Anatech - Linking Theory and Practice.

Concrete arch dams are typically constructed from individual cantilever blocks, as illustrated in Fig. 1, using
approximately 10’ thick mass concrete placements or lifts to build up each block. During placement and the initial curing of a lift, water is circulated through embedded pipes, as illustrated in Fig. 2, to control the peak
temperatures and thermal gradients. Once the individual blocks are completed to the crest height, water is again circulated to contract the blocks and open the contraction joints between the blocks. The open joints are then pressure grouted to form a monolithic arch dam. This type of mass concrete construction has two opposing
design considerations for the thermal behavior due to the heat of hydration. During the placement of the lifts,
excessive temperatures and thermal gradients must be controlled to prevent thermal induced cracking.
However, during the final cooling period, an adequate drop in the mean concrete temperature must be available to allow the contraction joints to open sufficiently for grouting. This paper discusses the methodology and
computer simulations currently used to evaluate the potential for cracking and the performance of the joints
during the final cooling period for grouting. In particular, several important modeling features needed to simulate this type of construction are described and highlighted. A coupled thermal stress analysis is conducted to simulate the incremental construction process using nonlinear concrete material behavior for creep and aging. A cooling coil model is used to simulate the active removal of heat through the embedded cooling coils. A method for addressing the construction process of placing lifts in the low blocks against the previously placed high blocks and the effect of the associated compressive load across the contraction joints for very young concrete is discussed. To illustrate this methodology for the thermal engineering of large concrete structures, the results of a study for the Portugues Arch Dam, which is to be constructed near Ponce, Puerto Rico, is presented.

Under the sponsorship of the Ministry of International Trade and Industry (MITI) of Japan, the Nuclear Power
Engineering Corporation (NUPEC) has investigated the seismic behavior of a Reinforced Concrete Containment Vessel (RCCV) through scale-model testing using the high-performance shaking table at the Tadotsu Engineering Laboratory. A series of acceleration time histories, representing design level seismic motions, are sequentially applied to the test model to evaluate design methods and structural performance under design level seismic loads. These tests are then followed by another series of tests using increasing amplifications of the seismic input until structural failure occurs in the test model to evaluate margins of safety for structural failure. In a cooperative program with NUPEC, the United States Nuclear Regulatory Commission (USNRC), through Sandia National Laboratories (SNL), is conducting analytical research on the seismic behavior of RCCV structures. As part of this program, pre- and post-test analytical simulations of the scale model tests are performed by ANATECH Corp. Previous papers at SMiRT (James, et. al. August 1999) and ICONE (James, et. al. April 2000) conferences
have presented results of these simulations for the pre- and post- design level tests. This paper describes the analytical simulations for the failure level tests on the RCCV test model. These simulations consider 3-dimensional time history analyses for reinforced concrete subjected to extensive, cyclic damage leading to structural collapse.

Over the last several years, renewed interest in the response of civil structures tosevere impact, such as the crash of large commercial aircraft, has prompted new research, analyses, and testing to study the impact dynamic characteristics of reinforced concrete structures. Most concrete civil struc-tures can withstand significant damage, and analytically capturing the failure mechanisms in reinforced concrete, including severe cracking, crushing, shear plug formation, and rebar rupture or bond slip and pullout, is a formidable challenge. Modeling of these failure mechanisms has steadily been improved over the years, including analyses of bridge and building failures during severe earthquakes, over-pressurization and seismic collapse of reinforced concrete containments, and more recently potential air-craft crash into nuclear power plant structures. This paper presents recent developments for advanced constitutive modeling of reinforced concrete and analysis methods with emphasis on damage evaluation from severe impact loads.

Analytical predictions of the response of high-risk structures to energetic loadings, such as blast, missiles and aircraft impact, are described. The fundamental characteristic of these predictions is to enable the development and implementation in structural-design practice of design-incorporated mitigation measures and protective features. The overall approach consists of several activities: (a) analytical simulation of energetic loading for the perceived threat, (b) characterization of structural behavior through the application of advanced analytical methods in structural modeling and computational dynamics, and (c) expert utilization of the results of structural response computations for implementation of design changes and mitigation features. Emphasis is placed on aircraft impacts on robust concrete structures, typical of nuclear-reactor containments and auxiliary buildings, and civil infrastructure protection from man-made explosions of various kinds. The material and computational modeling methodology developed for this application combines two unique tools: ANACAP-U material model capable of capturing the wide range of material behavior of reinforced and pre-stressed concrete, and TeraGrande, a computationally robust explicit-dynamics finite-element-based computer program. Illustrative examples are presented for selected structures ranging from the high-resistance structure subjected to commercial-aircraft impact to low-resistance structures exhibiting perforation, spalling and back-surface scabbing under blast loadings.

