Torsional Ring Research Articles

Sand–geotextile interface shear strength by torsional ring shear tests

The torsional ring shear apparatus was developed to evaluate the residual shear strength of soft soils. It has the advantage of allowing large displacement to take place while shearing. In using geotextiles for geotechnical engineering applications, the soil–geotextile interface shear strength is an important design parameter. Hence this paper describes the evaluation of the soil–geotextile interface shear strength using the torsional ring shear test. Dry medium sand and nonwoven polypropylene geotextile were used. The test program consisted of three series of tests for parametric study as well as the fourth series that compares the results from the direct shear and ring shear test. This test program was the first in a series aimed at studying the feasibility of measuring the soil–geotextile interface shear strength using the ring shear apparatus. The test results show that the peak friction angle and residual friction angle of the sand–geotextile interface is not significantly affected by the nominal mass of geotextile. The results also show that the sand–geotextile interface peak and residual friction angles are not greatly influenced by the rate of shear. However, the results show that the tests should not be conducted at a strain rate higher than 10 deg/min, beyond which erratic readings were observed. The results also show that the friction angle of the sand–geotextile interface decreases as the overburden pressure increases. Finally tests were conducted using the ring shear and direct shear operating at similar conditions. The results show that measurements of sand–geotextile interface friction angle measured by both equipments is almost identical at small shear displacement of less than 3 mm. Beyond the 3 mm small shear displacement, the direct shear test indicates higher friction angle than the ring shear test. The direct shear test is unable to measure interface shear strength at a displacements larger than about 15 mm, whereas the ring shear test can measure residual interface shear strength at displacement of more than 200 mm.

Gas phase reaction of F − with chlorocyclopropane. Ab initio study of elimination and substitution

The stereochemistry of elimination in chlorocyclopropane was investigated using ab initio (6-31(+)G ∗//HF/6-31(+)G ∗) calculations. The competitive S N2 route was also considered. Transition states were located for the E2(anti), E2(syn) and S N2 reactions. The three-membered ring has a pronounced effect on the syn/anti preference of E2 elimination; the barrier of syn elimination (22.2 kcal mol −1) is only 3.6 kcal mol −1 larger than that of anti elimination. The small syn/anti difference is related to the inherent periplanarity of the syn transition state and the torsional ring strain of the anti transition state. Comparing the reaction of F − with cyclopropyl, cyclopentyl and cyclohexyl chlorides, it was found that the tendency for anti elimination is especially reduced in the three-membered ring because of the non-periplanar conformation of the anti transition state. According to theory, the initial reactant complex can react further via the E2(anti) pathway or S N2 substitution. The barrier to substitution is 2.5 kcal mol −1 and the S N2 pathway dominates over elimination in this system. At the MP2/6-31(+)G ∗//HF/6-31(+)G ∗ level, the S N2 pathway has a lower activation barrier by 7.3 kcal mol −1 compared with the E2(anti) pathway.

Concentrated ring loadings in a full space or half space: solutions for transverse isotropy and isotropy

In this analysis solutions for concentrated ring loading in a transversely isotropic full space or half space are found. The elastic field is derived by integrating the known fundamental point force solutions along a circular ring. Three cases of ring loading are considered. Taking the z axis along the material axis (the z = 0 plane is the isotropic plane), the first case studied is when the ring load is in the z direction, referred to as normal loading. The other two cases are shear ring loads directed in the plane of isotropy. In the first instance, the ring load is unidirectional and independently applied in either the x or y direction. The second case considers the axisymmetric radial and axisymmetric torsional ring loads. The solution for ring loading applied to the surface of a half space is first obtained. Subsequently the solutions for ring loading in a full space and buried ring loads in a half space are found. In all cases the elastic displacement and stress fields are evaluated in terms of closed form expressions containing complete elliptic integrals of the first, second and third kinds. An interesting feature of the full space solution is that the potential function and its radial derivatives exhibit a cylindrical discontinuity for negative z values. However, it is shown that these discontinuous functions do provide continuous displacement and stress fields. A limiting form of the solutions for transverse isotropy also provides the corresponding results for isotropic materials.

