Integrity Analysis of the Sheath Considering Temperature Effect under Deep and Large-Scale Multi-Section Hydraulic Fracturing

Different operations make the borehole temperature change and cause periodic stresses, which often cause variations in the stress state of the sheath or damage. In this paper, the effect of temperature on sheath integrity is investigated. First, the mechanical model of sheath is established and analyzed by shakedown theory. Then, compression experiments of well cement at different temperatures are carried out, and the law of mechanical properties with temperature is obtained. Finally, combining the theoretical analysis and mechanical experiments, the results show that (1) when only the temperature inside the sheath cyclically varies, the negative influence of temperature caused by the practical operations can be negligible. (2) When the internal pressure and temperature act together, the effect of temperature on the sheath is reflected in temperature stress and the change of the cement properties. (3) With the increase of temperature difference (∆T), the cohesion of cement decreases while the internal friction angle increases, and the plasticity characteristics of the cement are enhanced, and the negative effect on the Pmax ascends slowly. (4) The temperature stress is in a positive relationship with the ∆T, and its weakening on the Pmax is about 6% to 7%. (5) Combining the temperature stress and the change of the cement properties, total negative effect of temperature on the sheath accounts for 10% to 12%, when ∆T ranges from 60 to 110 °C.

Laboratory Study on the Stability of Large-Size Graded Crushed Stone under Cyclic Rotating Axial Compression

In this paper, the stability of large-size graded crushed stone used for road base or cushioning under repeated load is investigated. Using an in-house developed device, large-size crushed stone mix was compacted and molded by the vibration and rotary compaction method. Cyclic rotating axial compression was applied, and the shakedown theory was used to study the cumulative deformation of the large-size crushed stone specimens. The effects of gradation parameters on the cumulative strain and stability behavior were analyzed, and the critical stability and failure loads were determined according to the shakedown theory. The test results indicate that there are three obvious instability behavior stages of large-size graded crushed stone under cyclic rotating axial compression: elastic stability, plastic creep, and incremental plastic failure. Large-size graded crushed stone has a higher critical stability load stiffness than conventional-size graded crushed stone. The critical shakedown load of the specimen is mainly affected by the skeleton structure performance, and the critical failure load by the properties of the crushed stone material. Increasing the content and compactness of large-size crushed stone in the specimen can improve the stiffness and stability performance, and to achieve improvements, the content of large-size crushed stone should be controlled between 22% and 26%. The critical shakedown load increases with the increase in the California bearing ratio (CBR) value, while, on the other hand, the CBR value has little relationship with the critical failure load.

High-Cycle Fatigue Criterion for Shape Memory Alloys Based on Shakedown Theory

Based on a recently developed shakedown theory for non-smooth nonlinear materials, we derive a criterion for high-cycle fatigue in shape memory alloys (SMAs). The fatigue criterion takes into account phase transformation as well as reorientation of martensite variants as the source of fatigue damage. The mathematical derivation of the criterion is based on the requirement of elastic shakedown for a given structure to achieve unlimited fatigue endurance. Elastic shakedown is defined as an asymptotic state in which damage due to time-varying load becomes confined at the mesoscopic scale, or the scale of the grain, with no discernable inelasticity at the macroscopic scale. From an energy standpoint, elastic shakedown corresponds to a situation where energy dissipation becomes bounded and the response elastic after a certain number of loading cycles. A sufficient condition to achieve this state was established by Melan (1936) [1] and Koiter (1960) [2] for elastoplastic materials and later generalized to hardening plasticity by Nguyen (2003) and to non-smooth non-linear materials by Peigney (2014). The latter formulation is applicable to SMAs obeying the ZM constitutive model (Zaki & Moumni, 2007) and is shown here to allow the derivation of a high-cycle fatigue criterion analogous to the one proposed by Dang Van (1973) for elastoplastic materials. The criterion allows establishing a safe domain in stress deviator space at the mesoscopic scale consisting of a hypercylinder with axis parallel to the direction of martensite orientation. The hypercylinder is delimited along its axis by two transverse hyperplanes representing bounds on admissible stress states consistent with the loading conditions for phase transformation. Safety with regard to high-cycle fatigue, upon elastic shakedown, is conditioned by the persistence of the macroscopic stress path, as the load varies and at every material point, strictly within the hypercylinder. The size of the hypercylinder is shown to strongly depend on the relative amount of martensite present in the SMA.

