Showing papers on "Discontinuity (geotechnical engineering) published in 1975"

Unified theory of the onset of folding, boudinage, and mullion structure

Abstract: A mathematical study of the flow of a layered fluid shows that homogeneous pure shear aligned with the bedding is a “possible” state of motion in the sense that it is an exact solution to the governing equation. In the case of a single layer of a Newtonian material between two thick layers of different viscosity, such a state of motion is unstable to small disturbances. The growing disturbances have foldlike or pinch-and-swell form, depending on whether the applied compression is parallel or perpendicular to the layering and on whether the layer is more or less resistant to deformation than the surrounding rock. The combination of these two factors gives four distinct cases. One of these, labeled inverse folding, is of no interest because its growth rate is too small. The other three cases correspond qualitatively to folding, boudinage, and mullions. This result suggests that these three geologic structures are caused by the same mechanism: a secondary flow driven by an interfacial discontinuity in normal stress.

Penny-shaped cracks

Abstract: The Somigliana formula is used to reduce an arbitrary elastic crack problem to a system of three integral equations for the components of displacement discontinuity. For the case of a penny shaped crack situated in an infinite isotropic medium with the crack faces subjected to arbitrary tractions, the integral equations are solved explicitly. In particular integral formulae are obtained for the stresses on the plane of the crack beyond the crack-tip, and hence for the stress intensity factors. The special case of uni-directional shear traction on the crack is examined.

Improving one's touch.

Abstract: DRAWING the finger tips across a smooth surface usually induces sensations of pressure, warmth or cold, and roughness or smoothness. Any abrupt discontinuity is easily felt: it has been claimed that eminences no higher than 0.001 mm etched on to smooth glass can be detected, provided some movement of the finger tips is permitted1. We describe here an effect which does not seem to have been reported previously, even though we think that it must be familiar to certain craftsmen.

Lines of discontinuity for displacements in the theory of plasticity of plain and reinforced concrete

Abstract: Synopsis The internal plastic work in a line of discontinuity for displacements is calculated for a material that obeys Coulomb's modified yield criterion. This is then usedfor the determination of the carrying capacity of a number of selected examples of plain and reinforced concrete. Good agreement is found between theory and tests in respect of the selected examples. The application of discontinuity lines in concrete thus means an extension of the possibilities for plastic analysis of plain and, particularly, reinforced concrete.

Sinuosity of strike-slip fault traces

Abstract: A mechanical basis for the occurrence of curvature or sinuosity on strike-slip faults is postulated from finite-element simulation of an earthquake sequence on the Parkfield, California, segment of the San Andreas fault. Using discontinuity fields from measured displacements associated with the M ≅ 5.3 earthquakes of June 1966, motions along 16 km of ground breakage are modeled to investigate the displacement fields and stresses during faulting. An originally rectilinear fault trace, subjected to a variable single-shear couple in terms of displacements, is curved into the extensional quadrant during the simulation. Displacement magnitudes normal to the fault trace have magnitudes similar to the relative discontinuity vector. Calculated moments M b , = 3.2 × 106 dyne-cm cause the curvature. Shear stress drops of Δ τ = 10.8 × 10 6 dyne/cm 2 occur in the fault zone. It is postulated that successive earthquakes at the same place would enhance this initial sinuosity by repeated motion along weakened sections of the fault. The amount of curvature that can occur is a function of material properties, the magnitude of displacements during the earthquake(s), and the bending moment, which would eventually become large enough in rock masses adjacent to the fault to “lock” the broken segment. Younger rectilinear fault traces would occur with further motion, explaining certain aspects of the origin of braided fault traces and bedrock slices.

Method and apparatus for measuring the distance of a discontinuity of a glass fiber from one end of the fiber

Abstract: A method and apparatus for measuring the distance of a discontinuity in a glass fiber from one end of the fiber characterized by coupling a pulse into the one end, sensing a pulse of light reflected by a discontinuity as it leaves the one end and measuring the time lapse between the pulse to determine the distance of the discontinuity from the one end.

Reflection and Transmission of Ion Acoustic Waves from a Plasma Discontinuity

Abstract: We calculate transmission and reflection coefficients for an ion acoustic wave incident from the upstream direction upon a plasma discontinuity of width much less than the wavelength. In the limit of an infinitely strong discontinuity there is complete in phase reflection.

Seismic evidence for local undulation of olivine–spinel phase boundary

Abstract: A DETAILED P-wave velocity distribution has been determined (S.D.-S. and R.A.W., unpublished) for the upper mantle in western Canada. The analysis was based on differential travel-time and relative-amplitude observations of multiple arrivals for seismograms between 14 and 40°. Three velocity models were determined for three different regions. All of these models are characterised by discontinuities at 410 and 650km. The reflection from the 410-km discontinuity is best observed between 14 and 18°. While analysing seismograms between 14 and 18°, a group of the 410-km discontinuity. Here we present these observations and give a speculative explanation for the undulation, of 410-km discontinuity. Here we present these observations and give a speculative explanation for the undulation.