Lifeline safety structures, such as, for example, concrete dams, nuclear power plants, and highway bridges, are designed to high levels of safety using traditionally conservative methods. Events of recent years, however, have raised public concerns about the degree of vulnerability of these structures to deliberate attacks involving large-airplane crash or close-proximity blast loading. This paper presents recent development in the state of the art of finite-element-based constitutive modeling and computational methodology of reinforced concrete with emphasis on severe damage modeling and failure evaluation. Verification and validation of the developed methodology is illustrated using high-velocity impact tests conducted in the U.S. and Japan. This involves explicit finite element computations for high velocity rigid missiles impacting reinforced concrete walls. Application of the methodology to nuclear fuel facilities is discussed.

Finite element modeling is used as a basis for characterizing the initiation and growth of fatigue cracking at welded connections for input to probabilistic based reliability evaluations. The objective of the reliability study is to determine the optimum time for replacing the structure as opposed to continued maintenance costs from an economic standpoint but with structural safety as a basis. The finite element modeling is used to characterize the fatigue crack initiation and growth rates over a range of variations in loading and material conditions so that sampling with random values can establish failure rates and hazard functions.

Pre- and post-test analytical predictions of the dynamic behavior of a 1:10 scale model Reinforced Concrete
Containment Vessel are presented. This model, designed and constructed by the Nuclear Power Engineering Corp., was subjected to seismic simulation tests using the high-performance shaking table at the Tadotsu Engineering Laboratory in Japan. A group of tests representing design-level and beyond-design-level ground motions were first conducted to verify design safety margins. These were followed by a series of tests in which progressively larger base motions were applied until structural failure was induced. The analysis was
performed by ANATECH Corp. and Sandia National Laboratories for the United States Nuclear Regulatory
Commission, employing state-of-the-art finite-element software specifically developed for concrete structures. Three-dimensional time-history analyses were performed, first as pretest blind predictions to evaluate the general capabilities of the analytical methods, and second as post-test validation of the methods and interpretation of the test results. The input data consisted of acceleration time histories for the horizontal,
vertical and rotational (rocking) components, as measured by accelerometers mounted on the structure’s basemat. The response data consisted of acceleration and displacement records for various points on the structure, as well as timehistory records of strain gages mounted on the reinforcement. This paper reports on work in progress and presents pre-test predictions and post-test comparisons to measured data for tests
simulating maximum design basis and extreme design basis earthquakes. The pre-test analyses predict the failure earthquake of the test structure to have an energy level in the range of four to five times the energy level of the safe shutdown earthquake. The post-test calculations completed so far show good agreement with measured data.

A Design by Analysis procedure has been developed to incorporate the results of thermal cracking analyses into the linear based design methods for reinforced concrete containment structures. Current practice employs linear based analyses and accounts for stress reduction due to thermal induced cracking on a section by section basis. Under thermal loading, in addition to a reduction of the section forces and moments for cracked sections, concrete cracking also reduces the structural stiffness and thus the constraint against thermal expansion or contraction for the whole structure, which in turn reduces the thermal induced stresses as compared to a linear (un-cracked) analysis. The design by analysis approach employs nonlinear thermal cracking analyses using detailed
modeling of the complete structure. By comparing these stress distributions with those from a linear analysis of the same model, stress reduction factors can be developed for critical sections that also include global stress redistribution. These stress reduction factors can then be used to correct linear based thermal stresses in the design basis calculation for all load combinations that include thermal loads.

The proposed geologic repository under development at Yucca Mountain, Nevada, will employ multiple shell metallic containers (waste packages) for the disposal of nuclear waste. The waste packages represent a primary engineered barrier for protection and containment of the radioactive waste, and the design of these containers must consider a variety of structural conditions to insure structural integrity. Some of the more challenging conditions for structural integrity involve severe impact loading due to hypothesized event sequences, such as
drops or collisions during transport and placement. Due to interactions between the various components leading to complex structural response during an impact sequence, nonlinear explicit dynamic simulations and highly refined models are employed to qualify the design for these severe impact loads.

This paper summarizes the Design by Analysis methodologies employed for qualification of waste package
design under impact loading and provides several illustrative examples using these methods. Example evaluations include a collision of a waste package by the Transport and Emplacement Vehicle (TEV) and two scenarios due to seismic events, including WP impact within the TEV and impact by falling rock. The examples are intended to illustrate the stringent Design by Analysis methods employed and also highlight the scope of structural conditions included in the design basis for waste packages to be used for proposed nuclear waste storage at Yucca Mountain.

