Soil-structure interaction parameters from finite element analysis

A series of two-dimensional finite element computer runs were made to compute the frequency dependent soil-structure interaction coefficients. Variations in the element size, mesh dimensions, boundary conditions, and soil hysteretic damping ratio to determine their influence on the computed interaction coefficients were made. From the calculations, it has been determined that the primary requirement of the mesh is a transmitting boundary formulation. For low damping conditions, roller support boundary conditions must be placed exceedingly far from the structure to ensure convergence of the results to the analytic solution. In addition, with such boundary conditions, the addition of artificial hysteretic soil damping cannot be used to simulate radiation damping behavior of the continuum. A frequency dependent criteria is also presented to determine minimum size elements that must be used in any calculation.     

A review of explosive characteristics of prestressed secondary containments near the ultimate load

The principles of load-structure interaction as they pertain to secondary containment structures are reviewed. These principles are illustrated by simple computations for a 1:14 scale model test structure. It is demonstrated that the pre-ultimate behavior should be identical for both pneumatic and hydraulic loading systems but that the post-ultimate behavior will differ substantially. However, in each case the post-ultimate behavior may be explosive. Implications with respect to complete and local failures of real containments are also briefly examined.     

Soil-structure interaction — an engineering evaluation

The two methods of analysis for soil-structure interaction, the impedance and the finite element methods, are reviewed with regard to their present capabilities to address the significant factors of the problem. The objective of the paper is to evaluate if an adequate engineering solution to the problem is provided by either approach. Questions related to the reduction of seismic motions with depth, scattering of incident waves, the three-dimensionality of the real problem, soil damping, strain dependency of soil properties and the uncertainties associated with all of the above are discussed in sufficient detail. All conclusions made are based on referenced material. It appears that, although both methods as presently practised have not yet completely solved the problem, the impedance approach has come closer to addressing the more significant issues. Because of this finding, in addition to its simplicity and low cost, the impedance approach is the preferred engineering method for soil-structure interaction.     

Soil-structure interaction: Continuum or finite element?

A survey of both the continuum and the finite element approaches to the soil-structure interaction problem is made. The limitations and advantages of both methods are evaluated with an emphasis on the present state of the art. Some recommendations are made regarding the circumstances under which either approach should more appropriately be used.     

Observations on analysis, testing and failure of prestressed concrete containments

The paper reviews the mechanics which indicate that a bursting failure with large energy release is the failure mechanism to be expected from ductile lined containment structures pressurized to failure. It reviews a study which shows that, because of leakage, this is not the case for unlined prestressed containments. It argues that current practice, since it does not specifically address the bursting failure problem for lined prestressed containments, is inadequate to ensure that this type of failure could not occur. It concludes that, in view of the inadequacy of the current state-of-the-art to predict leakage from lined structures, the logical remedy is to eliminate all possibility of bursting failure by making provision for venting of containments.     

Soil-structure interaction for transient loads due to safety relief valve discharges

Dynamic responses of BWR Mark II containment structures subjected to axisymmetric transient pressure loadings due to simultaneous safety relief valve discharges were investigated using finite element analysis, including the soil-structure interaction effect. To properly consider the soil-structure interaction effect, a simplified lumped parameter foundation model and an axisymmetric finite element foundation model with viscous boundary impedance are used. Analytical results are presented to demonstrate the effectiveness of the simplified foundation model and to exhibit the dynamic response behavior of the structure as the transient loading frequency and the foundation rigidity vary. The impact of the dynamic structural response due to this type of loading on the equipment design is also discussed.     