A Review of State-of-the-Art Methods for Pressure Vessels Design Against Progressive Deformation

Progressive plastic deformation is one of the damage mechanisms which can occur in pressure vessels subjected to cyclic loading. For design applications, the main rule proposed by codes against this failure mode is the so-called 3f (or 3Sm) criterion. During the last decade, studies have shown that this condition can be unreliable, and its application should be restricted. In parallel, theoretical developments enabled shakedown analyses to be considered in design methodology, and to be incorporated in codes and standards (EN13445, CODAP) from the early 2000s. This paper gives a review of innovative methods based on shakedown theory, which can be used in the determination of elastic shakedown limits, ratchet limits, or cyclic steady state. These approaches are based on different concepts, such as elastic compensation linear matching method (LMM), Gokhfeld theory (uniform modified yield, load dependent yield modification (LDYM)), or the research of stabilized cycle direct cyclic analysis (DCA). Each method is presented and applied on a Benchmark example in abaqus, and results are compared. A final assessment focuses on computation time, and underlines the benefits that could be expected for industrial applications.

Repeated Loading of Cohesive Soil – Shakedown Theory in Undrained Conditions

The development of industry and application of new production techniques could bring about extraordinary problems that have been neglected. One of these challenges in terms of soil mechanics is high frequency cyclic loading. Well constructed foundation may reduce this troublesome phenomenon but excluding it is usually uneconomic. In this paper, shakedown theory assumptions were studied. Cyclically loaded soils behave in various ways depending on the applied stress rate. Common cohesive soils in Poland, i.e., sandy-silty clays are problematic and understanding of their behaviour in various conditions is desired. In order to study repeated loading of this material, cyclic triaxial test were carried out. Cyclic loading tests were conducted also in one way compression. These methods in small strain regime allow permanent strain increment analysis with resilient response after numerous cycles. This behaviour was subsequently exploited in the study of shakedown theory. This paper contains some conclusions concerning the above-mentioned theory.

Development Of A Pavement Rutting Model Using Shakedown Theory

The rutting of flexible pavements during their exploitation is considered to be one of the main problems in UK as well as worldwide. It is a serious mode of distress alongside fatigue in bituminous pavements that may lead to premature failure, as indicated by permanent deformation or rut depth along the wheel load path, and results in early and costly rehabilitation. This kind of pavement distress makes a negative impact to the serviceability characteristics of the flexible pavement, to the residual life of pavement structure and also to the safety and ride quality for traffic. Two design methods have been used to control rutting: one to limit the vertical compressive strain on the top of subgrade and the other to limit rutting to a tolerable amount usually around “12 mm”. Although experimental data and practical experience have been introduced into these design methods through empirical parameters, there is not a simple relationship between the elastic strain and the long-term plastic behaviour of pavement materials. This paper describes a method based on the kinematic shakedown theorem for constructing a mathematical model to predict the long-term behaviour of pavement structures under the action of repeated and cyclic loadings imposed by moving traffic. This method seeks the mechanism from within a class of mechanisms that minimises the shakedown limit load for pavement structures consisting of layers of Mohr-Coulomb materials. The model differs from extant models, in that the cyclic nature of the loading on a pavement is recognised from the outset, and the current method which is based upon foundation analysis, is replaced by a procedure employing shakedown theory that features the capabilities and applications of the developed technique for assessing rutting in flexible pavements. The basic concepts are outlined together with the most recent calculations of the critical design shakedown load. The influence of the design parameters such as, the strength, stiffness and depth of the granular base-course material as well as the consequences of traffic loading (number of equivalent standard axel loads – ESAL’s) are discussed.