Multiscale Coupled-Hygromechanistic Approach to the Life-Cycle Performance Assessment of Structural Concrete

Maekawa, K.; Ishida, T.; Chijiwa, N.; Fujiyama, C.

doi:10.1061/(ASCE)MT.1943-5533.0000984

Open access

Technical Papers

Nov 15, 2013

Multiscale Coupled-Hygromechanistic Approach to the Life-Cycle Performance Assessment of Structural Concrete

Authors: K. Maekawa [email protected], T. Ishida, N. Chijiwa, and C. FujiyamaAuthor Affiliations

Publication: Journal of Materials in Civil Engineering

Volume 27, Issue 2

https://doi.org/10.1061/(ASCE)MT.1943-5533.0000984

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Abstract

Moisture and cracks are scourges of structural concrete, and understanding the multiscale interactions between the two is key to determining long-term durability performance. This paper uses three-dimensional integrated micromaterial structural modeling to address moisture migration/balance and associated volume changes of concrete with creep in prestressed concrete bridge viaducts that are experiencing excessive deflections. It is found that moisture migration–related deflections driven by the capillary surface tension and disjoining pressures in cement micropores account for 25 to 45% of the macroscopic deflections. These apparent kinematics can be approximated by adding the moisture-related time-dependent deflections to the mechanistic-induced creep by external loads. This paper also addresses water–crack interaction in cracked RC bridge decks under moving loads in view of the coupled hygromechanics. It is found that the water presence on the upper deck parts, when subjected to high-speed traffic, can shorten the fatigue life of the deck by one-and-a-half order of life span. This reduction in life is discussed in terms of high-water pressure developing over large numbers of wheel passages, in addition to the reduced shear transfer along crack planes.

Introduction

Currently, many worldwide bridges are severely deteriorated. This accounts for approximately 25% of the total RC bridges [National Institute for Land and Infrastructure Management (NILIM) 2011] in Japan, and approximately 15–42% of national roads or all roads, respectively, in Europe (Daly 2000). Concerns over durability have grown because serviceability for safe transportation is seriously affected. Cracking appears to be the most prevalent factor that haunts the durability of RC. RC bridge decks are particularly susceptible to cracking. Owing to wheel load movement, surface cracks may form, existing cracks may propagate—either open or close and slip—and become the driving factor for the accumulation of fatigue damage. Internal cracks, owing to wheel movement, can also play a latent role in RC deck deterioration. At the beginning stage of deterioration, these cracks are invisible from the outside and cannot be easily detected, but they may propagate and become the triggers for potholes and spalling of the concrete cover (Matsui 1987).

Water is another prevalent factor in destructive mechanisms. Because water exists between crack planes, high water pressure may develop when subjected to high-speed traffic (Maekawa and Fujiyama 2013). This phenomenon was experimentally and analytically found to worsen fatigue life (Maekawa et al. 2006; Matsui 1987). In addition to its presence in cracks, the migration of water in concrete micropore structures been recently found to affect the serviceability of prestressed concrete (PC) bridges. Although water inside the concrete pores obviously migrates at a slow rate, it is responsible for a significant portion of the excessive deflections observed in many PC bridges (Ohno et al. 2012; Maekawa et al. 2011).

Although cracks and water are clearly two interlinking scourges of concrete bridges, engineers have approached these problems separately. From the standpoint of material engineers, it is of interest to develop a concrete with satisfactory crack control (Li 2003). However, when used in bridge decks, the material has met limited success, possibly owing to the snowball effects of water (Mitamura 2007) and shear at cracks (Suryanto et al. 2010). From the viewpoint of a structural engineer, it is of interest to use posttension forces on one hand to satisfy structural requirements, and on other hand to maintain the concrete in uncracked states. The water-induced time-dependent behavior, if not carefully anticipated in design, may become the critical limit states for long-term serviceability, as is currently occurring in many PC bridges worldwide (Bazant et al. 2010; Burdet 2010; Hata et al. 1993). Clearly, water–crack interaction is complex, involving circumstances at various scales from microconcrete pores to macrostructural scales.

Given the complexity of the problems at hand, the authors have developed a multiscale, multichemophysics analysis of structural concrete, namely DuCOM-COM3 (Maekawa et al. 2008). This platform is used to predict the serviceability of PC–RC bridges in practice. The static capacity of RC members under high self-desiccation and the life assessment of bridge decks under moving loads are also conducted to investigate the effects of water–crack interaction based upon the coupled microdurability and macrodurability mechanism. In this study, the unified approach is taken to the practical issues in the use of coupled hygromechanics with multiscale concept developed in the past decade.