Geotechnical aspects of tunnelling in discontinuous rock, with particular reference to the lower chalk

Abstract: Discontinuities, defined as breaks or interruptions of the mechanical properties of a solid, are recognised in the literature as being of vital importance in controlling the behaviour of rock during tunnelling. This thesis presents a detailed study of an experimental tunnel excavated in discontinuous rock (Lower Chalk) at Chinnor in Oxfordshire. The work falls into three main areas of study. Prior to tunnel excavation, detailed discontinuity surveys were carried out using an orthogonal scanline technique on exposed faces in the Chinnor quarry and in a 3m diameter shaft. This work, supported by subsequent surveys in the tunnel during its excavation- established - in numerical terms - the discontinuity characteristics of the Lower Chalk at Chinnor.p Ground behaviour during tunnel excavation was monitored in boreholes, and in a trench excavated across the tunnel line. Ground movement results, when viewed in the light of data obtained from finite element analyses, have emphasised the non-elastic discontinuous response of the ground. The actual behaviour of the ground at Chinnor was found to be equivalent to that of a material having a deformation modulus that was approximately l/20th of the Young's modulus of chalk determined from laboratory tests on intact samples. This modulus reduction was a direct result of the interaction between the tunnel excavation system and the discontinuous ground. Having established the role of discontinuities in controlling the behaviour of the ground during tunnelling, and recognising the importance of discontinuity spacing as an index of discontinuity frequency, a detailed study of various statistical and geotechnical aspects of discontinuity spacings in rock is presented. The distribution of discontinuity spacing values obtained from measurements in three tunnels in the UK was found to closely follow a negative exponential distribution. The implications of this relation are that a single parameter expression can be, adopted to describe the discontinuity spacing characteristics. By integrating this expression between the appropriate limits, a formula giving a precise value for the RQD (Rock Quality Designation) of the reck exposed can be obtained. In addition, important conclusions concerning optimum sample size and precision can be made once the discontinuity spacing distribution has been described in these simple mathematical terms. Subsidiary to the three main areas of study outlined above, three additional peripheral subjects are considered. These include an evaluation of the hydrological characteristics of the chalk and an examination of chalk cutability. In addition, data concerning the shear strength characteristics of discontinuity surfaces in the chalk (obtained from laboratory tests) are incorporated in an analysis of stability near the tunnel at Chinnor, using a computer program on file at the University of Durham.

The uniaxial strain compression of porous and fully dense beryllium

Abstract: Compressive stress versus uniaxial compressive strain curves obtained using a simple closed die are presented for SP-100-C beryllium of initial fractional porosities varying from 0.05 to 0.26, and for fully dense ingot beryllium. The relationship between porosity and compressive yield stress is found to be linear over the entire porosity range with a discontinuity at 0.065 fractional porosity. It is suggested that the discontinuity is related to the transition from isolated to predominantly interconnected porosity.

Elastic wave-motion across a vertical discontinuity

Abstract: Exact solutions are obtained for the displacement field in an elastic half-space composed of two quarter spaces welded together. The configuration is excited by a plane SH wave impinging upon the discontinuity at an arbitrary angle. The application of the Kontorovich-Lebedev transform to this boundary value problem leads to two simultaneous integral equations which are solved exactly. It is shown that the discontinuity may enhance the spectral displacements up to a factor of two. The results could be applied to propagation of seismic shear waves past fault zones in the earth's crust.

Quantification of the discontinuities of rock and rock masses - methods and applications

Abstract: The breaking up of rock may be considered on two different scales - (1) the scale of the tool which attacks and penetrates the rock' that is the scale of the miner's pick, of the toothed wheel, of the drill bit of the pneumatic drill, of the cutting edge of the ripper; it is also the scale of the test sample. (2) the scale of the rock mass within which the structure is constructed: gallery, chamber, shafts or trenches. The discontinuities affecting rock at those two levels having an important role in the process of breakdown and mechanical excavation, two methods have been developed. The first uses the rock quality index defined on the basis of measurements of wave velocity in samples. This permits the detection, the quantification and the description of discontinuities affecting the rock at the scale of the sample (porosity, micro-cracking). The second is concerned with the description of the rock mass: utilizing the possibilities offered by mathematical morphology, and texture analysis, it enables a quantitative characterisation (extension, opening) of the discontinuities to be made in so far as these affect the rock mass and the excavation for the structure on the basis of graphical representations. Examples of the application concern the mechanical excavation of rock. /TRRL/

Tunnel stability with special reference to the shear strain energy criterion

Abstract: A comparison of the results of the application of the finite element method and of a modified KIRSCH's solution for the calculation of stress around an unlined tunnel in London Clay is undertaken. Some conventional methods and the finite element method for the calculation of stress and displacement around a tunnel are referred to. An estimate of the reduction of the shear strength parameters along fissures is obtained by laboratory tests on fissured and intact samples of London Clay. On the basis of the MOHR-COULOMB criterion of failure and by the use of a computer technique a delimitation of potentially unstable orientation zones on equal area projections is obtained for all the elements around a tunnel in London Clay. The shear strain energy stored around the discontinuities, which fall in the potentially unstable zones, is computed for the case of a non-random discontinuity fabric of London Clay and the values are normalized to the values corresponding to an equivalent isotropically discontinuous fabric. Then the instability of each area around the tunnel is defined in terms of the principal stresses σ(_1), σ(_2), σ(_3), the shear strength characteristics of the material and the discontinuity fabric.