Soil-structure interaction with separation of base mat from soil (lifting-off)

In reactor buildings having a separate base mat and a shield-building (outer concrete shell) of large mass, large overturning moments are developed for severe earthquake loading. The standard linear elastic half-space theory is used in the soil-structure interaction model. For a circular base mat, if the overturning moment exceeds the product of the normal force (dead weight minus the effect of the vertical earthquake) and one-third of the radius, then tension will occur in part of the area of contact, assuming distribution of stress as in the static case. For a strip foundation the same arises if the eccentricity of the normal force exceeds a quarter of the total width. As tension is incompatible with the constitutive law of soils, the base mat will become partially separated from the underlying soil.Assuming that only normal stresses in compression and corresponding shear stresses (friction) can occur in the area of contact, a method of analyzing soil-structure interaction including partial lifting-off is derived, which otherwise is based on the elastic behaviour of the soil. A rigorous procedure to determine the nonlinear impedance function of a rigid plate of arbitrary shape, only in partial contact with the elastic half-space, is developed. Complex dynamic influence coefficients for displacements are used which can either be determined with the finite-element method or based on solutions of displacements on the surface of an elastic half-space at a certain distance from a rigid subdisk. Constant and variable stiffness methods of solving the non-linear equations of motion are explained which also determine the area of contact. Slipping of the entire mat or of a part thereof can also be taken into consideration.A simpler approximate method is discussed. For a given force and moment acting on the rigid plate, the area of contact is determined by iteration or based on quadratic programming techniques using the static influence coefficients for displacements. The complex-valued impedance function is estimated by substituting an equivalent circular plate for the actual area of contact. Transforming the equivalent lumped system to the centre of the plate, the non-linear stiffness and damping matrices of the soil are derived. Formulae are given for the partial lifting-off of a disk and a strip. The results of the numerical method are compared to rigorous solutions for full contact. As an example, the dynamic response of the reactor building of a 1000 Mw plant to earthquake motion is calculated using the rigorous and approximate methods. Parametric studies are carried out. The influence of the frequency on the impedance function and on the distribution of stress in the area of contact, which determines the beginning of lift-off, is discussed.     

Soil-structure interaction of nuclear reactor structures considering through-soil coupling between adjacent structures

The theoretical problem concerning the influence of through-soil coupling between adjacent structures on the seismic loading of nuclear reactors has been investigated by considering a soil-structure interaction model in which several three-dimensional flexible structures are bonded to an elastic half-space. These structures, which are allowed to be either similar or dissimilar, are modeled as conventional discrete systems mounted on separate base slabs of close proximity. For the purpose of this study, it is assumed that the stiffness of any structure such as piping connecting the adjacent buildings is negligible.For purposes of comparison, the seismic responses of structural masses are determined both with and without the influence of nearby structures. Both transient and steady-state results are presented and discussed for some typical simplified two- and three-structure complexes. Emphasis is placed on the effects of through-soil coupling on the dynamic response of the system rather than actual magnitudes of response which have previously been treated for plants erected on a single base slab. The significant findings are that nuclear power plants can be designed to achieve a reduction in seismic loads due to interaction with neighboring structures. Conversely, improper plant design and layout may result in mutual reinforcement of resonances with increased loads.     

Soil-structure interaction analyses by finite elements — State of the art

In this paper the authors have attempted to summarize the current capability for evaluating soil-structure interaction effects during earthquakes using finite element procedures. A concise summary of methods available, together with their capabilities and relative costs is presented. It is suggested that finite element procedures provide a powerful tool for use in the design of nuclear plants, especially for embedded structures, and their applicability in this respect is illustrated by comparing computed results with those recorded in a nuclear plant during a strong motion earthquake. It is concluded that when the methods are used in conjunction with good engineering judgment and with full recognition of their limitations, they provide evaluations of response with a level of accuracy entirely adequate for engineering design.     

Early-age behaviour of concrete nuclear containments

A numerical model has been developed to predict early-age cracking for massive concrete structures. Taking into account creep at early-age is essential if one wants to predict quantitatively the induced stresses if autogenous or thermal strains are restrained. Because creep strains may relax internal stresses, a creep model which includes the effects of hydration and temperature is used. For the prediction of cracking, a simple elastic damage model is used. Numerical simulations are performed in order to predict the behaviour of a massive wall and a concrete containment of a nuclear power plant. They show that significant relaxation of stresses (due to creep) occurs only after about 10 days, after cracking occurs. Moreover, since temperature in concrete may reach important values in massive concrete structures, it appears that effect of temperature on creep must be taken into account for an accurate prediction of cracking.     

