1

WES SPILLWAY STRUCTURAL DESIGN AND STABILITY

Raquel Rosa1

1Instituto Superior Técnico, University of Lisbon

Av. Rovisco Pais, 1049-001, Lisboa, Portugal

Keywords: Spillway, Structural design, Stability, Hydrostatic pressure, Concrete, Finite element

design.

Abstract: Spillways are hydraulic works of large dimensions, in which safety is of utmost importance,

not only due to the high costs associated to this work, but also to the damages caused in case of

accident. The impact of the negative consequences related to this last scenario requires a careful

structural stability evaluation through an appropriate structural design.

This work concerns the structural stability evaluation through the development of a safe and proper

design, at a preliminary level, of a WES spillway type (Waterways Experiment Station), inserted in

an earth dam in Mozambique.

The following data were provided: water levels upstream and downstream the structure; geotechnical

properties; as well as the structure’s geometry.

The structure is composed by 10 identical modules (19 m length). Each module will be composed by

the spillway body (15 m) and a structural reinforced concrete wall (4 m).

This work is divided in two sections. In the first section, the design of the spillway body is carried out

based in a global stability analysis, using safety factors prescribed by the “Normas Portuguesas de

Barragens”. The second section concerns the design of the walls and the reinforcement detailing.

1. Introduction

Spillways are hydraulic works made of

concrete inserted in dams, in which the main

goal is the discharge of water in order to

ensure the safety of the dam [1].

Given the high risk that comes with such an

endeavor, and the eventual need to extend its

lifetime when compared to the initially

estimated in the project, dam structural

safety is still a topic of interest.

The presented work, a preliminary draft,

aims to provide the design of a WES

(Waterways Experiment Station) spillway

type, located in Mozambique.

The spillway structural design takes into

account several aspects, amongst which the

type of dam in which the spillway operates,

1 e-mail: raquel.h.rosa@ist.utl.pt

the topographical and hydraulic conditions,

the foundation conditions, as well as the

mass needed to ensure the stability of the

structure.

Provided good foundation conditions, this

type of spillways, when accurately projected

and built, has a high degree of reliability and

low maintenance costs. However, they

present high economic impacts.

The spillway geometry definition takes into

account the stability analysis and it is based

on the following data:

Downstream and upstream water

levels at full water level and at

maximum flood level;

2

Foundation resistance and

deformability conditions ;

Shape of the hydraulic surface of the

face in contact with the flow.

2. General work description

The dam spillway will be formed by 10

modules with 19,00 m in length each. These

modules are individually composed by the

spillway’s threshold (hydraulic span of

15,00m), and by pillars (thickness of 4,00m),

for a total extension of 190,00 m. Each

module has an approximate volume of

15530 m3 (Figure 2.1).

‘

Figure 2.1- Layout of structure

The spillway will be implanted in the area

where the sound rock foundation is

available.

The spillway is a WES spillway, with

adherent water blade, with the surface level

at 97,00m. . It is constituted by 10 modules

each with 19,00m of length, in a total of

190,00m. The flow is controlled by radial

gates.

The pillars that separate the spans of the

spillway threshold have an elliptic shape,

4,00 m thick, which extend approximately

6,25m upstream (Figure 2.2). The

roadbridge makes the connection between

the spillway and the road along the full

extent of the dam.

The 3d model of the structure is represented

in Figure 2.2.

Figure 2.2- Tridimensional model of the spillway

module..

3. Spillway body

3.1. Threshold geometry

The threshold of the spillway is a WES type,

and the flow is controlled by radial gates.

Figure 3.1 represents the adapted geometry

for the threshold, as well as the relevant

points for the profile definition (Table 3.1)

and for the exponential equation of the

central section of the threshold (𝑌 =

0,055𝑋1,84).

Figure 3.1- Profile of the WES threshold

Table 3.1- Coordinates (X,Y) of the points that

compose the spillway threshold

Points X (m) Y (m)

P1 -3,7500 1,4275

P2 -2,1424 0,3000

3

P3 0,0000 0,0000

P4 18,5496 11,8603

P5 21,9921 15,9103

P6 39,9946 17,0000

C1 -1,3184 3,1846

C2 0,0000 7,8000

C3 31,5163 7,8147

3.2. Materials and actions

The concrete used is presented in Table 3.2.

