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The friction force is independent of the apparent area of contact The friction force is independent of velocity Slide4: Physical origins of friction Material surfaces are rough at a molecular scale, as shown in this sketch of a ground metal surface. Contact only occurs at surface asperities At each contact the stress reaches a limiting value, sc equal to the indentation hardness The normal force, N, is then given by Where Ac is the contact area Slide5: Physical origins of friction The surfaces are welded together at the points of contact. The shear force required to break the welds is given by The shear stress tc is the stress required to cause shear failure which is related to the yield stress of the material, and to the indentation hardness. Hence = constantSlide6: Physical origins of friction Let us consider what happens as a hammer made of tool steel, sc = 4000 MN/m2, weighing 2 kg is put down on an anvil. The contact area Ac will be This can be compared with a superficial area of approximately 500 mm2 (based on a 25 mm diameter hammer). Slide7: Coefficients of friction Metals exposed to air, apart from gold, are surrounded by an oxide film. This reduces m. Slide8: Lubrication This has two objectives to reduce friction and wear Ideally this is achieved by putting a fluid (oil) between the metal surfaces that prevents metal to metal contact, and has a low shear resistance. There are four main methods Boundary lubrication Solid lubrication Hydrodynamic lubrication Elasto-hydrodynamic lubricationSlide9: Class discussion (1) The friction between waxed skis and snow increases from m = 0.02 to about m = 0.4 as the temperature drops from -10oC to -15oC. For example in Scott’s expedition to the South pole it was recorded that friction on the sledge runners increased as temperature fell causing the expedition considerable hardship. Why? Hint: Snow remains on house roofs at slopes of 25o Slide10: Class discussion (2) According to the laws of friction, the frictional resistance is independent of the area. Why then do racing cars have big tyres? How do tyres work on wet roads?Slide11: Soil materials Soils are comprised of particles in contact. They are essentially frictional materials whose strength and behaviour is governed by interactions between the individual particles. Natural soils are composed of a variety of mineral types covering a wide range of sizes. The table shows the names used for different sized particles (mm). Slide12: Grading curves for natural soils The finest 25% usually control the soil properties. If the fine particles are uniformly distributed through the soil mass they will: Control pore size - and hence the ease of drainage Control frictional propertiesSlide13: Soil minerals Quartz Feldspar Olivine Enstatite Augite Hornblende Calcite Mica Clay minerals kaolin, illite, montmorillonite Increasing hardness = Increasing particle sizeSlide14: Large particles - shape Shape can be described by the quantities Sphericity as opposed to platiness Roundness as opposed to angularity Roughness as opposed to smoothness Decreasing scaleSlide15: Large particles The hardest particles are comprised of quartz (silica, H7, fm 25°) and Feldspar (alumino-silicates with potassium, sodium or calcium, H6, fm 35°). Both of these minerals possess a strong three-dimensional atomic structure, which gives them their hardness. The high resistance of quartz to abrasion (hardness) is responsible for its widespread occurrence in sands and gravels, and for its relative rarity in finer soils. The particle size is limited by the higher probability of imperfections and brittle fracture in large particles. For sand and gravel grains the shape is controlled by mechanical effects, principally abrasion as particles are transported by wind or water. It is found that particles become rounder with age.Slide16: Clay particles The softest particles are the clay minerals. The main clay minerals are kaolinite, illite (alumino-silicates, H <1, fm 10°) smectite or montmorillonite (alumino-silicate with sodium, potassium and calcium, fm 5‑7°). These clay minerals tend to form plate like particles with thicknesses of between 10 mm for kaolin and 0.01 mm for smectite. These particles are so small that electrical and chemical effects become more important in controlling their behaviour. These minerals are sheet silicate structures – phyllosilicates. Slide17: Clay particles Silicon tetrahedral layer Octahedral layer Clay particles are formed by combinations of two sheet structuresSlide18: Kaolin Hydrogen bonds between layers – relatively strong Relatively large particles S = 15 m2/gm CEC = 5 meq/100 g fm = 12oSlide19: Montmorillonite Van der Waals bonds between layers – relatively weak Relatively small particles S = 800 m2/gm CEC = 100 meq/100 g fm = 5oSlide20: Double layers A consequence of the negative charge of the clay particles is that there is a layer of water surrounding each particle containing the cations that balance the negative charge. This layer of water is known as a “double layer”, and is bound to the clay. + + + + + + + + + + + + + + + + + + Clay particle Double layer -Slide21: Double layers The behaviour of the double layer can be described by the Gouy-Chapman theory of potential. The potential ψ is given by where nio = concentration of ions (i) in