Fundamental Research on Creep and Shrinkage of Concrete

It is shown that swelling of hardened cement paste is influenced by two different mechanisms: 1)In the lower vapour pressure region (r.h. < 38%) a reduction of the surface energy of the gel particles leads to an expansion of the single particles.2)In the upper vapour pressure region the whole structure is widened by a change of interparticle attraction in the small gel pores, (disjoining pressure) Both effects can clearly be distinguished. The creep velocity of specimens stored at constant but different humidities increases at values above 40% r.h. This increase can be correlated to that part of the swelling which results from the expansion of the structure of hcp. A theoretical explanation is made through adapting the “Extended Munich Model” and using the “thermodynamic approach”.

The paper discusses the use of activation spectrum theory to produce a practical model of concrete creep behaviour. The model is shown to be attractive because it naturally allows for the complex and readily changeable concrete microstructure; yet there is no need for a detailed description of the microstructure. The validity and practical potential of the theory are demonstrated by: (1) the realistic description of qualitative creep behaviour over all time ranges, (2) the production of an accurate equation for irrecoverable creep at constant temperature. The theory’s potential to produce comprehensive creep prediction equations, and some of the theoretical refinements necessary to achieve it, are discussed.

A method based on the rate theory is developed to describe the total creep deformation, the total strain rate and the apparent free energy of activation curves.At the time where the creep curve starts its tertiary stage, the strainrate-time curve shows a minimum and the apparent free energy of activation has a maximum. This means that during the primary and secondary creep the material is able to build up higher energy harriers against the work contributed by the external effective stress. During the tertiary stage however the material does not have this capacity and starts to break. No assumption is made concerning the micro structural mechanisms of the rate processe, but it can be concluded that during this third stage the propagation of cracks takes place.It was also possible to describe the total σ ɛ, diagram.

Measurements of length changes during drying and rewetting were correlated with weight changes and microstructural data for two hydrated alite pastes. It is concluded that the irrecoverable shrinkage that developed during first drying probably resulted from a rearrangement of the hydrate particles under the action of capillary tension stresses. The irrecoverable shrinkage exhibited a maximum at a relative humidity of about 0.35 which was also reflected in the total shrinkage. Recoverable shrinkage is thought to result from changes in surface energy of the solid phases and capillary tension effects. There was evidence that the change in microstructure during first drying can be partially recovered by the development of a disjoining pressure between hydrate particles during resaturation.

A hypothesis relating to microstructural changes in the cement paste following creep is presented. The changes are such as to render the microstructure of cement paste in a more stable configuration and thereby, to impart ‘pseudo’ strain-hardening to the composite. A part of the irreversible creep in maturing concrete is caused by such microstructural changes which can be taken as a measure of the stabilisation effects. The creep response of concrete under subsequent stress applications is reduced because of the microstructural changes and is a function of the stabilisation caused by the previous stress history. Phenomenological evidence in support of the hypothesis is provided by experimental data on creep under constant and variable stress regime.

The results are reported of shrinkage and swelling tests on tubular specimens of hardened cement paste with a 1mm wall thick-ness. Attention is concentrated on the first cycle of humidity from saturation to complete dryness. The resulting hysteresis and irreversible shrinkage is examined in the light of parallel measurements of moisture movement. For this purpose two states of water are identified by thermogravimetric methods and the two states identified as A — free and adsorbed water and B — water associated with the structure of ettringite and C-S-H gel. Reversible shrinkage is attributed to the movement of type B water, while irreversible shrinkage is thought to derive from the movement of type A water leading to the permanent closing of spaces between hydrate particles; this in turn leads to the formation of additional spaces accommodating type B water.

Cylindrical specimens between 100 and 500 mm in diameter have been used to investigate shrinkage of two different concrete mixes. In addition the influence of varying the composition of the cement paste on shrinkage of concrete was studied using cylinders 160 mm in diameter. Six different paste compositions were tested. Shrinkage was followed for four months under controlled climatic conditions of l8°C and 65% R.H. the final shrinkage being determined by extrapolation. During the first few days variation in the measured shrinkage was influenced by the precision of the measuring technique. However, after a drying period of about one month, the scatter of the materials properties became dominant. The values of shrinkage obtained indicate that the predictions given by the CEB-FIP and various other standards considerably underestimate the deformations caused by shrinkage.

So far only few reports on the variability of creep and shrinkage have been published. In many practical cases, however, it is necessary to know the probability of occurence of extreme values. Therefore four different test series, each consisting of indentical concrete specimens with a given mix proportion, have been prepared. Shrinkage and creep have been measured for 300 days. For the creep experiments a load of 20% and 40% of the corresponding prism strength has been applied. In each test series between four and eight identical specimens have been tested. Experimental results have been evaluated statistically. For shrinkage a coefficient of variation in the range of 0, 07 and 0, 14 was found. For the total time-dependent deformation (creep plus shrinkage) the coefficient of variation after 300 days of loading was found to be between 0, 05 and 0, 10. Creep recovery was measured for 28 days.