Analysis Platforms: DUCOM and COM3

The coupled DuCOM-COM3 (Maekawa et al. 2008) proposed in this paper is a multiscale analysis platform that links DuCOM (Maekawa et al. 1999) and COM3 (Maekawa et al. 2003), which were developed in the past decades, as shown in Fig. 1. DuCOM is a microdurability platform, capable of simulating cement hydration, micropore structure formation, and mass transport in concrete ranging from nm to μm scales, whereas COM3 is a 3D mesoscale platform to handle mechanistic actions for structural concrete ranging from mm to m scales, with in-depth considerations of time-dependent, cyclic, and fatigue behavior of uncracked and cracked concrete.

Fig. 1. Schematic illustration of DuCOM and COM3

If the intentions are to trace the change in concrete material properties, to consider the effects of ambient conditions, and to take these effects into account for predicting the response of structural concrete, DuCOM-COM3 might be the current practical choice. If the intentions are to trace the time-dependent responses of RC structures under short-term dynamic, long-term sustained, and fatigue loading conditions, with few impacts from ambient actions, the single task–based code COM3 is recommended for simplicity. Recently, Maekawa and Fujiyama (2013) incorporated the mesoscale model of water inside cracks. Here, the anisotropic nature of water motion through crack planes is treated with the multidirectional crack concepts, making it appealing for studying water–concrete interaction in a detailed manner.

Because DuCOM-COM3 is composed of many material and structural model formulations, verification of different scales in each chemophysics event is of critical importance, as is verification at the large-scale level of infrastructures. The careful experimental verification of the microscales and mesoscales has been conducted (Maekawa et al. 2008) in terms of (1) micropore size distribution, (2) rate of heat hydration, (3) cyclic moisture isotherm based upon the thermodynamic theorem, (4) gaseous and liquid diffusivity through the pores, (5) pore humidity in cement paste, (6) autogenous shrinkage, (7) free stress volumetric change by drying, (8) apparent creep at wider range of temperature, (9) shear stress transfer across crack planes, (10) tension stiffness and softening, and (11) compression softening. Furthermore, the verification at the level of structural members is indispensable. The platform in this study has been examined and checked (Maekawa et al. 2009) by using the experimental data of (1) in-plane and out-of-plane shear of RC panels; (2) shear failure of RC beams and slabs with different reinforcement ratios, strength of materials, and effective depths; (3) creep deflection of beams and slabs under sustained loads; (4) highly cyclic fatigue life of RC beams and slabs; (5) low-cycle dynamic responses and ductility of RC columns and shells; (6) shaking table tests of structural concrete; (7) capacity of corroded RC beams and ducts; (8) cracking patterns of corroded members. This paper is primarily focused on the real-scale infrastructures as an integrated simulation of many microscaled behavioral simulations.

Here, users of the platform are requested to input (1) concrete mix proportion, (2) composition of cement minerals, (3) specific gravity of cement and aggregates, (4) absorption ratio of aggregates, (5) initial temperature of fresh concrete, (6) ambient temperature and humidity, (7) dimension and shape of the target structure by discretizing the analysis domain into finite elements, (8) location and amount of reinforcement. It is not necessary for users to input the strength of concrete and its mechanical properties such as creep, shrinkage, temperature rise, diffusivity, and permeability, because these are computed inside the platform as variables.

Long-Term Deflection Simulations of PC Bridges

In this section, emphasis is given to the characteristics of the integrated DuCOM-COM3 analysis, not only in predicting the deflection of long-span prestressed concrete viaducts, but in explaining two primary factors triggering the excessive deflections: mechanically and thermodynamically induced components in time.

Modeling

Four old long-span PC bridges in Japan are modeled: Tsukiyono, Konaru, Fukatani, and Urado Bridges. Fig. 2 shows a summary of the time-dependent constitutive model used in this study, linked with moisture states in the fine pores of concrete (Asamoto et al. 2006), and dimensions of each bridge (Ohno et al. 2012). The cement hydration model and micropore formation provide the total porosity and pore size distribution of hardening cement paste based upon the ambient temperature and cement mineral compounds. The use of these micropore spaces may solve the moisture saturation of the interlayer, gel, and capillary pores by using thermodynamic requirements for vapor and condensed water. This information is forwarded to the solidification modeling, as shown in Fig. 2. In accordance with the hydration process, the step-by-step cluster formation is assumed, consisting of fictitious dashpots, which represent the microkinematics of moisture. The summation of cluster stress is assumed to be the total stress in concrete composite. Then, the creep coefficient and drying shrinkage are not necessary to be input for computation, because these characteristics are automatically considered on a multiscale basis. For example, when the moisture is lost by drying, the capillary surface tension and the disjoining pressure are created, and these internal forces are used as a driving force to deform the fictitious dashpot units, as shown in Fig. 2.