Design and behaviour of French containments

In this report, the point is made that the French nuclear installations have two types of containments:

• - The first consisting of a pre-stressed concrete inner containment with a leakproof liner.

• - The second consisting of a pre-stressed concrete inner containment without a leaktight liner and an outer containment of reinforced concrete concentric with the former. The space between the two containments is maintained at a negative pressure, to intercept any leaks from the internal containment, which are filtered and discharged outside in the event of an accident.

After covering the mechanical design of these two types of containments, this report examines the existing safety margins for aircraft crashes and explosions resulting from the industrial environment.The report then considers in greater detail the leaktightness results of the double containments obtained during acceptance tests, as well as the leaktightness conditions while the reactor is operating.Finally, the report describes, for the case of containments with leakproof liners, the conditions of aging of the concrete and the associated pre-stressing.     

Seismic effects in secondary containments: Research needs

The purpose of this paper is to discuss the status of current and projected research on the behavior of nonprestressed secondary containment structures carrying combined pressurization and seismic shear. Ongoing experimental research at Cornell University on specimens carrying combined biaxial tension and static cyclic shear is described. The remainder of the paper treats research needed to better predict the response of containments to seismic effects and to serve as the basis for improved design methods for reinforced concrete containments.     

Evaluation of prestress losses in nuclear reactor containments

The most critical safety barrier in a nuclear power plant, the concrete containment, is prestressed by hundreds of tendons, both horizontally and vertically. The main purpose of the containment is to prevent radioactive discharge to the environment in the case of a serious internal accident. Due to creep and shrinkage of concrete and relaxation of the prestressing steel, tendon forces decrease with time. These forces are thus measured in Swedish containments with unbonded tendons at regular in-service inspections. In this paper, the prestress losses obtained from these in-service inspections are compared to losses estimated using several prediction models for creep, shrinkage and relaxation. In an attempt to increase the accuracy of these models, existing expressions for the development of shrinkage were modified using previous findings on the humidity and temperature inside two Swedish containments. The models which were used and modified for predicting creep and shrinkage were CEB-FIP Model Codes 1990 and 1999, ACI 209, Model B3 and GL2000. Eurocode 2 was used for the prediction of relaxation. The results show that the most accurate of the models were CEB/FIP MC 99 and ACI 209. Depending on the model, the accuracy of the prediction models was increased by 0.5-1.2 percentage points of prestress losses when using the modified development of shrinkage. Furthermore, it was found that the differences between the different models depend mainly on the prediction of creep. Possible explanations for the deviation between the calculated and measured models can be the influence of reinforcement on creep and shrinkage of concrete and the influence of friction on horizontal tendons.     

Failure internal pressure of spherical steel containments

An application of the British CEGB's R6 Failure Assessment Approach to the determination of failure internal pressure of nuclear power plant spherical steel containments is presented. The presence of hypothetical cracks both in the base metal and in the welding material of the containment, with geometrical idealizations according to the ASME Boiler and Pressure Vessel Code (Section XI), was taken into account in order to analyze the sensitivity of the failure assessment with the values of the material fracture properties.Calculations of the elastoplastic collapse load have been performed by means of the Finite Element System SAMCEF. The clean axisymmetric shell (neglecting the influence of nozzles and minor irregularities) and two major penetrations (personnel and emergency locks) have been taken separately into account. Large-strain elastoplastic behaviour of the material was considered in the Code, using lower bounds of true stress—true strain relations obtained by testing a collection of tensile specimens.Assuming the presence of cracks in non-perturbed regions, the reserve factor for test pressure and the failure internal pressure have been determined as a function of the flaw depth.     