The magnitude of creep is regarded as a stochastic quantity, because of random variations of important influential factors. A test-program on a statistical basis has been carried out to investigate the influence of actual variations of the concrete composition (wcr;acr), on creep. The 28-day creep tests (under compression) were performed at 25 °C; 50% RH as well as at two ambient conditions with alternating temperature and relative humidity, derived from the real conditions in The Netherlands. Portland and Portland blast-furnace cement was used in the test program. It is concluded that extensive variations of the creep deformations will be caused by actual variations of the water-cement ratio’s, and by variations of the temperature even in the normal range.

The variation of reversible and irreversible creep of compact structural concretes with strengths of 13, 5 to 45 MPa was studied experimentally as a funktion of age of concrete at the load application.It is shown that the variation of the reversible creep is influenced by the interaction and the time development of two factors namely of gradual development of microdestructions and the factor of development of hydration products in the time under loading.The obtained experimental results are compared with the time development of the coefficient of reversible and irreversible creep given in the CEB-FIP 124/125 Recommendations of April 1978.

Experiments to check the principle of superposition have been carried out on concrete test pieces subjected to permanent compressive stresses.A series of test pieces was loaded under a stress σ at 7 days another under the same stress at 28 days and a third series was loaded from 7 to 28 days under a stress σ, the stress then being doubled at 28 days. Deformation after 1700 days loading was measured under three stresses (25, 50 and 75 bars).The BOLTZMANN principle of superposition is proved valid by interpretation of results taking into amount the different types of testing inaccuracies although there remaind a difference of 10% between theory and test figures.

The general kinetics of concrete drying is now known and can be determined for each particular case by gamma-ray absorption measurements. Time-dependent variations in water content and its distribution within a concrete element is such that, in most cases, specimens subjected to creep testing are far from being homogeneous from the viewpoint of water content.It is possible by means of different hypotheses to deduce the new stress distribution from the difference in water content, i.e. the difference in behaviour between the internal concrete which remains saturated for a long time and the peripheral concrete which dries very quickly.The significance of this rapid distribution has been confirmed by experimental observations.As a result, it can be said that: in most creep tests, specimens are not subjected to a continuous uniform stress;the phenomena involved are not all the same for a loaded specimen and for a control specimen;the cracking of structures in service is not necessarily related to tensile stress in the considered zone.

Using the principle of superposition, we may write for the total strain e at any time t: (1a)$$ \varepsilon \left( t \right) = \frac{{\sigma \left( {{\tau _o}} \right)}}{{E\left( {{\tau _o}} \right)}}\left[ {1 + \varphi \left( {t,{\tau _o}} \right)} \right] + \int\limits_{\tau = {\tau _o}}^t {\frac{{\partial \sigma \left( \tau \right)}}{{\partial \tau }}} \bullet \frac{1}{{E\left( \tau \right)}}{\text{[}}1 + \varphi \left( {t,\tau } \right)] \bullet {\text{d}}\tau $$and with a constant modulus of elasticity(1b)$$ {\varepsilon _t} = \frac{{{}^\sigma o}}{E}\left( {1 + {\varphi _t}} \right) + \frac{{{}^\sigma {t^{ - \sigma }}o}}{E} + \frac{1}{E}\mathop \int \limits_{\tau = {\tau _o}}^t \frac{{\partial \sigma \left( \tau \right)}}{{\partial \sigma }} \bullet \varphi \left( {t,\tau } \right) \bullet d\tau $$ With this principle of superposition only, one has to solve creep problems (i.e. calculation of deformations under a known stress history) as well as relaxation problems (i.e. determination of the stress at any time under specified conditions of strains or deformations).

In connection with the development of the pressure vessel of a nuclear reactor, extensive tests have been carried out to determine the rheological properties of a concrete subjected to a temperature of 200°C. The paper includes a description of the tests along with the presentation and discussion of the results.

The deformation characteristics of unsealed concrete specimens during heating have been studied in connection with fire research and a hypothetical core failure in a nuclear reactor. A substantial increase of creep rates was observed during the temperature increase in the concrete. It is not possible to compare the non-steady state creep with those creep deformations, which have been observed under isothermal creep conditions. Even if concrete is treated as a material without memory and the appropriate law of superposition is applied the deformations under transient (rapid heating) conditions cannot be described by creep laws being derived under isothermal conditions. The test results suggest a creep law, which is directly related to the concrete deformations being observed under transient temperature conditions.

