Investigation of Percolation-Driven Fluid Transport in Rock Salt under Repository-Relevant Conditions (PeTroS)

According to the state of the art in mining and repository research, undisturbed rock salt is impermeable to fluids. Hence, rock salt formations are considered as host rock for nuclear waste repositories. Viscous, polycrystalline salt rock with low humidity contains no connected pore spaces. Two mechanisms are known for fluid transport: (a) damage due to large deviatoric and tensile stresses generates dilatancy, and hence permeability. (b) Fluid pressure exceeding the minor principal stress can open pathways (pressure-driven percolation, Minkley et al., 2013). To assess barrier integrity of rock salt barriers, the dilatancy and minimal stress criteria have been derived. Recently (Ghanbarzadeh et al., 2015; Lewis and Holness, 1996), high permeabilities in rock salt have been postulated under certain conditions. In particular, at high stresses and temperatures, including possible repository conditions, rock salt is claimed to develop a connected, thus permeable, pore space. In the PeTroS project (Minkley et al., 2020), we investigated fluid transport in the supposedly permeable region. Five points in pressure-temperature space were defined – pressures of 18 and 36 MPa, temperatures of 140, 160, and 180 ∘C. At each point, experiments with both nitrogen and saturated NaCl solution (brine) were performed. Samples were prepared from natural rock salt of German Zechstein formations, both bedded and domal salt. Sample material was generally relatively pure rock salt with minor impurities. Cylindrical samples (diameter 100 mm, length 200 mm) were loaded in a triaxial (Kármán) cell. Fluid pressure was applied to a central pressure chamber; any transmitted fluid was collected and extracted at the secondary side. The entire cell was heated to the specified temperature. Experiments generally comprised an isotropic phase (several stages of fluid pressure almost up to the confining stress) and a fluid breakthrough phase (lowering of axial stress by strain-controlled extension). After the test, a coloured tracer fluid was injected to visualise fluid discharge points. Fluid breakthroughs with fluid pressure above the minor principal stress were observed at all five pressure-temperature conditions. Some samples showed an approximately Darcian flow at fluid pressure below the minor principal stress, with permeabilities in the order of 10−22 m2, as is regularly observed due to the small size and initial damage from sample preparation (Popp et al., 2007). Tests consistently showed a gradual decrease of flow rate, i.e. reduction of the initial damage. A stable permeability over longer times, as would be expected due to the formation of a connected pore space network, was not observed in any of the experiments. Intriguingly, experiments with brine showed no initial permeability even though the wetting fluid should plausibly favour the formation of a stable connected pore network. Predictions of the static pore scale theory (Ghanbarzadeh et al., 2015) could thus not be confirmed. Regarding repositories for heat-generating waste, it can be concluded that from a geomechanical point of view, the dilatancy and minimal stress criteria are the relevant criteria for barrier integrity even at higher pressure and temperature.

Interior dynamics of tidally-locked super-Earths: the case of LHS 3844b

<p>The vigour and style of mantle convection in tidally-locked super-Earths may be substantially different from Earth's regime. Earth's surface temperature is spatially uniform at 300 K, which is sufficiently cold to drive strong downwellings into the interior (i.e. subduction). In contrast, a tidally-locked super-Earth can have a large temperature contrast between the dayside and nightside, which we infer could lead to a dichotomy of the interior dynamics. We therefore use constraints from astrophysical observations to infer the possible pattern of flow in the interior of a tidally-locked super-Earth, using super-Earth LHS 3844b as a case study. We run mantle convection models using the code StagYY with two-dimensional spherical annulus geometry and parameters from the literature that are appropriate for LHS 3844b. The majority of the mantle is either perovskite or post-perovskite with the phase transition occurring around 1700 km depth (the total mantle depth is 3757 km). An upper and lower bound for the viscosity of post-perovskite is provided by previous theoretical calculations. We include plastic yielding to model the brittle nature of the lithosphere; plastic yielding occurs when the local stress state exceeds a prescribed yielding criteria and is commonly applied in studies of Earth to produce surface behaviour similar to plate tectonics.</p><p>For a low yield stress criteria (promoting a weak lithosphere), we find that plumes are generally evenly distributed between the dayside and nightside, albeit strong downwellings form on the nightside. Plumes on the nightside have less lateral mobility than on the dayside because they are confined by downwellings either side. In contrast, for a high yield stress criteria, the interior dynamics are mostly driven by a prominent downwelling on the dayside which flushes hot material from the lower thermal boundary layer around the CMB towards the nightside where plumes preferentially arise. This, in turn, leads to a return flow of colder material from the near surface of the nightside towards the dayside. This seemingly counterintuitive pattern of flow is a consequence of weak lithosphere (due to temperature) on the dayside that is able to deform and thereby subduct, whereas lithosphere on the nightside is too stiff to subduct.</p><p>Our models therefore show that the vigour of convection and the distribution of upwellings and downwellings of tidally locked super-Earths are sensitive to the strength of the lithosphere: plumes can either be equally distributed around the planet or preferentially occur on the nightside. In the first case, the cold downwellings are also equally distributed but more prominent on the nightside, whereas in the second case they are preferentially on the dayside. Somewhat unexpected, we do not observe a preference for hot plumes to congregate on the dayside. Our results have implications for space missions such as TESS, CHEOPS, JWST, PLATO and ARIEL that will discover and characterise super-Earths, thereby potentially probing for signals of volatile outgassing and volcanism.</p>

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.