Slope Stability Analyses in Stiff Fissured Clays

Results of torsional ring shear, direct shear, and triaxial compression tests on cohesive soils reveal that the fully softened shear strength is stress-dependent and related to the type of clay mineral and quantity of clay-size particles. An empirical relationship for the fully softened friction angle is presented that is a function of liquid limit, clay-size fraction, and effective normal stress. Studies of first-time slides, i.e., slopes that have not undergone previous sliding, in stiff fissured clay with a liquid limit between 41 and 130% suggest that the mobilized shear strength along the failure surface can be lower than the fully softened shear strength. Recommendations are presented for estimating the mobilized shear strength in first-time slides based on soil plasticity. Soils with a liquid limit greater than 30% exhibit a large difference between the fully softened and residual friction angles. In these soils, the presence or absence of a pre-existing shear surface should be clarified.

Shear Behavior of an Unreinforced Geosynthetic Clay Liner

Dry and hydrated specimens of an unreinforced geomembrane-backed geosynthetic clay liner (GCL) were sheared against a textured geomembrane using a torsional ring shear apparatus to study the shear behavior of geomembrane encapsulated bentonite. Shearing of the dry GCL against a textured geomembrane at high normal stresses resulted in failure occurring within the GCL adhesive that attaches the bentonite to the geomembrane backing and not the GCL bentonite/geomembrane interface. This type of failure occurred when both smooth and textured geomembranes were used as the GCL backing material. Conversely, shearing of the hydrated GCL against a textured geomembrane resulted in failure occurring at the GCL bentonite/textured geomembrane interface. The order of hydration and normal stress application was found to significantly affect the GCL/textured geomembrane interface shear strength. The mobilized shear strength of the GCL/textured geomembrane interface does not equal the drained shear strength of bentonite because of the effect of geomembrane texturing and the lack of drainage during dry and hydrated GCL testing, respectively. Finally, the hydrated GCL/textured geomembrane interface exhibits an increase in peak shear strength of approximately 13% per log cycle of the shear rate. Therefore, the selection of a shear displacement rate is important for unreinforced geomembrane-backed GCL/textured geomembrane interface shear tests.

HDPE Geomembrane/Geotextile Interface Shear Strength

This paper describes torsional ring shear tests on interfaces comprised of high-density polyethylene (HDPE) geomembranes/nonwoven geotextiles and a drainage geocomposite. Four textured geomembranes with three different manufacturing techniques are utilized to investigate the effect of geomembrane texturing on interface shear resistance. In addition, the effects of geotextile fiber type, fabric style, polymer composition, calendering, and mass per unit area on textured HDPE geomembrane interface strengths are investigated. The textured HDPE geomembrane/nonwoven geotextile and drainage geocomposite interfaces exhibited a large postpeak strength loss. This strength loss is attributed to pulling out or tearing of filaments from the nonwoven geotextile and orienting them parallel to shear, and polishing of the texturing on the geomembrane. At high normal stresses, the strength loss can be caused by damage to or removal of the texturing on the geomembrane surface.

Strain-Softening Behavior of Waste Containment System Interfaces

Laboratory test results indicate that many geosynthetic interfaces in liners and covers for waste containment exhibit strain-softening behavior. A peak shear strength is mobilized at small displacements, but post-peak strength reductions occur with increasing displacement. Mechanisms that contribute to strain-softening include clay particle reorientation, geosynthetic polishing, and geosynthetic failure. Test results obtained from direct shear and torsional ring shear devices are summarized to illustrate these mechanisms. The design implications of strain-softening behavior are then investigated using analytical and numerical models. Deformations in the waste under gravity are sufficient in many cases to limit the available shear resistance along an interface to less than the peak strength. It is recommended that a factor of safety greater than one be achieved in all containment system slope designs, assuming that residual strengths are mobilized along the base of the entire containment system.