Fig. 2. Time-dependent creep model and targeted bridges

All of the bridges have a hollow shaped girder with varying depth. In the analysis, these bridges were modeled as statically determinate cantilevers, representing the girder above the support to the hinge at the center span, with the exception of Fukatani Bridge, on which the center hinge was connected after 10 years.

Fig. 3 shows the finite-element discretization representing the geometry of the bridges. The element size near the structural surface exposed to ambient atmospheres is set on the order of mm-scale owing to the high gradients of the local moisture and the pore water pressure at early ages. The element length along the longitudinal direction is assumed to be 0.5–1.5 m. To avoid shear-locking of the finite elements, enhanced strain formulation is applied (Kasper and Taylor 1997). For this flexure-dominant mode, the selected sizes are confirmed to be efficient, satisfying thermodynamics and mechanistic requirements. The monthly average temperature and humidity are considered to occur at the inside and outside surfaces of the girders, except for the outmost top surface, in which moisture migration is considered to not occur owing to the presence of pavement.

Fig. 3. Discretization of the targeted bridges, showing only half models

The live load is not considered; instead, just self-weight is considered. The prestressing forces are simulated by applying prestrains to the tendon elements that were anchored to the concrete two weeks after concrete casting. In analysis, this is considered to be the time that the deflection started to progress, as opposed to the time at the completion of one-span construction (approximately six months). Time steps of 0.01 and 25 days are considered at early ages and after a couple of months (when local moisture gradients had stabilized), respectively.

Analysis Results

Fig. 4 shows the comparisons of the measured, design predicted, and analysis predicted deflections of the bridges. As shown, the analysis reasonably estimates the measured deflections in the past decades, whereas the design code predictions based upon the basic creep under moisture states provides significant underestimations, especially after 10 years, although the design code formulae almost match the initial deflection up to 2 years after construction. The case of Urado Bridge is exceptional. The design code model seems to provide reasonable predictions. However, in this case, the design creep coefficient is intentionally set approximately 60% higher than the code specification for safety, because Urado Bridge was the first challenge of a long-span PC viaduct over 100 m in Japan. The fluctuations in the analysis predicted deflections are caused by temperature and humidity seasonal variations.

Fig. 4. Comparison of predicted and observed long-term deflections of the four bridges

Roles of Thermohygro and Mechanistic Creep

To develop a better understanding of the mechanisms affecting excessive deflections observed, three parametric analyses are made: Case I, with full exposure to ambient atmosphere and no loads; Case II, considering self-weight and external loads, but no internal driving forces provoked by concrete drying in the concrete micropores; and Case III, considering all interactions. Thus, Cases I, II, and III represent the thermohygro, mechanistic, and apparent creeps, respectively. The ambient temperature and relative humidity (RH) are maintained at 15.8°C and 67%, respectively.

The deflection of Case I is primarily associated with the different volumetric shrinkage and amount of reinforcement of the upper and bottom flanges, because the rate of water loss from both flanges differs owing to different thicknesses. The fictitious deflection of Case II is attributed to both concrete basic creep under wet conditions and deformational restraint by reinforcement. In this case, time-dependent plastic flow proceeds, but the computed fracturing associated with microcracking is negligibly small. Thus, much less material damage is accompanied in this analysis.

Fig. 5 shows the parametric analysis results. The contribution of the thermohygral deflection (Case I) is notable at approximately 25–45% of the total deflection. Clearly, full consideration of moisture transport in small concrete pores is critical. Furthermore, the deflections of Case III are consistently similar to those of Cases I and II added together, although each is highly nonlinear with regard to thermodynamic states of moisture. Thanks to the stress level, this is within the serviceability limit state that made this summation possible. This finding provides a great deal of valuable information that can be used to benchmark practical measures on the deflection of PC bridges.

Fig. 5. Importance of thermohygro and mechanistic creeps to apparent deflection

Fatigue Life of Bridge Decks under Wet Conditions

The code COM3, which incorporates the mesoscale pore-water model (Maekawa and Fujiyama 2013), is used to study the effects of water–crack interaction on bridge decks under moving loads.

