Effect of Moisture Content on the Shakedown Limits of Base Course Materials

This paper summarizes the results of a laboratory testing program that was conducted to determine the effects of moisture content on the shakedown limits of unbound granular base materials. Two different types of granular base materials were investigated in this study, namely limestone and sandstone. Multi-stage repeated load triaxial tests were performed on these materials. The results of the tests were analyzed within the framework of the shakedown theory. The results indicate that the moisture content had an influence on the slope of the elastic and plastic shakedown limits lines. The effect of the moisture content was more pronounced on the slope of the elastic shakedown limit line, however. The moisture content affected the intercept of the elastic and plastic shakedown limits lines more significantly than the slope of these lines. The limestone material exhibited greater decrease in the intercept of the elastic and plastic shakedown limits with increase in moisture content compared with the sandstone material. This was explained by the limestone’s finer gradation.

Gray Correlation Analysis and Prediction on Permanent Deformation of Subgrade Filled with Construction and Demolition Materials

Construction and demolition (C&D) materials obtained from the demolition of buildings are proven to be qualified and sustainable subgrade fillers. The permanent deformation response of subgrade C&D materials under different moisture contents, degrees of compaction, deviator stresses, and confining pressures was revealed by carrying out dynamic triaxial texts. Then, using a four-factor and three-level orthogonal test and by calculating the Gray correlation degree of each factor, the influence degree of each factor on the permanent deformation was determined. The results indicated that two different response types of the permanent deformation of subgrade C&D materials, plastic shakedown and plastic creep, were identified as reason behind the increase in stress levels. Also, according to the Gray correlation analysis results, the permanent deformation of highway subgrade filled with C&D materials is influenced by the deviator stress most significantly, followed by moisture content, degree of compaction, and confining pressure. Finally, a permanent deformation prediction model about this kind of subgrade filler with a reasonable prediction accuracy was proposed.

Direct Analysis of Post-Shakedown Quantities With the STPZ Considering Multi-Parameter Loading

If a structure is subjected to cyclic loading, strain, displacements etc. may accumulate cycle by cycle due to a ratcheting mechanism. Design Codes frequently require strain limits to be satisfied at the end of the specified lifetime of the structure. Usually, this is requested to be done considering all load sets pairwise. However, this leads to the fact that ratcheting cannot be detected, if it occurs only because of multi-parameter loading. Ordinary incremental step-by-step calculations can easily exceed time and hardware resources. This is particularly true for travelling loads, where many load steps are required for one load cycle. As an alternative, the Simplified Theory of Plastic Zones (STPZ) is used in the present paper. Being a direct method, effects from load history are disregarded. The elastic-plastic behavior in the state of either elastic or plastic shakedown is estimated on the basis of purely elastic analyses. Two kinds of linear elastic analyses are to be performed, fictitious elastic analyses for each set of loading, and a number of modified elastic analyses. Few of these analyses are usually sufficient to obtain reasonable estimates of the post-shakedown quantities. Trilinear material behavior is adopted along with kinematic hardening, a Mises yield surface and an associated flow law. The modified elastic analyses are performed making use of modified elastic parameters (Young’s modulus and Poisson’s ratio) in the plastic zone and applying suitably defined initial strains. The results obtained can be improved iteratively. The theory of the method is briefly explained and its application is shown using an example with multi-parameter loading.

Nonlinear Analysis in Pressure Vessel Design Codes: Recommendations for Codified Rules Improvements

During the past 30 years the main rules to design pressure vessels were based on elastic analyses. Many conservatisms associated to these different elastic approaches are discussed in this paper, like: stress criteria linearization for 3-D components, stress classification in nozzle areas, plastic shake down analysis, fatigue analysis, Ke evaluation, and pipe stress criteria for elastic follow-up due to thermal expansion or seismic loads... This paper will improve existing codified rules in nuclear and non-nuclear Codes that are proposed as alternatives to elastic evaluation for different failure modes and degradation mechanisms: plastic collapse, plastic instability, tri-axial local failure, rupture of cracked component, fatigue and Ke, plastic shakedown. These methods are based on limit loads, monotonic or cyclic elastic-plastic analyses. Concerned components are mainly vessels and piping systems. No existing Code is sufficiently detailed to be easily applied; the needs are stress analysis methods through finite elements, material properties including material constitutive equations and criteria associated to each methods and each failure modes. A first set of recommendation to perform these inelastic analysis will be presented to improve existing codes on an international harmonized way, associated to all material properties and criteria needed to apply these modern methods. An international draft Code Case is in preparation.

Shakedown-Ratcheting Analysis of a Spherical Pressure Vessel by Anisotropic Continuum Damage Mechanics

In cyclic loading and when plastic flow occurs, discontinuities grow. In this research, interaction diagram of Bree has been developed when the spherical pressure vessel contains discontinuities such as voids and microcracks. Bree’s diagram is used for ratcheting assessment of pressurized equipment in ASME III NH. Nature of these defects leads to an anisotropic damage. Anisotropic Continuum Damage Mechanics (CDM) is considered to account effects of these discontinuities on the behavior of the structure. Shakedown – ratcheting response of a hollow sphere under constant internal pressure and cyclic thermal loadings are studied by using anisotropic CDM theory coupled with nonlinear kinematic hardening of Armstrong-Frederick m’s model (A-F). Return mapping method is used to solve numerically the developed relations. Elastic, elastic shakedown, plastic shakedown and ratcheting regions are illustrated in the modified Bree’s diagram. Influence of anisotropic damage due to the plastic deformation is studied and it was shown that the plastic shakedown region is diminished because of the developed damage.

Detection of Ratcheting in Finite Element Calculations

The distinction between a ratcheting and non-ratcheting response is critical for many high temperature design methods. Non-ratcheting is generally considered safe — deformation remain bounded over the lifetime of the component — while ratcheting is undesirable. As a particular example, the elastic perfectly-plastic (EPP) design methods described in recent ASME Section III, Division 5 code cases require a designer to distinguish ratcheting from non-ratcheting for finite element analyses using a relatively simple, elastic perfectly-plastic constitutive response. However, it can be quite difficult to distinguish these two deformation regimes using finite element (FE) analysis particularly in the case where the actual ratcheting strain is small. In practice FE analysis of structures that are analytically in either the plastic shakedown or ratcheting regimes will result in small, cycle-to-cycle accumulated strains characteristic of ratcheting. Distinguishing false ratcheting — the structure is actually in the plastic shakedown regime — from true ratcheting can be challenging. We describe the characteristics of nonlinear FE analysis that cause these false ratcheting strains and describe practical methods for distinguishing a ratcheting from a non-ratcheting response.