Table 3.2- Concrete used in construction and

corresponding application zones.

Concrete

class Zone of application

C16/20 Core of the spillway

threshold

C30/37

1,0 m thick after the

spillway clime area and in

the pillars

The considered actions, according with the

Portaria 846/93, artigo 22., of Normas

Portuguesas de Barragens (NPB) [2] were:

Structure self-weight ;

Self-weight of the gate and deck;

Hydrostatic pressures;

Uplift hydrostatic pressure

Earth pressures;

Seismic actions;

The water levels taken into account in the

design according to the NPB are (Table 3.3)

[2]:

FWL (full water level): regular level of the

reservoir, allowing for its full exploration;

MFL (maximum flood level): maximum

level corresponding to the occurrence of a

major flood.

Table 3.3- Water levels upstream and downstream

of the dam

Upstream Downstream

FWL [m] 112,00 80,50

MFL [m] 113,00 92,00

Figure 3.2 shows a scheme of the pressure

diagrams of the several actions taken into

account, and the resulting actions that the

dam undergoes, considering a 19m module.

Figure 3.2- - Scheme of the actions that the dam

undergoes

The self-weight is the major stability action.

The spillway is usually designed and

calculated to solely resist by its self-weight

to the several actions that undergoes to [3].

The hydrodynamic pressures are obtained

with the integration of the pressure diagram.

With the purpose of reducing the value of the

uplift pressure, drainage galleries are

introduced. The k parameter accounts for the

percentage of pressure that is dissipated with

the drainage system.

It was considered a 𝑘 = 1/3, as

recommended by the NPB [2], 1993 and [4].

The uplift pressure diagram will be done

accordingly with the shape of the dam

foundation, as illustrated in Figure 3.3.

Figure 3.3- Uplift diagram

The seismic action was quantified as

indicated in Table 3-4 where:

OBE- operating basis earthquake

4

MDE- maximum design earthquake

Table 3.4- Base accelerations

aearthquake,h

[g]

aearthquake,v

[g]

OBE 0,100 g ± 2/3.

aearthquake,h

MDE 0,150 g ± 2/3.

aearthquake,h

In the presence of a seismic event, the

hydrodynamic pressure diagram has a

parabolic shape (Figure 3.4), and it is

calculated through the expression [3]:

𝑝(𝑧) = 𝐶 × 𝛼 × 𝛾 × ℎ (3.1)

Figure 3.4- Hydrodynamic pressure diagram

The action of the fine-grained sediments is

calculated using the Rankine’s theory,

neglecting the cohesion and using the soil

parameters of Table 3.5:

𝑒𝑎𝑟𝑡ℎ 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒

=𝛾𝑠 × ℎ𝑠

2

2𝑘0

(3.2)

Table 3.5- Soil parameters

Parameters

Terrain s [kN/m3] c’ [kPa]

Sandy 18 28 0

In the event of a seism, the generated terrain

impulse due to seismic action should be

taken into account, and should be considered

accordingly to the formulation of

Mononobe-Okabe, as presented in

EN1998:5 [5].

Thermal actions were not considered in this

preliminary draft, since some requirements

to the study of thermal actions related to

construction factors are yet to be defined.

3.3. Global stability analysis

The global stability analysis consists of two

points:

Guarantee of the safety of the

spillway against fluctuation,

overturning and sliding;

Stress and displacement

verifications.

3.3.1. Load scenarios

According to the NPB Portaria n.º 846/93,

artigo1.[2], it should take into account two

scenarios: usual scenarios (normal

conditions of exploration, to which the

construction should not deteriorate) and

extreme scenarios (situations which are less

likely to occur, for which the construction

should not rupture).