Modeling of Water–Crack Interaction from Millimeter Scale

Water in nanoscale pores in concrete composites before cracking behaves in an isotropic manner, and thereafter in an anisotropic manner owing to its crack orientation. Before concrete cracking, relative motion of the vapor and condensed water inside micropores is computed based on the DuCOM scheme with moisture equilibrium and flux modeling (Maekawa et al. 2008). After cracking, it is assumed that the mesoscale pore water pressure acts perpendicular to the crack plane(s). Fig. 6 provides a schematic illustration of the multiphase modeling (Maekawa and Fujiyama 2013).

Fig. 6. General scheme of solid crack-water interaction: (a) fluid-skeleton modeling; (b) moisture density in crack; (c) permeability of cracked concrete (Wang et al. 1977)

The water–concrete interaction is taken into account by satisfying the dynamic equilibrium of the two. Fig. 6(a) shows the contrast and common points of formulation for the soil–pore-water system often used for consolidation analyses and the cracked concrete–water system proposed in this study (Biot 1941, 1962). The total stress of the two phases is assumed to be a simple summation of the effective stresses carried by skeleton solids and pore water inside cracks. The effective stresses are computed in use of the cracked concrete constitutive modeling. Here, the shear stress of the pore-water phase is ignored, but the isotropic hydrostatic pressure is accounted for with the same manner as that of soil foundation modeling.

It is considered that the kinematics of the two phases can interact to produce dragging forces, which can be related to the permeability of pore water in concrete pores and in each crack direction (Lepech and Li 2005; Aldea et al. 1999). The volumetric stiffness of pore water under compression is considered to be linear constant and based on the value under atmospheric pressure of 0.1 MPa. The pore-water pressure can be both positive and negative, depending on the extent of crack opening/closure under repetitive loading. When the water pressure drops below the vapor pressure, a cavitation process may occur (Delannoy and Kueny 1990; Sinmura and Saouma 1997; Sagan et al. 2012), turning the liquid water into vapor. The occurrence of cavitation in general RC elements has never been reported in the civil engineering literature and the model is developed to cover all possible events of mechanics.

Bridge Deck Model

The details and dimensions of the RC decks tested by Matsui (1987) were used to define the geometry of a hypothetical deck model. The out-of-plane shear mode of failure was identical in the experiments. As a matter of fact, actual bridge decks also exhibited the same failure mode. Taking advantage of the symmetry, only one half of the hypothetical deck was modeled, resulting in dimensions of

1,000 \times 3,000 \times 190 mm

(Fig. 7). This deck model was divided into 20, 10, and 5 elements along the longitudinal, transverse, and vertical directions, respectively. All reinforcements were considered in a smeared manner. The deck was supported vertically along its one longitudinal and two transverse edges. Over 1,800 mm of the free edge, an 80-kN rolling wheel load was applied by simultaneous loading and unloading two adjacent and two previous nodes at every four loading steps. The magnitude of the load applied corresponds to approximately 43% of the static punching shear capacity.

Fig. 7. Details of the target bridge deck: (a) amplitude-cycle diagram; (b) RC slab to be simulated; (c) moving load machine and water on the slab: cracked bottom surface of fatigue-damaged slabs

Two parameters are considered: wheel-load movement speeds (77 and

0.77 km / h

) and water saturation conditions (completely saturated over the whole deck thickness, fully saturated only over the two upper elements, fully saturated over the two lower elements, and completely dry). Water–concrete interaction in the saturated elements is represented by overlapping the standard RC elements with the pore-water elements. The constitutive laws of cracked concrete (Maekawa et al. 2008) are used, with an explicit consideration of the effects of moisture on the damage evolution of crack shear transfer (Sato and Kawakane 2008; Gebreyouhannes and Maekawa 2011). To clarify the impact of pore-water pressure and the corresponding concrete fracture and damage (Solwik and Saouma 2000), the specified concrete tensile strength is used, rather than a custom value.

