 see Fig. A

6. Transition zone Gravels 2,15 0,2 1000 Gmax=22(σm)

0,5

4 see Fig. A

7. Transition zone Sand 2,15 0,2 700 Gmax=20(σm)

0,5

4 see Fig. A

8. Concrete face Concrete 2, 5 0 20000 G= E

dyn/ [2(1+ν)]

5 --

2-nd stage dam (H=82 m)

9. Embankment

zone

Gravels 2,2 0,15 2000 Gmax=40(σm)

0,5

5 see Fig. A

10. Embankment

zone

Gravels 2,2 0,15 2000 Gmax=40(σm)

0,5

5 see Fig. A

11. Transition zone Gravels 2,15 0,2 1000 Gmax=22(σm)0,5

4 see Fig. A

12. Transition zone Sand 2,1 0,25 700 Gmax=20(σm)

0,5

4 see Fig. A

13. Concrete face Concrete 2,5 0 20000 G= Edyn

/ [2(1+ν)] 5 -

14. Downstream zone

with 2 berms Pebbles 2,15 0,2 1500 G=E

dyn/[2(1+ν)] 5 see Fig. A

The dam zones with the shear stress state of soils are painted in orange and zones with the

tension stress state of soils are painted in blue (Figure 3.9).

Under action of the Mar-Chile Earthquake the dam would suffer elasto-plastic deformations

with large plastic displacements in the wide zone of the downstream slope (Figure 3.10).

The large plastic (residual) deformations modified the dynamic stress-strain state of the dam

and its foundation (Figures 3.10-3.11).

The horizontal and vertical displacement in the dam after the Mar-Chile Earthquake in the

upper part of the downstream slope are, respectively, 2.0 and 1.0 m; in the upper berm - 2.2 and

1.1 m; in the lower berm - 2.5 and 1.3 m and at the toe of the slope - 6.0 m and zero (Fig. 3.10).

The intensity of shear deformations (Figure 3.11) is concentrated in the narrow zone in the

lower part of the downstream slope of the dam.

Fig. 3.10. Horizontal (a) and vertical (b) displacements in Limon dam (82m) after Mar-Chile Earthquake

Fig. 3.11. Intensity of the shear deformations in Limon dam (82m) after the Mar-Chile Earthquake

Fig. 3.12. The time history of the residual horizontal (a) and vertical (b) displacements of the crest of

Limon dam (82 m) during the Mar-Chile Earthquake

The time history of the residual horizontal (a) and vertical (b) displacements of the dam crest

during the Mar-Chile Earthquake is shown in Figure 3.12. The maximum horizontal and vertical

displacements of the dam crest during the Mar-Chile Earthquake are, respectively, 1.5 and 1.1 m

Conclusions

1. Horizontal and vertical displacements after the Mar-Chile Earthquake of the downstream slope

(between the dam crest and lower berm) are, respectively, 2.0-2.5 and 1.0-1.3 m. The maximum

horizontal and vertical displacements of the dam crest during the Mar-Chile Earthquake are,

respectively, 1.5 and 1.1 m and after the Earthquake - 0.4 and 0.3 m. These displacements about

two times lower than those in the previous variant 1 of the dam with the downstream slope of

(V/H=1/1.7) and the under-laying rockfill without berms.

2. In comparison with the previous variant 1 of Limon dam (H=82 m) with the downstream slope

of (V/H=1/1.7) and the under-laying rockfill without berms this variant 2 of Limon dam (H=82

m) with additional gravel zone with two berms on downstream slope is much more stable and

safe under action of very strong MCE of the Mar-Chile Earthquake. Therefore, this variant 2 of

Limon dam can be adopted in the following detailed final design of 82 m high CFRD Limon.

4. Example of dynamic analysis of 150 m high CFRD

As an example the dynamic analysis of 150 m high CFRD with upstream and downstream

slopes 1.5H/1V is considered.

Fig. 4.1 shows 3D model of the system dam-foundation and its discretization by finite elements.

Totally about 150 thousand finite elements, mainly 3D elements with 8-nodes and partially 3D

elements with 6-nodes in dam contact with abutments. Concrete face is simulated by 3D shell

elements. On face-dam contacts, in the deformation joints of face, on face-abutments contacts

one-sided links (contact works only in compression) are organized, taking into account the

friction on the contact surfaces. Some researches were previously specified on 2D models.

Fig. 4.1. 3D model of dam for analysis of 3D

stress-strain state:

1 - concrete face; 2 - rockfill; 3 - loose layer;

4 – foundation massif

Special combination of loads is considered:

hydro-static pressure of reservoir, dead weight of the dam (the initial stress state) and seismic

load in the form of three-component accelerograms applied to the lower surface of foundation

massif. Rockfill and transition zone materials are considered as a linear-elastic, nonlinear elastic

and elastic-plastic medium.

Fig. 4.3 shows the development of detachment (separationt) of the dam with face from both

abutment slopes. The upper figure shows the detachment of the dam and face from the left

abutment slope after 8 seconds of the earthquake. As can be seen from the lower figure, after

11.4 seconds of the earthquake detachment is observed only on the right abutment slope in the

central section of the dam (approximately under its crest).

Fig. 4.3. Deformations of the dam during seismic load

a - upstream view, t=8 sec; b - deformations of the central longitudinal section of the dam,

t=11.4 sec.

Fig. 4.4 shows the openings of face joints under static loads and after 8 sec. and 8.6 sec. of

earthquake.

Fig. 4.4. Openings of joints of concrete face:

a - under static load; b - under earthquake action in zone A of face after t=8 sec;

b - under earthquake action in zone A of face after t=8 sec.

It should be noted that implementation of full computational studies required to obtain enough

reliable dam response, required high qualification of researchers and appropriate computational

and technical support.

5. Prospects of construction of high CFRDs in Russia

Analysis of intensive construction of high CFRDs in China, Brazil, Colombia and some other

countries and experience of their operation have shown that under certain natural conditions

(favorable topographic and geotechnical conditions, availability of the necessary constructional

materials, etc.) the choice of this type of dam compared with the other type (rockfill dams with

clay or asphaltic concrete cores, RCC or concrete dams) can be the most efficient and

economical solution. This is due to the much smaller volume of rockfill materials, hydraulic

safety of CFRD with high piping resistance, static and seismic stability and effective compaction

of its rockfill and transition zones, concrete plinth and faces, retaining wall on dam crest.

According to long-term plan of the development of hydropower industry in Russia up to 2020

the main regions for construction of new hydropower plants are the North Caucasus, Altai,

Siberia and the Far East. Natural conditions for the construction of CFRs in the North Caucasus

are close enough to those conditions in which a large number of foreign CFRDs were

constructed. Therefore, CFRDs dams may be atractive especially in the Northern Caucasus and

some CIS countries (Tajikistan, Kirgizstan, Uzbekistan and Kazakhstan).

As for the construction of CFRDs in Siberia and the Far East some additional problems may

arise with regard to the concrete face behavior in its upper part under action of extreme low

temperatures. However, the experience of construction of 200 m high CFRD in Iceland shows

the ability to solve these problems.

On other side, the experience of construction of rockfill dams with asphaltic concrete cores in

Siberia, Norway and Canada shows that these dams are safer than CFRD in severe climate of

these countries.