Creep of Dam Concrete-j.1475-1305.2011.00818.x

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Creep of Dam Concrete Evaluated from Laboratoryand In Situ Tests

C. Serra, A. L. Batista and A. Tavares de Castro

Concrete Dams Department, National Laboratory for Civil Engineering, Av. do Brasil, 101 Lisbon, Portugal

ABSTRACT: One of the most important phenomena of the delayed behaviour of mass concrete used in dams is creep, i.e., the increase in

deformation over time when subjected to constant stress. Although several studies concerning concrete creep were carried out throughout

the last decades in a structural and material level, the physical and chemical phenomena are yet to be fully understood. This paper presents a

study on the Alqueva dams concrete deformability in which a parameter evaluation was performed using the Baz ant and Panulas basic creep

function, based on both in situ and laboratory creep test results. In the first part of the paper, the approach and material properties that

better fit the experimental data of a dams mass concrete are presented. In the second part, the fitted function for each in situ test was

validated using a finite element numerical model that takes into account the time-dependent behaviour, the applied stress and the monitored

temperatures.

KEY WORDS: concrete creep, dam concrete, FEM analysis, in situ and laboratory tests, non-linear regression models, prediction models

NOTATION

t time, age of concrete (days)

t0 age of concrete at loading (days)

J(t, t0) creep function strain (creep strain plus

instantaneous strain) at timetcaused by a

unit uniaxial constant stress at age t0 (GPa)1)

E(t0) modulus of elasticity at age t0 (GPa)

e(t, t0) total strain

r(t0) applied stress (MPa)

ei(t0) instantaneous strain

ec(t, t0) creep strain

e

0

(t) prescribed strainef(t, t0) specific creep (GPa

)1)

eesp(t, t0) specific strain (GPa

)1)

etotal(t, t0) experimental total strain

eautog(t, t0) experimental autogenous strain

fcilc t0 cylinder compressive strength at aget0 (MPa)

fcubec t0 cube compressive strength at age t0 (MPa)

fc,k k-day cylinder compressive strength (MPa)

Ec,j j-day modulus of elasticity in compression (GPa)

w/c water/cement ratio of concrete (by weight)

a/c aggregate/cement ratio of concrete (by weight)

s/c sand/cement ratio of concrete (by weight)

a/g aggregate/gravel ratio of concrete (by weight)

q unit mass of concrete (kg m)3)

v Poissons ratio

Introduction

One of the most important phenomena of the delayed

behaviour of mass concrete used in dams is creep, i.e. the

increase in deformation over time when subjected to con-

stant stress. Although several studies concerning concretecreep were carried out throughout the last decades in a

structural and material level, the physical and chemical

phenomena are yet to be fully understood. Some studies

suggest that creep is related with displacement diffusion

mechanism, adsorbed water movements on the surface of

the hydrated cement, viscous deformation of the hardened

cement, solubility increase with the applied stress and

atomic rearrangement at the nanoscale [13].

Concrete creep is influenced by intrinsic factors, such as

the properties of each component, the mix proportions

and the concreting conditions, as well as by external fac-

tors, such as, for example, the loading age, the temperature

and humidity levels, the intensity and type of loading

[4, 5]. The mass concrete used in dams presents particular

characteristics and maturity conditions over time and

needs to be studied in detail. In addition, only a few

studies related directly to this matter and which are based

on long-term in situ experimental results have been pre-

sented [69].

The majority of the concrete creep laws currently avail-

able were developed taking into account the results of testscarried out mainly with concrete from buildings and

bridges [10, 11]. Throughout the last decades, the work

developed at Northwestern University and by FIB, ACI and

RILEM extended the experimental database to several types

of structures, including dams, to achieve a more universal

expression for the phenomenon of concrete creep and

shrinkage [12]. Each creep law is normally sustained by an

empirical or analytical formulation that determines the

expected creep values using parameters such as the con-

cretes ultimate compressive strength or the concretes mix

data.

