Showing papers on "Discontinuity (geotechnical engineering) published in 1972"

Cohesive force across the tip of a longitudinal‐shear crack and Griffith's specific surface energy

Abstract: The cohesive force across the fault plane is considered in order to understand the physical mechanism of rupture at the tip of a longitudinal-shear crack. The elastic field around the tip of a crack and the condition of rupture growth are systematically derived from the assumption that the cohesive force is given as a function of the displacement discontinuity. This assumption is more physically meaningful than those originally used by G. I. Barenblatt in 1959 and 1962. The stress field around the tip is calculated for several models of cohesive force, and is shown to be nonsingular even at the tip. The condition of rupture growth that is used to determine the rupture velocity turns out to be equivalent to the Griffith criterion and the relation employed by B. V. Kostrov in 1966, but the specific surface energy is defined more clearly in this paper.

Dissipation and breakdown of a wing-tip vortex

Abstract: The solutions of the incompressible quasi-cylindrical momentum-integral equations describing the flow in the viscous core of a wing-tip vortex are obtained in a closed form and are shown to have two distinct branches. The discontinuities of these solutions have infinite axial gradients and therefore, following Hall, are assumed to signal the inception of the vortex breakdown. Benjamin's finite transition, with its excess flow force dissipated, is shown to give results equivalent to a sudden cross-over, upstream of the discontinuity, from one branch solution to another. The critical point of such a cross-over is downstream from the cross-over, at the discontinuity. Sarpkaya's experimental data, and the nature of the solutions ahead of the discontinuity, suggest that the physical manifestation of the discontinuity is the spiral breakdown, whereas the cross-over seems to be related to the rapidly expanding and subsequently contracting axisymmetric bubble. This therefore implies that the beginning of the spiral breakdown is the all important disturbance which triggers off not only the downstream asymmetric departure of the flow from its quasi-cylindrical form but also the formation of the upstream axisymmetric cross-over bubble. Solutions for the turbulent flow downstream from the spiral breakdown indicate that the wing-tip vortex breakdown can result in an appreciable reduction of the maximum circumferential velocity and should thus lessen the danger that trailing vortices present to following aircraft.

Equations of state for silicates in the metallic form

Abstract: We re-examine the problem of the mantle-core discontinuity. By means of theoretical equations of state for silicates in the metallic form, we conclude, once more, that it is a composition discontinuity rather than a phase transition.

Structure of the Icelandic Basalt Plateau and the Process of Drift

Abstract: Conventional stratigraphic mapping of parts of the Icelandic flood basalt succession and regional studies of the palaeomagnetic stratigraphy suggest that in at least two areas the basalt pile is composed of large lenticular shield-like lava units. Each unit is related spatially to its own feeding dyke swarm and is the result of a protracted period of dominantly fissure volcanism from a single fissure zone. The geophysical evidence suggests that the most important seismic discontinuity is the boundary between layers 2 and 3: P seismic velocities 5.1 and 6.3 km/s respectively. This seismic discontinuity has been mapped over large areas of Iceland by Palmason who has shown that it is generally at a depth of between 2 and 5 km below sea level. In eastern Iceland the discontinuity is approximately horizontal and markedly discordant with the observed dip of the individual lavas at sea level. It is suggested that, under Iceland, layer 3 is composed of intrusive dykes and gabbroic masses, whereas layer 2 is made up of extrusives cut by dykes and smaller intrusions. The observed relationships of the lava lenses constituting layer 2 are compatible with a crustal spreading model. The drift away from the axial zone, largely accommodated by dyke injection, appears to be at about 1 cm/year, a rate comparable to that observed on the adjacent Reykjanes Ridge.