Table 3.6- Load combinations that are considered

in the global stability analysis

Scenario Actions

Usual

Static actions (FWL)

Seismic combination (FWL and

OBE)

Extreme

Static actions (MFL)

Seismic combination (FWL

MDE)

3.3.2. Safety verifications to fluctuation,

overturning and sliding

In the spillway global stability analysis the

following partial safety coefficients were

considered, presented in Table 3.7 as

recommended in Artigo 31. da Portaria

846/93 [2] and in [6].

Table 3.7- Safety coefficients for the global stability

analysis

Safety

factor

Current

Scenario

Fracture

Scenario

S.F.Fluct. 1,3 1,1

S.F.Roll. 1,5 1,2

S.F.Slid. 1,5 1,2

The geotechnical parameters used to

characterize the rock-concrete interface are

shown in Table 3.8.

5

Table 3.8- Adopted geotechnical parameters for the

rock-concrete interface

Current

scenarios

Fracture

scenarios

Friction

angle (R-C) 45 45

Cohesion(c) 100

[kPa](*) -

(*)Cohesion was considered null in all scenarios,

except for the maximum seismic action scenario where

it was adopted the 100 kPa value.

The safety factors are defined through the

expressions present in Table 3.9.

Table 3.9- Safety formulas to fluctuation, sliding

and overturning

Safety

factor Formula

S.F. Flut t. 𝐹𝑆𝐹𝑙𝑢𝑡. =∑ 𝐹𝑉

𝑈

S.F.Roll 𝐹𝑆𝐷𝑒𝑟𝑟. =∑ 𝑀𝐸𝑠𝑡.

∑ 𝑀𝐷𝑒𝑟𝑟.

S.F.Slid. 𝐹𝑆𝐷𝑒𝑠𝑙.𝑅𝑒𝑠. =

∑ 𝐹𝑉 .𝑡𝑔(𝛿𝑅−𝐶)

𝐶𝑆𝛿+ 𝐿. 𝑐/𝐶𝑆𝑐

∑ 𝐹𝐻

≥ 1.0

S.F.Slid. 𝐹𝑆𝐷𝑒𝑠𝑙. =∑ 𝐹𝑉 . 𝑡𝑔𝛿

∑ 𝐹𝐻

≥ 𝐶𝑆𝛿

The safety factor results are summarized in

Table 3.10.

Table 3.10- Safety factors to fluctuation, sliding and

overturning

Scenario S.F. Flut. S.F.Slid. S.F.Roll.

FWL 3,13 ✓ 1,93 ✓ 4,25 ✓

FWL+OBE 2,94 ✓ 1,39 × 2,96 ✓

MFL 1,78 ✓ 1,23 ✓ 3,86 ✓

FWL+MDE 2,86 ✓ 1,20 ✓ 2,43 ✓

Since the safety check for sliding was not

performed for the current scenario, it was

necessary to calculate the safety factor to the

residual sliding, considering cohesion

(100kPa).

𝐹𝑆𝐷𝑒𝑠𝑙.𝑅𝑒𝑠. = 1,1 ≥ 1,0 ✓

Therefore, all safety coefficients established

by the NPB (Table 3.7) were complied.

3.3.3. Stress verification at the foundation

Tensile stresses are not usually accepted at

the foundation base, in order to avoid

cracking. This is equivalent as applying the

resulting attenuating forces inside the central

core of the dam.

To the concrete with class C15/20

(fcd=10,7MPa e fctm=1,9MPa), and applying

the safety factors recommended by the NPB,

the maximum admissible tensions at the dam

are:

Table 3-11- Maximum tensions admitted to usual

and extreme scenarios

F.S. σmax.comp.

[MPa]

σmax.tensile

[MPa]

Usual S. 2,5 4,28 0,76

Extreme S. 1,2 8,92 1,58

Making sure that the resulting forces are

inside the central core, the following tensile

stress values were obtained (Table 3.12)

through the following expression:

𝜎𝑖 =𝑁

𝑏𝐿±

6𝑁. 𝑒

𝑏𝐿2 (3.3)

Table 3.12- Transmitted tensions to the foundation

massif

Combinations σm [MPa] σj

[MPa]

Usu

al

S.