Pressure release of containments during severe accidents in Switzerland

As required by the Swiss Federal Nuclear Safety Inspectorate (HSK) all Switzerland's five nuclear power plants have to install a containment filtered venting system. The integrity of the containment (the last barrier for radioactive releases to the environment) can be threatened by overpressure due to inadequate heat removal. Design requirements have been provided for a specific class of severe accident scenarios. In general the capacity of the system is considered sufficient if it is able to vent the steam production corresponding to a decay heat level of 1% of the thermal reactor power. The mitigation capacity for the reduction of released radioactive material is specified by a retention factor of 1000 for aerosols to prevent or limit a long term ground contamination and a factor of 100 for elementary iodine for prevention or limiting of thyroid doses and to avoid short term evacuation. Besides existing requirements for design, maintenance and operation, additional claims such as passivity and operability at any pressure conditions inside the containment have to be met. Passivity implies that the system can be initiated after a severe accident without any operator action. The system also has to allow early manual venting. Various filtered venting systems are presently available. The nuclear power plants of Beznau, Gosgen, Leibstadt and Muhleberg have already selected such systems and already implemented them or are going to install them step by step. Beznau selected the Sulzer-EWI system which is using a water pool with nozzles-baffle plates and mixing elements to achieve the required filtration of the aerosols. In both Beznau units, the systems are installed and in standby mode. Gosgen, a pressurized water reactor as well as Beznau, is going to implement a filter system developed by Siemens-KWU, known as sliding pressure venting process, combining a venturi scrubber in a water pool and a mesh filter. The boiling water reactor of Leibstadt also selected the same system as Beznau while Müheberg choose the ABB system but not in the common design. The venturi pipes are thereby integrated in the water pool of the outer torus. The system in all five nuclear power plants is fully operable and in standby mode since December 1993.     

Investigations of PCRV and nuclear reactor containments in China

This paper describes the state-of-the art of the research work on the mainland of China pertaining to the prestressed concrete reactor vessel and to nuclear reactor containment. The results of tests of scale model of a PCRV and its deep end slab are presented. The 3D linear and nonlinear stress analyses and ultimate load of these models are also described. A new type of containment, a steel-plate-concrete composite containment, is proposed and evaluated. At last, a survey of the Qin Shan Nuclear Power Plant is described.     

A heat, mass, and momentum transport model for hydrogen diffusion flames in nuclear reactor containments

It is now possible to analyze the time-dependent, fully three-dimensional behavior of hydrogen combustion in nuclear reactor containments. This analysis involves coupling the full Navier-Stokes equations with multi-species transport to the global chemical kinetics of hydrogen combustion. A transport equation for the subgrid scale turbulent kinetic energy density is solved to produce the time and space dependent turbulent transport coefficients. The heat transfer coefficient governing the exchange of heat between fluid computational cells adjacent to wall cells is calculated by a modified Reynolds analogy formulation. The analysis of a MARK-III containment indicates very complex flow patterns that greatly influence fluid and wall temperatures and heat fluxes.     

Long-term aging of light water reactor concrete containments

This paper evaluates the aging of light water reactor concrete containments and identifies three degradation mechanisms that have the potential to cause widespread aging damage after years of satisfactory experience: alkali–silica reactions; corrosion of reinforcing steel, steel liner, and prestressing steel; and sulfate attack. The aging evaluation is based on a comprehensive review of the relevant technical literature. Low-alkali cement and slow-reacting aggregates selected according to ASTM requirements cause deleterious alkali–silica reactions. Low concentrations of chloride ions can initiate corrosion of the reinforcing steel if the hydroxyl ions are sufficiently reduced by carbonation, leaching or magnesium sulfate attack. Magnesium sulfate attack on concrete can also cause loss of strength and degradation of cementitious properties of the containment concrete after long-term exposure. The techniques for inspecting, mitigating and repairing these long-term aging effects are discussed.     

Experimental verification of accident loads for PWR containments

The principal loads which a nuclear power reactor containment is designed to withstand are produced by internal fluid caused static and/or dynamic pressures. They can be generated during failure events which release mass and energy into the containment atmosphere. An overview of the events which can generate substantial internal loads is provided. Representative experimental programs initiated for the investigation of the relevant physical phenomena are described. Illustrative examples of measured data are presented and discussed.