This paper describes the finite element analysis methods used to develop reliability-based models for the structural deteriorization of mass concrete due to Alkali Aggregate Reaction (AAR). Since there is insufficient data available to describe the concrete constitutive relations for the AAR growth rate, the expansion characteristics are simulated by benchmarking the model to known cracking patterns and displacements recorded at the site, and using the model to project possible conditions as continued growth occurs. Finally, reliability models are constructed through a series of finite element based deterministic analyses for variations in material characteristics, such as concrete compressive strength and the growth rate. Functional relations of structural performance in time are constructed for variations of these problem parameters for input to a probabilistic based reliability models.

An extensive analytical effort is performed to establish the pressure fragility for the ESBWR primary containment system, including the steel lined reinforced concrete walls, the drywell head, and a typical equipment hatch having a pressure-unseating closure configuration. The probability of failure with internal pressure is characterized with a lognormal probability density function (PDF). The effect of uncertainties in material properties, failure criteria, accident conditions, and analytical modeling are quantified through parametric variation of finite element analyses to establish the respective contribution in the logarithmic standard deviation for the PDF. Global 3-dimensional nonlinear modeling is employed to establish mode of failure and pressure capacity of the reinforced concrete containment system considering liner tearing, rebar yield and rupture, and concrete cracking, crushing, and shear capacity. Detailed local modeling, using boundary conditions extracted from the global model, are used to determine failure modes and pressure capacity in the drywell head and equipment hatch considering buckling, tearing, and flange deformations. A matrix of calculations are performed using combinations of median and 95% confidence values for key parameters, such as material properties and failure criteria, to establish the variance due to uncertainty in each key parameter. The analyses are performed for different thermal environments representing different accident conditions. The result is a cumulative probability of failure versus containment pressure at various temperature conditions for each of the critical components in the primary containment system.

GE’s latest evolution of the boiling water reactor, the ESBWR, has innovative passive
design features that reduce the number and complexity of active systems, which in turn provide
economic advantages while also increasing safety. To incorporate these passive cooling features,
the Isolation Condenser Passive Cooling Containment System Pools (IC/PCCS) are integrated
onto the top slab of the primary containment structure. The top slab spans the 36-meter diameter
containment drywell with a central 10.5-meter diameter opening for the drywell head while
supporting the water and equipment in these upper pools. The walls of the upper pools along with
the refueling floor slab over the pools are designed as a deep beam girder as part of the structural
system of the top slab. During normal operations, the Isolation Condenser (IC) pool will undergo
duty cycles where the water gets rapidly heated to boiling for some period of time and then cools
back down. This top slab structural system is subjected to the elevated temperatures that occur in
the IC pools and to thermal cycling due to temperature changes in the pools and in the drywell
portion of the containment during shutdowns. These cyclic thermal demands interact with a
changing structural condition because of concrete cracking, creep, and property degradation at
elevated temperatures. Thus, there is a potential for structural ratcheting of the slab that would be
manifested by continually increasing deformations over time under the thermal cycling while
supporting the pool loads. The long-term structural integrity of the top slab as a containment
boundary must be verified for this duty cycle operation over the 60-year design life.

The Economic Simplified Boiling Water Reactor (ESBWR), under development by
General Electric, is the next generation reactor design for electric power production using
nuclear energy. The new simplified design has innovative passive design features that reduce the
number and complexity of active systems, which in turn provides economic advantages while also
increasing safety. These passive systems used for emergency cooling also mean that the primary
containment system will experience elevated temperatures with longer durations than
conventional plants in the event of design basis accidents. During a Loss of Coolant Accident
(LOCA), the drywell in the primary containment structure for the ESBWR will be exposed to
saturated steam conditions for up to 72 hours following the accident. A containment spray system
may be activated that sprays the drywell area with water to condense the steam as part of the
recovery operations. For this analysis, it is assumed that the containment spray is activated at the
end of the 72-hour period. A backpressure, acting between the liner and the concrete wall of the
containment, can occur as a result of elevated temperatures in the concrete causing steam and
saturated vapor pressures to develop from the free water remaining in the pores of the concrete.
Additional pore pressure also develops under the elevated temperatures from the non-condensable
gases trapped in the concrete pores during the concrete curing process. Any buildup of this pore
pressure next to the liner, in excess of the drywell internal pressure, will act to push the liner away
from the concrete with a potential for tearing at the liner anchorages. This paper describes the
methods and analyses used to quantify this liner backpressure so that appropriate measures are
included in the design of the liner and anchorage system. A pore pressure model is developed that
calculates the pressure distribution across the concrete wall considering the time-dependent
temperature distribution that evolves following the LOCA. The pressure distribution at each time
increment is balanced for mass diffusion using D’Arcy’s Law for mass flux under a pressure
gradient. The total mass for the free water, the water vapor, and the non-condensable gases in the
pore volumes is tracked to maintain conservation of mass. The evolution of liner backpressure
with time is then based on detailed finite element modeling that incorporates the pore pressure
model into a concrete cracking analysis with full coupling between the temperatures, pressures,
and liner displacements.