Open air measurements made during testing in Jeddah, Saudi Arabia, were taken to demonstrate to what extent the usual stipulated values for limit shrinkage value and the chronological progress of shrinkage as set forth for concrete structures in moderate climates have to be modified for hot and dry regions. In the progress of testing, the influence of various curing and positioning conditions was simultaneously investigated in order to obtain data on intended reduction of the shrinkage deformations. The limit shrinkage values determined thereby for various concrete compositions were significantly greater, and were reached in shorter time, than can be calculated, for example, in formulas given in German standards.

Results are given of an investigation into the influence of symmetrically placed reinforcement upon the drying shrinkage behaviour of a range of concretes. It is shown that the observed shrinkage is influenced both by the level of reinforcement and the Young’s modulus of the concrete, and that the average tensile stress induced in the concrete can be higher than the short term tensile strength of comparable plain concrete specimens. Estimates of the magnitude of the specific creep showed no obvious dependence upon curing period, mix proportions or induced stress level.

A method is proposed for the interpretation of creep on flexed beams. Local deformations measured on longitudinal lines on the beam are taken into account to calculate a deflection curve Cf; it is supposed that the hypothesis of linearity can be adopted for this calculation, in spite of the big dispersion of the measures. A theoretical value Cth of the deflection is obtained from the consideration of creep laws applied to longitudinal fibers, laws which are derived from tests on samples under uniaxial compression. Comparison between Cf and the measured deflection Cm gives an information on the structural behaviour of the beam, between Cth and Cf and Cm allows to test the validity of applying to flexion creep laws of uniaxial compression.Four examples are given but more experimental data is needed to be able to have general conclusions.

The submitted paper deals with the behaviour of cement pastes in their early period of hardening. The proposed method enables to carry out measurements of volume changes from the first setting phase of the measured sample. The measurement is made in a special device by the contact way with the aid of inductance transducers. The mould of this measuring device has profiled movable fronts which transfer the length changes of the investigated sample to inductance transducers. The method can be applied for measuring volume changes of cement pastes, mortars and concretes.

A representation is introduced for the linear and non linear behaviour of concrete in the presence of time varying humidity, based in the state variables concept.

To get a tool for theoretical studies of drying shrinkage effects in different complex situations, material parameters, determined by fitting of shrinkage data in accordance with constitutive relations based on thermodynamics, are presented. The necessary fundamental data of basic creep and shape of free shrinkage in time are chosen according to some practical formulations, and for a number of shrinkage data sets and for two different creep functions, the obtained material parameters refer to a typical ordinary concrete and a typical cement mortar.

Various prediction methods for creep of concrete are compared with experimental data and evaluated by statistical methods. Predicted creep functions exhibit average coefficients of variation between 25, 0 and 39, 3 percent. Average errors of a final creep coefficient may range from 23, 2 to 61, 9 percent depending on the particular method considered. In a detailed evaluation the sources of errors are pointed out.

A composite theoretical method is demonstrated which predicts the rheological parameters applying to concrete — including the Young’s modulus and the shape of the creep developing function. Only three parameters control the creep function. These are the Young’s modulus, E_c, the delayed elastic coefficient, α_c, and the flow modulus, K. They are all three related in a simple way to concrete composition. That is water- and aggregates/cement ratios, W/C and A/C. The resulting creep function is dependent on the time of very first loading. Thus, the phenomenon of consolidation is included. The prediction method is consistent with methods of creep analysis previously developed by the author. These are the so-called Modified- or Improved Dischinger Methods.

Measured strains on concrete columns of two high-rise buildings and on three segments of one long span post-tensioned concrete box girder bridge are reported. For each structure, standard creep and shrinkage measurements were made on samples of concrete used in the structure.

Analysis of restrained concrete structures for creep and shrinkage. Examples of the detrimental effects of these internal strains are illustrated. A method of analyzing and designing for internal strains is presented in three case studies. The case studies are 1) a long span girder; 2) a deep beam; 3) a ring slab system. Each case is analyzed by computer and finite element techniques. The results are compared to the physical condition and were found in agreement.

The creep and shrinkage observation was made by various prestressed bridges. The results of long-term observations were shown by cantilever method erected bridges and one cast in place frame bridge. The strains were measured by checoslovakian vibro-wire embedded gauges. The results showed, that the Dischinger theory is acceptable for generally calculation of the creep on this type of structures.

An analytical method is described by which shrinkage stresses and deformations in concrete members are predicted. Nonuniform, time-dependent free shrinkage in structural concrete members is modeled by a diffusion equation. The moisture dependence of diffusivity and surface factor are considered. A finite element method is used to solve the nonlinear shrinkage diffusion equation. Inelastic properties and creep characteristics of concrete are considered in calculating the effect of nonuniform shrinkage on stress, deformation, and cracking. Predictions of shrinkage for various sizes of prism are compared to experimental data with good agreement. The effects of ambient relative humidity, surface conditions, and the material characteristics of concrete on shrinkage are discussed.