Research carried out at the National Laboratory for Civil

Engineering (LNEC) led to the conclusion that the creep

function and prediction suggested by Bazant and Panula

(BaP), known as the Double Power Law, is adequate to

2011 Blackwell Publishing Ltd j Strain (2012) 48 , 241255 241doi: 10.1111/j.1475-1305.2011.00818.x

An International Journal for Experimental Mechanics


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predict dam concrete behaviour [1315]. Therefore, the

BaP law is the basis of this study. In the first part of this

paper, the approach and material properties that better

fit the experimental data of a dams mass concrete are

presented.

In the second part of this work, it was possible to validate

the fitted function for each in situ test using a finite-element numerical model that takes into account the time-

dependent behaviour, the applied stress and the monitored

temperatures.

Determination of Creep Strains

Definition of creep strains

Total strain, e(t,t0), resultant of the stress, r(t0), applied at

the aget0and kept constant untilt, can be expressed as the

sum of an instantaneous strain, ei(t0

), and a creep strain,

ec(t,t0), to which a prescribed strain, e

0(t), can be added

(shrinkage/expansion):

et; t0 eit0 e

ct; t0 e0t (1)

The instantaneous and creep strains can be expressed as a

function of stress, defining the creep function, J(t,t0), as the

strain per stress unit:

Jt; t0rt0 eit0 e

ct; t0 (2)

Jt; t0 1

Et0eft; t0 (3)

eft; t0 ect; t0

rt0 (4)

Measurement of creep strains

In conventional concrete dams, the full-mixed concrete is

made, in general, with a low cement dosage (between 150

and 200 kg m)3) and aggregates with the maximum

dimension of 150 mm. These characteristics are very dif-

ferent from those of the concrete used in buildings and

bridges.

The accurate evaluation of the full-mixed concrete

deformability is a key element in the dams behaviour

assessment, whether to calibrate displacements based on

prediction models or to interpret the behaviour using

structural models.

Because of the large size of the aggregates, it is difficult

and expensive to wrap most monitoring devices and make

sustainable test specimens in full-mixed concrete. There-

fore, wet-screened concrete is more frequently used. This is

obtained from the full mixed by sieving aggregates greater

than 38 mm or 75 mm.

Thus, as it is of interest to make in situmeasurements of

concrete properties, creep tests are carried out on site with

both full-mixed and wet-screened concrete giving us thepossibility of evaluating the influence of screening on the

concrete behaviour. In the laboratory, it is only possible to

perform experimental long-term tests with wet-screened

concrete.

The characterisation of the wet-screened concretes

deformability enables the data interpretation obtained

from the embedded devices, such as strain and stress

meters, and allows the comparison between in situ and

laboratory creep test results.The in situ tests are possible with full-mixed and wet-

screened creep cells installed within the dam body, which

allow the determination of the modulus of elasticity at any

age and the creep strains time-history.

Creep cells are concrete cylinders embedded in the dams

body, subjected to the same thermohydrometric condi-

tions as the dam body, because the top of the cell is in

contact with the structural concrete, but isolated from the

stress field with a steel frame that creates an overall gap

between the cell and the dams concrete (Figure 1). The

experimental apparatus for each type of concrete is com-

posed by a creep cell subjected to a controlled stress, known

as active cell, and by another cell with free deformation,

known as non-stress cell. The first contains an embedded

Carlson strain meter that registers the total strain varia-

tions over time, etotal(t,t0), and the second contains another

strain meter that measures the stress-independent strains,

known as the autogenous strains, eautog(t,t0). As both cells

(active and non-stress) are concreted with the same mate-

rial, at the same time and are placed next to each other, it is

assumed that they are subjected to the same environmental

conditions. In addition, it is considered that the creep cells,

embedded within the mass concrete, are saturated because

of the water supply on the upstream face of the dam in

contact with the reservoir.The loading system of each active creep cell is composed

by a closed hydraulic circuit that controls the applied

pressure on a flat jack on the base of the concrete cylinder.