Stability problems caused by seams and faults

Abstract: OFTEN THE EXISTENCE OF FAULTS OR SEAMS ARE KNOWN PRIOR TO EXCAVATION, HOWEVER, SOMETIMES THE BEHAVIOR OF THESE ZONES HAS BEEN MISCALCULATED. SOME OF THE APPROACHES THAT ARE AVAILABLE FOR CONSTRUCTING OPENINGS THROUGH FAULTS AND SEAMS ARE REVIEWED. BIERBAUMER (1913), I. STINI (1950), L.V. RABCEWICZ (1957), AND H. LAUFFER'S (1958) CLASSIFICATION SYSTEMS ARE BRIEFLY REVIEWED TO ILLUSTRATE THAT ALTHOUGH CLASSIFICATION SCHEMES HAVE OFTEN BEEN PROPOSED THEY HAVE NOT ALWAYS BEEN CAREFULLY USED. THE IMPORTANCE OF TERZAGHI'S (1956) SYSTEM, EITHER IN ITS ORIGINAL FORM OR WITH SOME MODIFICATIONS, HAS SERVED AS THE MAJOR FOCUS OF CLASSIFICATION SYSTEMS. DISCONTINUITIES IN ROCK MASSES ARE DISCUSSED IN SOME DETAIL. DISCONTINUITIES ARE FORMED THROUGH FAILURE IN EXTENSION/TENSION, IN SHEAR, OR IN MORE COMPLEX FAILURE THROUGH A COMBINATION OF BOTH. THREE CRITERIA ESSENTIAL IN ANY KIND OF CLASSIFICATION ARE: (1) SCALE, BASED ON APERTURE, PERSISTENCE, AND TYPICAL SPACING, IS BROKEN DOWN INTO 5 CLASSES - MICROFISSURES, BEDDING AND FOLIATION PARTINGS, JOINTS AND SEAMS, MINOR FAULTS, AND MAJOR FAULTS. (2) CHARACTER, BASED ON SMOOTHNESS AND THE PROPERTIES OF FILLING MATERIAL OR COATINGS IF ANY, IS DISCUSSED IN TERMS OF 7 GROUPS OR PROBLEM AREAS - JOINTS, SEAMS, AND SOMETIMES MINOR FAULTS; CLEAN DISCONTINUITIES (WITHOUT FILLINGS OR COATINGS); CALCITE FILLINGS; CHLORITE TALC, AND GRAPHITE COATINGS OR FILLINGS, INACTIVE CLAY MATERIAL; SWELLING CLAY; AND ALTERED MATERIAL TO A MORE SAND-LIKE MATERIAL. THE MAJOR TYPES OF DOMINANT MATERIAL THAT CAN BE FOUND IN GOUGE AND THE POTENTIAL BEHAVIOR OF THE GOUGE MATERIAL IS PRESENTED IN TABULAR FORM. (3) STRENGTH AND DEFORMABILITY, BASED ON MEASURED VALUES OBTAINED IN THE LABORATORY AND FIELD TESTING, IS DEVELOPED THROUGH THE CONCEPT OF JOINT ELEMENT. THE STABILITY PROBLEMS THAT FAULTS AND SEAMS MAY CAUSE UNDERGROUND ARE DEPENDENT ON: THE SIZE AND SHAPE OF THE OPENING; THE METHOD OF EXCAVATION; THE METHOD OF SUPPORT; THE ORIENTATION OF THE OPENING IN RELATION TO THE STRIKE AND DIP OF THE FAULT OR SEAM; THE WIDTH OF THE FAULT ZONE; ADJACENT SEAMS AND FAULTS, IF ANY; THE FREQUENCY, ORIENTATION AND CHARACTER OF ADJACENT JOINT SETS, THE COMPETENCE OF THE WALL ROCK TYPE; THE GAUGE MATERIAL; TIME ELAPSED AFTER EXCAVATION; THE IN-SITU STATE-OF-STRESS; AND THE WATER QUANTITIES.

The Initial Wave Front Emitted by a Suddenly Extending Crack in an Elastic Solid

Abstract: It is the purpose here to determine the pressure discontinuity radiated out from a crack tip when the crack, which is initially at rest, begins to extend. A half-plane crack in an unbounded body of homogeneous, isotropic elastic materials is considered.

Elastodynamic near-field of a finite, propagating tensile fault

Abstract: Displacement, particle velocity, and acceleration wave forms in the near-field of a finite, propagating tensile fault have been computed by numerical integration of the Green9s function integrals for an infinite medium. The displacement discontinuity (dislocation) on the fault plane is assumed to have the form of a unilaterally propagating, finite ramp function in time. Computer generated wave-form plots are presented for a variety of close-in locations with respect to the fault plane and for two different fault lengths.