Large span bridges constructed according to the cantilever method may show considerable deflections because of creep and shrinkage. In order to achieve correct alignment the shuttering of every corbelling section in the construction of a bridge of this type should be adjusted to a certain excess heights The computation of these excess heights is very complex because of the many stages and load changes during the construction. To simplify these computations a computer program has been developed. With this program the construction of a bridge can be simulated completely. The time- dependent deformations are computed according to the CEB-FIP Model Code for Concrete Structures 1978 (l).

A typical case study is used to demonstrate the basic requirements which must be met by structural programs for creep and shrinkage analysis. Specifically, the condition that the sequence of construction-phases and the corresponding load history are to be modelled properly plays a dominant role in the design of the program architecture. In addition, some results of the numerical analysis are shown compared with those obtained by measurements.

A three-dimensional finite element creep analysis has been developed in which a special provision has been made for creep and creep recovery. Computer programmes have been developed to assess the influence of thermal creep on the operational behaviour of complex structures. The work has application to prestressed concrete nuclear reactor pressure vessels and to concrete gravity platforms for the storage of oil at sea. The results obtained illustrate the significance of creep and temperature on the stress behaviour of nuclear and oil containment structures.

Geometrically nonlinear viscoelastic deformations of shell structures are analyzed. On the basis of linear viscoelastic materials the stress-strain relations of orthotropic layers are developed. The inelastic effects of viscoelasticity are inserted into a computer code by means of the principle of virtual work, and the resulting integration technique leads to nonlinear equations which are solved by the modified Newton-Raphson method. Examples of the viscoelastic collapse of shell structures are given.

If the axial force and the bending moment are linearly dependent on the concrete relaxation function, the accurate values of stresses and displacements can be obtained through algebraic expressions. This procedure is a generalization of the well-known Bažant method{l}, which yields the accurate algebraic stress- strain relation for concrete, provided the strain is a linear function of the creep coefficient.

The solution of the relaxation problems that occurs very often in engineering practice when calculating the concrete structures is very complicated unless the calculations are based in the elementary methods as on the rate-of-creep method or perhaps on the principle of delayed elasticity. The more exact calculation of the stresses relaxation regarding the more complex expressions for the creep is rather tedious because the use of an iterative method is unavoidable. So it is when the creep and shrinkage predictions proscribed in the Recommendations of CEB-FIP (1978) are used, and thus the calculation of the stresses in the case of sustained deformations should be done by some iterative way which of course is not too favourite among the engineers.

Using the equivalent tensile force method predictions are made of the shrinkage induced curvature of reinforced concrete beams. It is shown that the predicted curvatures for uncracked concrete beams are in close agreement with published experimental data on singly and doubly reinforced beams. It is also shown that the total predicted curvatures, due to a combination of elastic movement, creep and shrinkage, of partially cracked beams are in approximate agreement with published data obtained by Stevens (6).

Les problèmes des effets différés pour des structures linéaires formées d’éléments viscoélastiques et purement élastiques sont traités sur la base d’un système général d’équations algébriques, établi à partir de la méthode classique des forces. L’étude de cas particuliers conduit à un système simplifié d’équations, puis à la formation d’équations indépendantes. La résolution de quelques problèmes types illustre cette méthode.

Une structure continue, réalisée par la liaison sur appuis entre des éléments préfabriqués, présente deux particularités: la transformation du système statique ayant pour conséquence une redistribution des effortsla présence de joints qui diminuent la continuité et la transmission des efforts sur appuis.

Un modèle bilinéaire est proposé pour le comportement à l’état de service des dalles en béton, compte tenu de la fissuration et des effets différés. Il permet de calculer la valeur intermédiaire de la flèche probable située entre les valeurs extrêmes en stades homogène et fissuré. La comparaison avec les résultats d’essais de longue durée est satisfaisante.

The static analysis of linear visco-elastic homogeneous structures subjected to additional delayed restraints introduced after the application of loads can be easily performed if the additional restraints are introduced all together. If the delayed restraints are introduced at different times, the state of stress in the structure has on the contrary to be determined following step-by-step the variation in time of the structural scheme. The paper presents the general solution of the problem under the hypothesis of elastic modulus constant in time and assuming that the initial structural scheme is statically determined. The solution is applied for the evaluation of the state of stress in a simple structure with two delayed restraints.

Creep causes a variation of the state of stress in redundant slender R.C. structures because the deformations of the single parts are not related by affinity and depend on the applied axial load. The general method of analysis of slender R.C. frame structures in which lateral displacements are prevented leads to a set of systems of integro-differential Volterra equations and is of rather complex application. For this reason an approximate procedure is presented, based on the Age Adjusted Effective Modulus Method (AAEMM) which allows to solve the problem through a particular elastic analysis especially recommended for practical uses. Two numerical examples show the application of the Method.