Effect of dynamization on gap healing of diaphyseal fractures under external fixation

We asked whether dynamization of externally fixed diaphyseal fractures could improve bone healing in comparison to rigid fixation of fractures having similar remaining gap sizes. To answer this question we evaluated metatarsal osteotomies in 12 sheep. The osteotomy with a 0.6-mm gap was stabilized with a specially designed high bending and torsional stiffness external ring fixator. Osteotomies in six sheep were stabilized rigidly (axial movement < 0.06 mm) or dynamically (axial movement 0.15–0.34 mm). The cyclical axial interfragmentary movement was caused by the load-bearing of the operated limb. With increasing healing time, the initially allowed movement was decreased by callus formation around the osteotomy. The reduction in interfragmentary movement was measured and monitored by a linear variable displacement transducer at the external fixator and a telemetry system. After 9 weeks the sheep were sacrificed and the healed bones were investigated biomechanically and histomorphologically. Compared to the rigidly fixed osteotomies, the dynamized osteotomies showed significantly ( P < 0.05) greater (+41%) callus formation and 45% greater tensile strength of the newly formed bone in the cortical osteotomy gap. Histological analysis indicated that the effect of dynamization occurred mainly after the 5th week.

Drained Residual Strength of Cohesive Soils

Results of torsional ring shear tests on cohesive soils reveal that the drained residual strength is related to the type of clay mineral and quantity of clay‐size particles. The liquid limit is used as an indicator of clay mineralogy, and the clay‐size fraction indicates quantity of particles smaller than 0.002 mm. Therefore, increasing the liquid limit and clay‐size fraction decreases the drained residual strength. The ring shear tests also reveal that the drained residual failure envelope is nonlinear, and the nonlinearity is significant for cohesive soils with a clay‐size fraction greater than 50% and a liquid limit between 60% and 220%. This nonlinearity should be incorporated into stability analyses. An empirical correlation for residual friction angle is described that is a function of liquid limit, clay‐size fraction, and effective normal stress. Previous residual strength correlations are based on only one soil index property and provide a residual friction angle that is independent of effective n...

Torsional traction on an open finite cylindrical cavity

This paper deals with the stress analysis of an elastic half-space with an open cylindrical cavity of finite dimension subjected to torsional shear tractions. Within the classical theory of elasticity, the boundary value problem is formulated as a generalized Cauchy singular integral equation from which fractional-order singularities in the stress distribution near the bottom of the hole can be deduced. As an illustration, the fundamental solution corresponding to a torsional ring load acting on the sidewall of the cavity is presented. The resulting load-induced as well as shape-induced singularities in the response are examined.

About torsion ring shear tests on remoulded clay

About torsion ring shear tests on remoulded clay

Step polymerization via reductive coupling of dicarbonyl compounds a fundamental study

A mechanistic and synthetic study of a new condensation type, step polymerization chemistry is being undertaken, wherein organometallic assisted reduction (McMurry Chemistry) may lead to essentially quantitative coupling of carbonyl functional groups. Initial studies dealt with the coupling of heterocyclic aldehydes in an attempt to elucidate the coupling mechanism. After formation of the intermediate using TiCl 4 and Zn in THF, the pinacol is obtained in high yield with hydrolysis in a 2:1 ratio of diastereomers. Separation and characterization reveals that the dl pair is formed predominantly over the meso isomer. Using 18O labeling experiments, the hydrolysis mechanism was determined not to proceed through a S N2 pathway. If the intermediate is exposed to reflux conditions, olefins are obtained in high yield. X-ray studies reveal valuable information concerning torsional ring angles. Coupling of the dicarbonyl compounds leads to both polypinacol and polyolefin formation. The polypinacol work to date has been most successful due to the high solubility of the existing hydroxyl groups. In contrast the low solubility of the polyolefins has made isolation and characterization difficult.

Undecidability of module homomorphisms

For finitely additively generated torsion free modules and rings, we show existence of module monomorphisms is decidable but of epimorphisms is undecidable.