The current design for the geologic repository of nuclear waste at Yucca Mountain, Nevada, uses steel storage containers, commonly referred to as waste packages, placed horizontally and end-to-end along emplacement drifts in the underground facility [1]. The waste packages represent a primary engineered barrier for protection of the stored highlevel radioactive waste, and the structural integrity of these waste packages is a key element in the design for long-term storage and possible retrieval of the nation’s radioactive waste. In addition to thermal and criticality design requirements, the waste packages are engineered for a variety of structural functions, including internal pressurization, emplacement and retrieval loads, falling rock, accidental drop and tip over, and missile impact from accidental airborne projectiles within the drift chamber. Because the repository design must consider time periods up to 1,000,000 years, the consequences of loads resulting from extreme seismic activity must also be addressed in the structural assessment and long term integrity of these waste packages.

The design rules for reactor containments and similar safety structures in nuclear power plants have been established decades ago based on their initial material and structural conditions, and design-based assumptions. However, as these plants begin to approach the end of their original design life and transition into the life-extension phase, analytical methods are needed to evaluate potential aging-related effects. In the case, of pre-stressed concrete containments, for example, the concrete is subject to long-term creep in the presence of time-varying loads due to tendon relaxation and possible re-tensioning, and service- and weather-dependent thermal cycling. Also, some PWR plants are facing the prospect of replacing steam generators, which require the cutting of large opening in the pre-stressed containment. Performing structural modification for such purposes should be guided by conducting detailed numerical simulations to avoid introducing new, or obscuring pre-existing, damage. This requires the use of qualified, well-validated analytical methodology with robust material-behavior representations of damage states, including the ability to model pre-existing cracks and other service-induced damage conditions. Such a methodology has been developed considering a wide range of structural behavior and service conditions. This paper describes the behavioral modeling attributes of this methodology and its application to the diagnostic evaluation of the effects of long-term service and environmental conditions on concrete infrastructures in nuclear power plants, including structural retrofitting and rehabilitation of reactor containments, and proof of performance for life-extension service.

Reinforced concrete, despite its apparent simplicity, presents one of the most difficult problems in constitutive modeling and numerical simulation. The difficulties in constitutive modeling of concrete structures stem from the fact that cracks can form at relatively low stress levels. This leads to highly complex interaction between postcracking behavioral regimes, which include: multi-directional cracking, crushing, shearing along rough crack surfaces and the consequential formation of rebar-reacted compression normal to crack surfaces. One observable manifestation of this interaction is the potential for split cracking parallel to the compressive stress field imposed by the tendon in a pre-stressed containment, especially if the tendons are located close to the external surface of the containment wall where concrete confinement is small. Such split cracking could grow with time and may lead to wall delamination, with potentially serious consequences for the containment’s design-basis function.

The ageing-dependent constitutive properties of the concrete material considered are: tensile strength, postcracking shear behavior, and compressive strength, with both, hardening effects due to the maturity of concrete compressive strength and softening effects due to environmental degradation, temperature, internal micro-cracking and past-loading-related macro cracks. A robust analytical treatment of these properties in a general three-dimensional stress-strain constitutive formulation that recognizes the interaction with the reinforcement is fundamental to the degree of fidelity of the predicted response to true physical behavior.

The existing navigational lock, located on the Monongahela River near Charleroi, Pennsylvania, consists of a landside 56-foot x 720-foot main chamber and a riverside 56-foot x 360-foot auxil-iary chamber. This lock was constructed in the 1930’s and is approaching the end of its useful design life. The U. S. Army Corps of Engineers is planning to replace the existing lock cham-bers with a new lock system to be named Charleroi Locks. The Corps of Engineers’ guidance for the design of unprecedented massive concrete structures for which limited experience is available is to employ the Nonlinear, Incremental Structural Analysis (NISA) methodology [2] to help evaluate the behavior of the structure during construc-tion as an aid in the design process. This methodology has been applied to other innovative con-struction methods, including float-in and lift-in precast concrete segments in-filled with tremie concrete, and also to arch dams where embedded cooling coils are used to actively remove heat [3]. For this project, the performance of the tremie concrete base layer as a cofferbox seal and the potential for thermal induced cracking in the dry placements are the main concerns.