Parametric Analysis

The progress of the midspan deflection of each deck is shown in Fig. 8. If the computed deflection of the slabs is drawn for the whole passages of moving loads, the trend of the evolved maximum and residual deflections cannot be observed accurately. Then, the response of the deflection is considered at the logarithmic sequence of 1, 2, 5, 10, 20, 50, 100… cycles and smoothly connected on Fig. 8 (Maekawa et al. 2008). For reference, the fatigue life obtained from Case DF (dry, high speed) is indicated by dotted lines. The rapid increase in the deflection at the final stage is primarily caused by out-of-plane shear failure. Fatigue rupture of the reinforcement did not take place under the moving wheel type loads, although the fixed point pulsation of cyclic loads usually causes rupture of the reinforcing bars before the failure of the concrete core. This has been known by past experimental investigations. High-speed wheel movement (F series) appreciably shortens fatigue life when the upper parts of the deck are wet (Cases A and U). The negative effects of high-speed wheel movement are particularly obvious when only the upper parts of the deck are wet (Case U). High-speed wheel movement does not have appreciable influence on the fatigue life under dry conditions (Case D). Because high-speed traffic loading does occur in reality, the worsening effects of water that may easily be accumulated at the bridge deck surface must be anticipated. Water–concrete interaction causes the responses of RC bridge decks to be rate-dependent.

Fig. 8. Progress of midspan deflections versus number of passages

Shown in Fig. 9 is the plot of water pore pressure versus concrete principal strains monitored from one representative element under the wheel passage. High-speed wheel load movement maintains high water pressure developing over a large number of passages and results in a rapid increase of concrete principal strain from the early numbers of passage (Cases AF and UF). Because concrete principal strain is a direct measure of concrete damage, it is clear that the high water pressure is responsible for the reduced fatigue life of bridge decks under wet conditions, as visible in Cases AF and UF. This simulation matches the reality of the shortened fatigue life RC slabs under wet conditions.

Fig. 9. Pore-water pressure and principal concrete strain versus number of passages

Here, the effect of the strain rates is considered as follows. The apparent fatigue life of dry concrete in compression is generally prolonged when the rate of loading is higher, because the time-dependent fracture lessens during the frequent repetition of stresses and strains (Award and Hilsdolf 1974). But, as stated previously, RC slabs covered by condensed water show less fatigue life. Thus, the reduced fatigue life of RC slabs cannot solely be explained by the effect of strain rates, because the rate effect is quite opposite. In this analysis, the time-dependency of concrete fracture is taken into account, together with the pore-water pressure rise (Maekawa et al. 2009), and much reduced fatigue life is successfully simulated.

Finally, attention is given to the pore-water pressure at the bottom surface of the deck center-span, where negative water pressure is evident. Again, high-speed traffic has a significant role because it brings the water pressure close to vapor pressure, implying the cavitation like process: the water inside concrete pores changes phases from liquid to vapor. The models under employment have not yet considered the negative effects of this phenomenon. The impact of moisture phase change and associated cavitation inside cracks is a topic of future study.

Conclusions

A coupled hygromechanistic computational platform has been formed in this study based upon the past development of moisture–solid interaction analysis methods over the multiscales of micropores and crack spaces from

10^{- 9}

to

10^{+ 2} m

. This integrated numerical analysis has been practically applied for the life-cycle assessment of reinforced and prestressed concrete structures. Because these disciplines are based upon material science and structural mechanics, wide ranges of ambient and mechanistic actions are possible to be addressed as a tool of practice. The following conclusions have been drawn:

1.

The integration of thermodynamics and mechanistic models of concrete provides a rational basis, regardless of size, time, and the long-term responses of structures.

2.

The migration of water at concrete micropores contributes appreciably to the long-term structural deflections of four in-service PC bridges.

3.

The multiscale chemomechanistic analysis of structural concrete is further verified as a reliable approach for the assessment of the shear capacity and postpeak ductility of RC beams under self-desiccation.

4.

High pore-water pressure, induced by high-speed traffic, can accelerate concrete damage on bridge deck surfaces. A shorter deck lifespan may result.

Acknowledgments

This study was financially supported by JSPS KAKENHI Grant No. 23226011 and the Construction Technology Research and Development Subsidy Program established by the Ministry of Land, Infrastructure, Transport and Tourism of Japan.

References

Aldea, C. M., Shah, S. P., and Karr, A. (1999). “Permeability of cracked concrete.” Mater. Struct., 32(5), 370–376.

Abstract

Introduction

Analysis Platforms: DUCOM and COM3

Long-Term Deflection Simulations of PC Bridges

Modeling

Analysis Results

Roles of Thermohygro and Mechanistic Creep

Fatigue Life of Bridge Decks under Wet Conditions

Modeling of Water–Crack Interaction from Millimeter Scale

Bridge Deck Model

Parametric Analysis

Conclusions

Acknowledgments

References

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