Fatigue Performance of Preloaded Ultra High Strength Threaded Fasteners

This experimental study investigates the high cycle fatigue (HCF) performance of preloaded ultra-high strength (UHS) threaded fasteners. Every sample is subjected to a cyclic uniaxial stress additional to a mean stress, which is arbitrarily set as half of the static tensile strength. Experimental results of UHS fasteners (Classes 14.9 and 15.9) and commercially available (CA) fasteners (Class 10.9) are analyzed: S-N curves are constructed following the ASTM standards and compared after normalization. Results indicate that the normalized fatigue strength of UHS threaded fasteners is lower than that of CA threaded fasteners. For each class, the experimental S-N curves are compared with the estimation obtained using Marin equation adjusted by mean stress criteria. It is concluded that the estimation by Marin equation did not show acceptable consistency to experimental data.

Establishing Fracture Mechanics Based Minimum Allowable Temperatures for Low Temperature Applications of ASME B31.3 Piping

Impact test exemption curves in ASME B31.3 [1] were adopted from ASME Section VIII Division 1 (VIII-1) [2] with subtle modifications. The VIII-1 exemption curves were generated based on early fracture mechanics methodologies and limited amount of test data with an assumption on maximum applied stress intended to correspond to the typical VIII-1 allowable stress criteria. The applicability of the exemption curves for low temperature applications of ASME B31.3 piping (such as blowdown events) is open to discussion because of potentially high longitudinal thermal expansion stresses that may exceed the VIII-1 allowable stress criteria. Additionally, unlike in VIII-1 and ASME Section VIII Division 2 (VIII-2) [3], there is no post weld heat treatment (PWHT) credit on Minimum Design Metal Temperature (MDMT) in ASME B31.3. Detailed fracture mechanics analyses have shown that PWHT can significantly reduce the risk of brittle fracture failures due to its relaxation effect on weld residual stresses, a major crack driving force. In this paper, a fracture mechanics-based methodology for establishing Minimum Allowable Temperatures (MAT) for low temperature applications of ASME B31.3 piping is presented. A state-of-the-art fracture mechanics methodology published in Welding Research Council (WRC) Bulletin 562 [4] is used to develop step-by-step Level 1 and Level 2 procedures for establishing MAT for low temperature applications of ASME B31.3 piping. For the Level 1 methodology, MAT screening curves are developed based on a likely conservative assumption that the stresses in the piping component are at the maximum code allowable stresses in both the hoop and longitudinal directions. For the Level 2 methodology, stress ratio verses temperature reduction curves are developed to consider the effect of lower operating stresses. Similar to VIII-2 [3] toughness exemption curves, the screening curves are generated for both As-Welded and PWHT conditions. The curves can also be used for impact tested materials. The established MAT can be directly coupled to different reference flaw sizes and integrated with an inspection criteria for piping components. Two examples of establishing MAT using both the proposed Level 1 and Level 2 methodologies are presented herein.

Stress concentration and strength prediction of 2×2 twill weave fabric composite with a circular hole

Stress concentration and strength prediction of 2 × 2 twill weave carbon fiber reinforced composite specimens with different hole sizes are investigated on numerical and analytical basis. Stress distribution around the hole is obtained using Lekhnitskii’s model together with Tan’s finite width correction factor and also finite element analysis. Validity of Lekhnitskii’s formula together with Tan’s correction is demonstrated for 2 × 2 twill weave composites with different w/d ratios. Tan’s correction factor is compared with finite element analysis results at a characteristic distance away from hole tip where the stresses are important for strength prediction. Applicability of point stress criteria and average stress criteria strength prediction methods for open hole specimens to 2 × 2 twill weave material is demonstrated. The performances of the point stress criteria and average stress criteria methods are compared in the case of eccentric tension loading. All analytical and numerical results are verified by experimental study.

Crack Propagation in the Human Bone. Mode I of Fracture

The problem of crack propagation in human bone is studied. We for- mulate and solve the mathematical problem for the pre-stressed crack in Mode I of classical fracture. Using the boundary conditions on the crack faces in the bone, regarded as an elastic composite material, we solve our Riemann-Hilbert problem. Using generalized Sih's strain energy density generalized and maximum stress criteria we find the direction of the crack path in Iliac bone, regarded as a pre-stressed orthotropic composite.