A condition afflicting some concrete structures, known as Alkali Aggregate Reaction (AAR), is produced by a continual chemical reaction between the aggregate and the alkali in the cement, which causes volumetric expansion in the concrete over time. In massive concrete structures, such as dams or monoliths of navigational locks, this expansive growth in the concrete, coupled with inherent restraints against movement, can cause severe concrete cracking. In addition, misalignment in mounted mechanical equipment can develop due to the relative movement of points on the structure, and this can lead to excessive component wear and eventual safety concerns. While the root cause of the AAR condition is understood, the structural effects are very complex since the expansive growth is a function of the induced stress, as well as the environment and even the distribution of the constituents within the structure. This condition can be prevented by insuring that the cement mix and the aggregate are compatible before construction. Thus, while many early vintage structures have this condition, most of the “more modern” structures do not, and little effort has been devoted to compiling experimental data and developing detailed constitutive models for simulating the AAR process. This paper describes an engineering approach used in the evaluation for the deteriorating effects of AAR. An existing concrete constitutive model, which includes aging, creep, and shrinkage, developed for the evaluation of young concrete, is adapted for AAR modelling by reversing the shrinkage terms for expansion. The distribution and rate of expansion for the specific structure evaluated is calibrated to field data for both surveyed movements and for the observed cracking history as a signature of the evolving stress distribution. The model is then used to project the future performance of the structure and assess reliability and safety. A probabilistic based assessment is wrapped around the deterministic analyses to account for uncertainties in the evaluation.

This paper presents methodology that is employed by the U. S. Army Corps of Engineers for evaluating and optimising the design and construction of massive concrete structures. The COE guidance for the use of this methodology is when designs call for unprecedented structures for which little experience is available or for structural configurations that are known to have problems with reliability or durability from past experience. The cornerstone of the method is a detailed concrete constitutive model that accounts for aging, creep, shrinkage, and with a time dependent cracking criterion. The analysis must track the concrete performance from the initial placement through many months of curing and interaction with other construction and finally for operational loads. A viscoelastic creep formulation is employed that accounts for the age at loading and load reversals. A coupled thermal-stress analysis is used to evaluate thermal induced cracking due to the effects of the heat of hydration relative to structural restraints and loads during construction. The analysis simulates the construction process with a changing mesh and boundary conditions as lifts are placed, forms removed, areas dewatered or re-flooded, or for interactions with adjacent structures. Typically, the analyses are continued for 1 full year after construction is completed to evaluate the effects of the following peak seasonal temperatures on the concrete and structural performance. Analyses using variations in design and construction parameters are employed to establish mitigation measures for cracking, if necessary, and to optimise design parameters, such as lift heights, lift placement rates and sequences, concrete placement temperature, reinforcement requirements, and possibly the characteristics of the concrete mix. The intent is to find the optimum balance between construction costs and long-term reliability, safety, and durability.

Following the flooding disaster in New Orleans, Louisiana, due to Hurricane Katrina in August 2005, the U. S. Army Corps of Engineers (COE) initiated a comprehensive program to survey, evaluate, and rank all dams and levees in the COE’s portfolio for risk of structural failure and associated economic consequences. One objective of this program is to improve safety and risk through efficient allocation of resources for rehabilitation efforts when needed. One area of great concern is internal stresses in aging concrete monoliths causing cracking. While some cracking in concrete monoliths is a common condition having little effect on the structural performance, extended cracking can lead to instability in parts of the monolith. Mass concrete monoliths generally are not reinforced, and cold joints at lift interfaces are a potential source of weak planes. Failure of concrete monoliths due to sliding instability along internal cracked planes can have serious consequences for loss of pool. This failure mode can occur quite suddenly, and detection of such cracking or the extent of such cracking is very difficult to establish from visual inspections or even core sampling. To help in this portfolio risk assessment, analysis methodology has been developed for establishing the structural risk due to cracking in mass concrete monoliths. Finite element modelling with automated mesh generation and employing advanced concrete constitutive relations for crack initiation, propagation, and arrest, are used to establish internal cracking. Monte Carlo based probabilistic analysis methods, directly coupled to the finite element analyses, are used to evaluate uncertainties and establish the probability of failure for increasing pool elevations and seismic hazards. The objective is to provide a probability of failure for possible pool elevations under current site conditions given that there is always some possibility of a range of seismic events that could occur at any given time.