PP 0,81 ✓ 0,04 ✓

FWL 0,35 ✓ 0,30 ✓

FWL+OBE(+) 0,21 ✓ 0,42 ✓

FWL+OBE(-) 0,50 ✓ 0,17 ✓

Ex

trem

e S

. MFL 0,28 ✓ 0,12 ✓

FWL+MDE(+) 0,12 ✓ 0,51 ✓

FWL+MDE(-) 0,59 ✓ 0,09 ✓

3.4. Structural Modeling

3.4.1. Conception

The structural model of the spillway was

developed using the finite elements program

SAP2000 and all elements used in the

spillway modeling are shell elements.

The model is bi-dimensional with the

deformation restrained in a perpendicular

direction to the spillway section and with

unitary thickness.

6

The module should take into account proper

boundary conditions. It was restrained the

displacements in x,y and z in the nodal

points located in the foundation periphery,

which reflects into the assignment of simple

supported boundaries, as outlined in Figure

3.5.

Figure 3.5- Finite elements model of the spillway

section

The main modes of vibration studied (with

at least 90% of modal mass participation in

each direction) are:

Mo

de

Frequency

[Hz]

Main direction

1 6,87 Translation (x)

(longitudinal)

2 8,95 Translation (z)

(vertical)

3 14,14 Rotation (y)

The following checks were performed:

Tensile stress check in the spillway

section;

Safety check to local fractures in

concrete;

Displacement evaluation.

The tensile stresses in the spillway body

ranges between 0,5 and 3,5 MPa, therefore

the safety is assured.

With regard to the maximum values of

displacements obtained, these are in the

range of 3mm. The safety is once again

assured.

Last, the safety check to local failure of

concrete is made with basis in a graphical

representation of tensions (Figure 3.6),

through the recommendations made by the

[2] – the cracking of an element occurs if the

tensile stress exceeds the resistant concrete

tensile stress (Rankine criterion) or if the

compression stresses are higher than the

ones defined by the Mohr-Coulomb

criterion. The value of k, is defined as the

least of the values obtained by both these

criteria, should be bigger than 2,5.

Figure 3.6- Safety check to local failure

Table 3.13- Safety factor for local fractures on

concrete

Comb. El. σc

[MPa]

σt

[MPa] K

C1 (PP) 848 3,41 0,11 2,8 ✓

C2

(FWL)

830 2,34 0,48 2,3 ×

773 1,0 0,3 3,7 ✓

C3

(OBE)

830 2,4 0,6 2,0 ×

773 1,0 0,3 3,8 ✓

776 1,1 0,2 5,2 ✓

4. Spillway pillars

In this case study, the spillway contains 11

pillars, 4,0m thick, spaced apart 19,0m. The

pillars contain a trunnion in each face, which

supports the segment gates (Figure 4.1).

In order to design the pillars, a

tridimensional model was developed, in the

finite elements program SAP2000, which

aimed to reproduce the structure to be

executed in construction, where some

simplified design methods to calculate the

reinforcement and prestress were used.

7

Figure 4.1- Spillway blueprint- 2 modules

4.1. Loads and Load combination

The actions taken into account in the pillars

design are:

Self-weight of the pillars;

Hydrostatic and hydrodynamic

impulse;

Prestress applied forces short and

long term losses;

Seismic action.

The load combination considered,

corresponding to distinct gate positions, are:

Scenario 1: Water level below the

gate (only permanent loads and

prestress, corresponding to the

application of prestress phase);

Scenario 2: One open gate and one

closed with reservoir in FWL;

Scenario 3: Two closed gates with

reservoir in MFL;

Scenario 4: Placement of a

cofferdam gate with the FWL;

Scenario 5: MDE earthquake with

two closed gates with the reservoir

in FWL.

4.2. Calculation methodology

The spillway pillars were designed to:

Endure the transmitted reactions by

the radial gates;

Support the pontoon deck over the

spillway.

The transmitted reactions by the pontoon to

the pillars are negligible, since they have an

order of magnitude significantly lower than

the remaining forces involved.

Regarding the transmitted reactions by the

radial gates, for the scenarios 2 and 4, it was

taken into account the unbalance of impulses

of water when one gate is open, and another

one closed.