The pressure can be kept constant with the aid of a mixture

of oil and nitrogen stored close to the creep cells (Figure 2).

This loading system allows fast stress variations to be ap-

plied in order to carry out modulus of elasticity tests at a

given age and ensures constant load for long periods of

time.

The traditional laboratory setup is used to obtain exper-

imental results of delayed deformations under constant

environmental conditions. In this study, the laboratoryapparatus involved copper-sealed specimens of wet-

screened concrete, to avoid water losses.

The specific strains, considered to be a measurement of

creep, are obtained by subtracting the autogenous strains,

measured in the non-stress cell, from the total strains,

measured in the active cell, and dividing by the applied

stress (Equation 5) [16].

eespt; t0 etotalt; t0 e

autogt

rt0 (5)

If stress is maintained constant since the first load, one

can compare experimental specific strains, eesp(t,t0), directly

with theoretical specific creep, ef

(t,t0).The complexity and variables involving the delayed

behaviour of the concrete requires planning and controlled

242 2011 Blackwell Publishing Ltd j Strain (2012) 48 , 241255doi: 10.1111/j.1475-1305.2011.00818.x

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concreting conditions. For the analysis of each creep cell

and laboratory specimen results, it is necessary numerous

related data, such as the concretes mix proportions, the

ultimate compressive strength and the modulus of elastic-

ity at different ages.

Methodologies for the Creep FunctionEvaluation

Prediction models

Creep prediction models give a first estimation of the

delayed deformations using required measured concrete

properties. These models are useful in the design stage and

when there are no specific test results available. In impor-

tant structures, such as large dams, specific and extensive

tests are commonly carried out to determine the concretes

compressive strength, modulus of elasticity and creepstrains, although major direct and delayed costs [17].

The prediction models are based on functions that

translate the physical phenomenon. The function param-

eters, usually obtained from known material properties

and, whenever possible, adjusted to experimental results,

allow creep strains estimation, considering established

hypothesis.

There are several formulations for the prediction of the

delayed deformations [11, 14, 1820]. However, studies

carried out at the National Laboratory for Civil Engineering

(LNEC) since the 1980s [4, 21, 22] have shown that the

prediction model proposed by BaP between 1975 and 1979

[1315], known as the Double-Power Law, provides a good

fit to the general monitoring results of the Portuguese

concrete dams [4].

The advantage of this type of function is the fact that

creep is computed as the sum of both basic and drying

creep. The basic creep holds the maturity process by

including a power of the age at loading, t0, and a power of

the time since loading, t) t0 (Equation 6).

Jt; t0 1

E0u1E0

tm0 att0n

(6)

whereE0, u1, m, a and n are given parameters.

The prediction of the static modulus of elasticity is

considered to be the inverse of the creep compliance con-

sidering 0.1 days as the loading time (Equation 7) [15].

Figure 2: View of the non-embedded devices of the creep cellloading system

Figure 1: Representation of the active and non-stress creep cells for both full-mixed and wet-screened concrete

2011 Blackwell Publishing Ltd j Strain (2012) 48 , 241255 243doi: 10.1111/j.1475-1305.2011.00818.x

C. Serra, A. L. Batista and A. Tavares de Castro : Creep of Dam Concrete Evaluated from Tests


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1

Et0

1

E0u1E0

10ntm0 a (7)

The parameters can be obtained by two different empir-

ical formulations. The first relies on the 28-day ultimate

concrete compressive strength, fc,28, and on the concretes

mix data (Equations 815) [15].

u1 103n

228m a (8)

a 1

40w=c (9)

m 0:28 47:541f2c;28 (10)

n 0:12 0;07x6

5130x6 sex >0

0:12 sex 0

(11)

x 2;1 a=c

s=c1;4 5;523 103f1;5c;28

w

c 1=3 a

g 2;2

" #a1 4 (12)

a11:0 cementtypeI ouII general0:93 cementtype III fast hardening1:05 cementtypeIV low hydration heat

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Creep of Dam Concrete-j.1475-1305.2011.00818.x