Ring pad stress coining tooling

Abstract: Tools to plastically deform a portion of a structural member into one or a pair of flat bottomed grooves to generate residual compressive stresses in the member adjacent a discontinuity therein which improve the fatigue strength of the structural member.

Tapping of Love Waves in an Isotropic Surface Waveguide by Surface-to-Bulk Wave Transduction

Abstract: A theoretical study of tapping a Love wave in an isotropic microacoustic surface waveguide is given. The surface Love wave is tapped by partial transduction into a bulk wave at a discontinuity. It is shown here that, by careful design of the discontinuity, the converted bulk wave power and the radiation pattern may be controlled. General formulas are derived for the calculation of these important characteristics from a relatively general surface contour deformation.

Influence of Progressive Failure on Slope Stabilities

Abstract: Analytical evidence is presented on the effect of cracking on the slope stability of idealized embankment-foundation sections. The embankment boundary had a circular shape and the bounded mass was homogeneous, isotropic, and linearly elastic. The technique of conformal mapping was the key to calculation of elastic stresses induced by body forces. Various combinations of parameters were applied to represent peak and residual shear strength conditions along the cracked and uncracked portions of the critical surface. The factor of safety against slope instability varies considerably with the degree of development of the crack. Full crack development yields the minimum value for progression from toe to crest. However, partial development of the discontinuity is the least safe state when the direction of development is from crest to toe. The findings seem significant, not only for slope stability, but for all problems involving a potential for progressive failures.

Rotary drilling apparatus

Abstract: Apparatus adapted to be mounted in a rotary drilling drill string. It encompasses an acoustic discontinuity so located relative to the bit as to enhance or inhibit longitudinal vibrations of the bit during drilling operations.

The Influence of a Stem Discontinuity on Xylem Development in Norway Spruce, Piceaabies

Abstract: Norway spruce stems were artificially weakened by cutting a hole through them. The wood subsequently formed near the discontinuity was observed after six growing seasons following the cutting. Enhanced xylem development persisted in the zone of the discontinuity long after wounding and partial girdling stimuli could be considered to have an effect. This evidence supports the mechanistic hypothesis of stem-form development because mechanical stress level along the stem, originating from wind loading, would be greatest in the region of the discontinuity.

Shrinkage stresses near a discontinuity in a fibre composite material

Abstract: The technique of photothermoelasticity has been used to analyse the shrinkage stresses near to a discontinuity in a model of a fibre composite material. The axial-shrinkage stresses away from the discontinuity are tensile in the matrix and compressive in the fibre, while, between the ends of the discontinuous fibre they are wholly compressive. Under an applied axial tensile stress the presence of shrinkage stresses would therefore tend to reduce the tendency for matrix cracking to occur in the gap between the fibre ends where the tensile-stress concentration is high. However, if the fibres are close together the shrinkage stresses can themselves cause matrix cracking. These observations are reinforced by the results of other work on the strength of single- and multiple-fibre composites.

Radiused mold walls for plastic tubs

Abstract: The impact resistance of a one piece molded plastic tub along necessary tub wall discontinuities is increased by preforming such discontinuities along a radius to decrease the notch effect characteristic of an abrupt discontinuity.

Propagation of an Electromagnetic Shock Discontinuity in a Non-Linear Isotropic Material

Abstract: The propagation of an electromagnetic shock discontinuity in a non-linear isotropic dielectric is studied The velocity of propagation and the electromagnetic vectors behind the shock surface are determined in terms of the unit normal to the surface, the electric and magnetic induction fields ahead of the shock and their magnitudes behind the shock

Surface wave incidence on a plane structure having a multi-mode discontinuity in impedance