Transient response of an elastic solid to a moving torsional load in a cylindrical bore an approximate solution

This paper is an attempt to apply Cagniard's technique to a transient problem of a dispersive medium. The transient response of an elastic solid to a moving torsional ring load in a cylindrical bore is considered. By making an approximation to the modified Bessel function, Cagniard's technique is applied. An approximate solution, which has explicit expressions for the wave front geometry and has a more suitable form for numerical computations, is obtained. The applicability of the solution is also discussed.

Transient response of an inhomogeneous elastic solid to a moving torsional load in a cylindrical bore

The transient response of an inhomogeneous elastic solid to a torsional ring load is considered. The load is suddenly applied to a cylindrical wall in the solid and then moves along a bore. The inhomogeneity of the solid is assumed as μ/μ0 = ρ/ρ0 = (r/a)λ so that SH-wave velocity is constant throughout the solid.A general form of solution is obtained for an arbitrary motion of the load. It can be applicable to both transient and steady-state problems of the moving/stationary load. Explicit expressions for the displacement are given for three types of the load applications; (a) impulsive load, (b) step pulse load, (c) uniformly moving load. Numerical computations are carried out for the displacement in detail. The displacement singularities at wave fronts and beneath the loaded point are also discussed.

Dust and oil slinger

A torsional vibration damper of the type having an inertia ring member and a hub member coupled together by an elastomer member. The hub member may be in the form of a disc and is adapted to be coupled to a rotating shaft subject to torsional vibrations, the elastomer and inertia ring member acting in a known manner to damp torsional vibrations. According to this invention a seal, termed a dust and oil slinger, is mounted on the hub. The seal overlies the elastomer and protects it from dust or other particles and from corrosive fumes and liquids. The seal may additional serve as a sacrificial member which will, in certain corrosive ambients, degrade prior to degradation of the elastomer connecting the hub and inertia ring. The seal is either integral with the working elastomer member, or is formed by adhering to the working elastomer member a sealing material of a different composition.

On extensions of nilpotent torsion rings by semisimple rings

A class of rings in which each member is the extension of a nilpotent torsion ring by a semisimple semiartinian ring is presented.

Four-fold torsion theories and rings of fractions

Four-fold torsion theories and rings of fractions

Relationship between torsional angles and ring-puckering coordinates

A relationship between torsional angles and ring puckering coordinates, applicable to any puckered ring, is deduced assuming infinitesimal displacements from a planar reference conformation. For equilateral polygons there is only one maximum torsion angle θ m and one phase angle φ m for each value of m, whereas for non-equilateral polygons there is one maximum θ m j,j+1 and a correction, ϵ m j,j+1 , to be applied to the phase angle φ m for each torsion angle θ j,j+1 . The resulting expressions for equilateral pentagons and hexagons are equivalent to the empirical ones proposed previously.

Torsion theories and ring extensions

Let ϕ:R→S be a ring homomorphism, and let ϕ∗:Mod-S -> Mod-R be the “restriction of scalars” functor. If Tis a hereditary torsion class for R, then T ∗={MεMod-S ≤ϕ∗(M)εTis a hereditary torsion class for S. We compare the quotient functors Qand Q∗of Tand T ∗respectively. Let ϕ∗:Mod-R→ Mod-S be the “extension of scalars ” functor:ϕ∗(M)=M⊗RS ∀MεMod-R. If ϕ∗ Q Q ∗is called S-good. If Tis S-good, then ϕ∗Q∗is a subfunctor of Qϕ∗If Sis also left R-flat, then ϕ∗Q∗≌,Qϕ ∗.We make an extensive investigation of the S-good property and give a number of ex-amples. The results are then applied to group rings and skew polynomial rings, where the invariance of Tunder ring auto-morphisms plays an essential role. In particular, for a group ring AG, if H◃ Gand Tis a hereditary torsion class for AH which is G-invariant, then Tis AG-good, and with equality if and only if G:H< ã or G:H=ãand Qcommutes with all free sums. In the special case when the right singular ideal of AHis zero and Tis the Lambek tor-sion class, the second condition above reduces to the condition that Q(AH)be semi-simple artinian.