The situation of an eventual maintenance to

the radial gates were also taken into account,

considering the existence of stoplog gates

(scenario 4).

The model built (Figure 4.2) considers the

following points:

The spillway body is modelled as a solid

element, 19,00m thick, and the wall as shell

elements, 4,0m thick. The wall consists of a

1 by 1,0m mesh.

Figure 4.2- Finite elements model performed for

the central pillars

The pillars are built-in the body of the

spillway, while the spillway is supported on

the ground.

8

Table 4.1- Hydrostatic pressure diagram

Action Impulse Diagram

Ba

sin

Hea

dw

ate

r

pre

ssu

re (

segm

ent

ga

te c

lose

d)

Hea

dw

ate

r

pre

ssu

re

(coff

erd

am

ga

te

close

d)

Op

en g

ate

Hyd

rod

yn

am

ic

pre

ssu

re

The seismic tridimensional dynamic

analysis action was represented by spectral

response.

The hydrodynamic effect caused by a

seismic event was considered, admitting that

the water mass is adherent to the pillars. The

hydrodynamic pressure was determined

through the Westergarrd expressions.

In order to support the gates reactions, the

pillars are prestressed with 8 tendons with 19

1,4 cm2 wires each.

Figure 4.3- Layout of the prestress tendon

4.3. Structural design

The pillars design required the safety check

to the following limit states:

1. Last limit state of resistance to

bending

2. Limit state of cracking

3. Limit state of maximum

compression of concrete

4. Limit state of decompression in

the direction of application of the

prestress.

The materials used in the elements structural

design of the reinforced prestressed concrete

were the following (Table 4-2):

Table 4-2-Materials used in the structural design

of the wall

Element Material

Wall Concrete C30/37,

Class XC2

Passive

reinforcement

Steel A400 NR

Prestress

reinforcement

(cables)

Steel Y 1860 S7-15,3

(de according to the

prEN 10138-3)

Prestress

reinforcement

Steel Y 1030 H

(according to the prEN

10130-4)

A # Φ 20//0,15 (20,94 cm2/m) mesh was

adopted in both faces, following the

recommendations of the American standard

ACI-350 [7] and, where it was necessary,

reinforcements were made .

The reduced bending moment evaluation

was made for some areas of the wall, in two

orthogonal directions (Figure 4.4).

9

Besides the transversal loads, the wall is also

subjected to axial loads, which concerns to

an unsymmetrical bending problem. The

axial loads emerge due to the self-weight of

the structure, in a vertical direction, and

prestress, in a horizontal direction.

Figure 4.4- Wall zones for stress analysis

Table 4-3- ELU direction x

Direction x

Sce. Msd

[kNm/m] m

Nsd

[kN/m] u

1 C3 -3200 0,010 -6700 -0,085

2 C5 -980 0,003 -3840 -0,049

3 C5 -7000 0,022 -1130 -0,014

4 C5 -2700 0,009 147 0,002

5 C4 2000 0,006 440 0,006

6 C4 125 0,000 -70 -0,001

7 C3 1100 0,004 -380 -0,005

Table 4-4- ELU direction y

Direction y

Sce. Msd

[kNm/m] m Nsd

[kN/m] u

1 C2 -886 0,003 -5000 0,063

2 C5 -890 0,003 -1600 0,020

3 C5 -7400 0,024 -2600 0,033

4 C5 -810 0,003 -1430 0,018

5 C4 -2500 0,008 -2700 0,034

6 C4 650 0,002 -1600 0,020

7 C3 -1030 0,003 -800 0,010

Since the values of μ are inferior to 0,20, the

adopted resistance classed is appropriate.

Zone 3 is the only zone where the

mechanical percentage of reinforcement was

larger that the minimum reinforcement

required. In this zone, it was adopted # Φ

32//0,15 (53,62cm2/m) mesh reinforcement

in both directions (Mrd=7358,11 kNm).

The verification of ultimate limit state of

cracking consists on the cracks opening

limitation (EN1992-1-1 [7]).

𝑤𝑘 ≤ 0,3 𝑚𝑚 in the reinforced concrete

zone;

𝑤𝑘 ≤ 0,2 𝑚𝑚 in the prestressed zones.