Abstract: The phenomenological theory of multi-mode surface wave propagation is applied to a plane structure having a multi-mode discontinuity in impedance. The resulting boundary-value problem is reduced to the solution of a Wiener-Hopf equation whose factorization is given in terms of the factorization that occurred in the one-mode case. Despite the complexity of the solution, the magnitudes of the surface wave excitation coefficients are elementary functions, as is the cylindrical power flow. On computing the power flow through the impedance surface, a definition of subsurface power flow \"inside\" the structure is suggested. The form can be taken so that the concept of modal power flow separability is maintained wherever the associated exterior field is primarily that of surface waves. It is further observed that without consideration of this term, power flow coupling occurs. Analogous results appear in the exact case of a dielectric slab having multiple simultaneously propagating surface wave modes. Lastly, conservation of power is verified by actual evaluation of the closed contour integral used to define the various components of power flow (surface wave, cylindrical, junction, and boundary). In fact, the following physical interpretation can be made for the magnitudes of the respective power flow distributions: the incident surface wave power (including the associated subsurface power) is equal to the excited surface wave power (including the associated subsurface power) plus the cylindrically radiating power. Introduction. Most exact problems of electromagnetic wave propagation are intractable. As a result, numerous approximate methods have been devised to discuss various aspects of the phenomena. In certain problems involving surface waves, it is known that this feature may be investigated by replacing the details of the structure with an impedance boundary condition. The class of problems to which we direct ourselves is characterized by discontinuous plane structures (infinite in extent) having the capability of supporting several surface wave modes. The orientation and geometry are such that the electromagnetic field produced is determined by solving a two-dimensional problem and all field components are derivable from a single unknown scalar wave function u(x, y). The plane structure will be replaced by the boundary conditions put forth by Karp * Received September 18, 1971. The research reported in this paper was supported partially by St. John's University and partially by the office of Naval Research under Contract No. N00014-67A0467-0075. Reproduction in whole or part permitted for any use of the U. S. Government. 300 R. C. MORGAN AND S. N. KARP and Karal [1], [2], These conditions have the form of generalizing the classical impedance condition to products of this type. Furthermore, they are derivable by approximating the reflection coefficient due to a plane incident wave (which may be known theoretically or experimentally). Previously, these conditions were applied to continuous structures in the papers [2], [3] and [4]. A discontinuity in the boundary condition for a two-mode problem on a right-angled wedge was treated in [5]. This paper will be directed toward solving the resulting mathematical problem of a two-mode discontinuity on a plane structure. A similar single-mode discontinuity problem was discussed by Kay [6]. It is interesting that despite the complexity of the solution, the physically important magnitude of the surface wave excitation coefficients is easily obtained (Kay observed this in the single-mode case). We take as our incident field an appropriate surface wave, and for simplicity, one half of the structure is allowed to be slightly thick (see [4]) while the other half is perfectly conducting. The various components of the power flow above the structure are computable by choosing an appropriate contour in physical space. In particular, on computing the power flow through the impedance surface, we are led to a definition of power flow inside and down the structure. The form is such that the concept of modal power flow separability is maintained wherever the associated exterior field is primarily that of surface waves. It is well known that, in the exactly solvable case of an infinite dielectric slab having simultaneously several propagating surface wave modes, surface wave modal power flow separability results if the power flow across a plane perpendicular to the slab is computed by including the associated power flow inside. Otherwise, there is in general a coupling of power when it is computed only above the slab. This phenomenon is observed also in our impedance model. For the case of the single real impedance, a consideration of this type does not occur because power is not transferred across the impedance surface and the model is one for which the power flowing inside the structure is negligible. In the case of the dielectric slab mentioned above, this corresponds to a slab of vanishing thickness. However, for a slab of finite thickness, the power flow inside may be significant. Thus, by our model, we provide an approximation that accounts for such power flow while the structure is also discontinuous. The exact problem of such a discontinuous structure has not been solved. However, we point out that the phenomenological theory is broader in context than the problem of the dielectric slab. Thus, we conjecture that our results herein are also. As a partial verification of our computations, conservation of power is checked for the contour used to define the various component field power distributions (i.e., surface wave, cylindrical and boundary). It is shown that the surface wave power (including that amount associated with flow inside the boundary) exactly cancels out the cylindrically radiated flow. The remaining boundary terms give zero power flow. As a result, we can state the following physical theorem for the magnitudes of the power flow distributions: the incident surface wave power flow (including \"inside\" term) is equal to the excited surface wave power flow (including \"inside\" term) plus the cylindrically radiated power flow. The boundary-value problem formulation is modeled after that used previously in proving uniqueness for a multi-mode right-angled wedge problem [11]. In addition, the junction condition assumed arises naturally upon reducing the problem to the solution of a Wiener-Hopf equation. Here the factorization is given in terms of the factorization that occurred in the one-mode case. SURFACE WAVE INCIDENCE ON A PLANE STRUCTURE 301 1. B.V.P. formulation and solution. The problem (see Fig. 1) we shall solve is posed by the following conditions: (i) (A + k)u{x, y) = 0, all x, y > 0 (ii) (d/dy + Xi)(d/dy + X2)w = 0, x < 0, y = 0, where Xi , X2 are taken as real positive constants. (iii) u = 0, x > 0, y = 0. (iv) u and its derivatives satisfy d'u (a) X) Z dx' ' dy' < M for r > R0 , where M is independent of r and 8 and R0 is some positive constant, (b) d2u/dy2 is integrable at the origin. (v) 11 ^incident *~i~ Wexcjted ~i~ Wradiftted winc. = A exp I — \\^y + i(k2 + X?)1/2a:], x < 0, y > 0, = 0 , x > 0, y > 0, and 2 w«=ited = X) Cm exp [-X„2/ i{k2 + X2)1/2z], x < 0, y > 0, m -1 = 0 , x > 0, y > 0. Here A represents the given incident surface wave amplitude and the C„ are constants that must be determined. (vi) wauled = u — wiD0. — uCTc,ted obeys the radiation condition lim \\/r (dWrad.M\" — ikurlli) = 0 r—*co uniformly in 6, 0 < 6 < tr. Following a method employed by Kane and Karp [7] and Kane [8], the solution is reduced to solving a Wiener-Hopf problem. The critical factorization required is that of the function x, , x.) f[ [l + ^ i->y,] (l.l)

Effect of a Discontinuity in Density or Conductivity on the Hydromagnetic Stability of a Vortex Sheet

Abstract: The hydromagnetic stability of a plane vortex sheet in incompressible, inviscid, and finitely conducting fluids is studied against small disturbances in the presence of a discontinuity in density or conductivity across the vortex sheet. In the equilibrium state the magnetic field is uniform and aligned with the direction of fluid motions. It is found that it is sufficient, for studying the stability of the vortex sheet, to consider only two‐dimensional disturbances that travel along the magnetic field. A discussion of the dispersion relation in several different cases shows that a discontinuity in density or conductivity has a stabilizing influence on the vortex sheet.

The introduction of discontinuities in high strength steel weldments

Abstract: : The objective of this study was to develop methods for consistently creating porosity, slag inclusions, lack of fusion, and hydrogen cross-cracking discontinuities in welds to evaluate their effects on the properties of welds. To accomplish this objective, weld deposition procedures were altered systematically to develop welding techniques capable of producing a specific discontinuity type and size. The techniques used included both electrical and mechanical perturbations of the welding parameters. It proved possible to implant weld discontinuities with good reproducibility. It was found, however, that mechanical perturbations were more reliable for accurate reproduction of discontinuities.

Stability of contact discontinuity in a strongly radiating gas

Abstract: A very simple flow—the two-dimensional steady infinite planar contact discontinuity in an inviscid non-heat-conducting gas without chemical reactions—is used as an example to study the effect of irreversible energy transport by radiation on the stability of motion with respect to infinitesimal perturbations of the interface.

Progressive failure and slope stability

Abstract: Analytical evidence is presented on the effect of cracking on the slope stability of idealized embankment-foundation sections. The embankment boundary had a circular shape and the bounded mass was homogeneous, isotropic, and linearly elastic. The technique of conformal mapping was the key to calculation of elastic stresses induced by body forces. Various combinations of parameters were applied to represent peak and residual shear strength conditions along the cracked and uncracked portions of the critical surface. The factor of safety against slope in stability varies considerably with the degree of development of the crack. Full crack development yields the minimum value for progression from toe to crest. However, partial development of the discontinuity is the least safe state when the direction of development is from crest to toe. The findings seem significant, not only for slope stability, but for all problems involving a potential for progressive failure.