Figure 4.5- Wall zones for stress analysis

Mfreq.

[kN.

m/m]

Nfreq.

[kN/m]

sS

[MPa]

wk

[mm]

3 (dir. x) 7065 1055 166,8 0,20 ✓

5 (dir. x) 1360 -1215 112,9 0,17 ✓

3 (dir. y) 7775 2631 111,4 0,10 ✓

1 (dir. y) 4700 2500 43,5 0,07 ✓

Regarding the limit states of

decompression, the prestressed tendons are

located in an “always compressed zone”, and

so the decompression is verified.

According to EN1992-1-1 [7], the

compression stresses limit in concrete, in a

way that limits the risk of longitudinal

cracking, for the rare load combination is:

𝜎𝑐 = 0,6𝑓𝑐𝑘 = 18,0 𝑀𝑃𝑎

The maximum obtained compression

stresses in concrete occurs in the zone of

application and prestress, and are in the

range of 2,0 𝑀𝑃𝑎 < 18,0 𝑀𝑃𝑎 ✓.

For the trunnion design, it was adopted a

compression-tension model presented in

Figure 4.5:

Figure 4.5- compression-tension model adopted

10

Table 4-5- - Calculation of the transversal

prestressed needed in the trunnions

𝑹𝑵𝑴𝑪

[𝒌𝑵] 𝑭𝒕,𝒔𝒅

[𝒌𝑵] 𝑨𝒔

[𝒄𝒎𝟐] 𝑨𝒔

adopted

𝑷𝒖

[𝒌𝑵]

10458 8824 294 10 bars

Φ40

Y1030H

6989

The net prestress was calculated taking into

account 20% for instantaneous losses and

10% for longterm losses. 10 rebar Φ40

Y1030H, (Figure 4.6) pulled at 75% of the

tensile strength.

Figure 4.6- Transversal prestressed reinforcement

disposition in the gate trunnion.

Two additional layers of passive

reinforcement (Φ25//0,15) were adopted, in

order to resist along with the prestress

reinforcement.

4.4. Conclusions

The conception and structural design of a

WES spillway entails a range of significant

aspects that relate to the complexity and

large dimensions of the construction, as well

as its lifespan (superior to 100 years). This

way, the nature of the spillway requires

special maintenance, in order to guarantee

the structural safety and a proper operation,

in a life cycle cost point of view.

The use of simple design methods, along

with the help of the bidimensional and

tridimensional models built with the finite

elements software SAP2000, enables the

construction design, regarding two elements:

the body of the spillway and the pillars.

Regarding the spillway body design, we

highlight the drainage importance that

diminishes the designing efforts and hence

optimizes the adopted solution. We

demonstrate that is critical to check the

sliding because through the observation of

safety coefficients that are lower in

comparison with the overturning and

fluctuation safety coefficients.

In respect to the pillars design, special focus

should be given to the reinforcement detail.

Such detailing should be done in the simplest

way possible, and thus large fluctuations

regarding the diameter level and adopted

spacings should not exist.

4.5. References

[1] Pinheiro, A. Nascimento (2007),

Descarregadores de Cheias em Canal de

Encosta – Dimensionamento e Implantação,

Instituto Superior Técnico;

[2] NPB. Normas de Projeto de Barragens.

Anexo à portaria n.846/93, Lisboa, 1993;

[3] Quintela, A.C. (1988), “Hidráulica

Aplicada II-Barragens”, Instituto Superior

Técnico;

[4] U.S. Army Corps of Engineers 1995 –

“Gravity Dam Design”;

[5] Eurocode 8- “Design of stuctures for

earthquake resistence, Part 5: Foundations,

retaining structures and geotechnical

aspects”, EN 1998-5:2004.

[6] Eletrobrás (2003), “Critério de Projeto

Civil de Usinas Hidroelétricas”;

[7] ACI 350-01 – Code requirements for

environmental engineering concrete

structures;

[8] Eurocode 2- “Design of concrete

structures, Part 1-1: General rules and rules

for buildings”, EN 1992-1:2004.