bulk suspension zi = valency of ions (i) T = temperature k = Boltzman's constant α = charge of an electron ε = dielectric constantSlide22: Double layers It can be shown that the "centre of gravity" of the double layer is located at x = 1/κ. That is the thickness of the double layer is inversely proportional to κ. Thus we can see that the double layer thickness is reduced by • increasing ionic concentration • increasing ion valency • reducing dielectric constant It is found that temperature has little effect because an increase in temperature leads to a corresponding decrease in dielectric constantSlide23: Double layers The double layer has a significant influence on the properties of clay minerals. It provides a low shear resistance leading to low friction angles, it limits the “free” pore space available for flow leading to low permeability, its thickness can change with changes in pore fluid chemistry. Slide24: Adhesion theory of friction and soils The indentation hardness of quartz is 7000 MN/m2 so only a small part of the superficial area is required to transmit the stresses encountered in soil engineering. The maximum stress of interest in soil mechanics 1000 kPa, this would occur at a depth of about 50 m. The required contact area at the asperities can be determined from Slide25: Adhesion theory of friction and soils The effect of the films of water (double layers) surrounding soil particles can now be understood considering that the coefficient of friction is given by Fluids strongly attracted to a surface will influence tc, but not the indentation resistance sc. The influence of the fluid layer is generally to reduce tc (this is the basis of lubrication). The thicker the double layer and the lower the particle roughness the greater will be the reduction of tc. This is observed with the lower friction angle for smectite compared to kaolinite.Slide26: Adhesion theory of friction and soils Water has an anti-lubricating effect with some minerals (e.g. quartz). It might be expected that different angles of friction would be measured for wet and dry soils because of the lubricating effect of water films. This is not observed in practice because: Air is never perfectly dry, there is always sufficient moisture in the air to form a layer on the soil surface. Sliding friction is only a component of the apparent frictional resistance of soils. Rolling of the soil grains is important.Slide27: Other factors affecting friction in soils N F SOIL Ideal frictional material F = m N = tan fm N dense sand loose sand Ultimate strength F Horizontal displacementSlide28: Shear Deformation Particles move by combination of rolling and sliding Particles are frustrated from rolling by their neighbours Loose sand - less frustration – less energy required Dense sand – more frustration – net expansion required to enable rolling Shearing involves a combination of local expansion and collapseSlide29: Dilation Volume change (dilation) accompanies shearing of soils. This has a significant effect on soil resistance. It has been found that the peak friction angle (= tan-1(F/N)) is given by Where fcs is the critical state friction angle, the value of f when no further volume change is occurring at large strains, and j is the dilation angleSlide30: Dilation The amount of dilation will tend to increase with particle angularity and roughness as both contribute to rotational frustration Maximum j 20o j reduces with increasing stress level j reduces with reducing densitySlide31: Critical state friction angle F N However, the friction angles measured are significantly higher than the inter-particle friction angles. For example, for quartz sands fcs = 35° whereas fm = 25°. The critical state conditions show a constant ratio of shear to normal stress indicating the frictional nature of soil strength.Slide32: Critical state friction angles Influence of particle shape, fcs increases with Increasing particle angularity increasing roughness Data for quartz sandsSlide33: Critical state friction angles Influence of particle grading, fcs increases with increasing uniformity The uniformity of the particle size is often expressed by Cu the coefficient of uniformity, where Cu = Slide34: Critical state friction angles Angular quartz sand 37° Rounded quartz sand 30° Angular carbonate sand (fm 32°) 43° Rounded carbonate sand 35° Sandy silty clay 30° Clay (see chart) 20° increasing clay content kaolin - illite - montmorilloniteSlide35: Residual friction angle (platey particles) random particle orientation fpk, fcs particles lined up on failure plane fr 1 m 3 mm Displacement F For some soils f can drop from its critical state value to a lower residual valueSlide36: Residual friction angle Slide37: Residual friction angle - application In soil engineering the critical state friction angle is generally considered to provide safe and conservative designs. Provided a shear plane does not develop on which large displacements occur this approach is reasonable. Where large pre-existing slips have occurred, for instance due to ancient landslides, the residual friction angle needs to be used in analyses. Residual friction angles may also be relevant for first time slides in highly compacted soils. This can occur because during compaction the clay particles align with their flat surfaces perpendicular to the vertical, the direction of the greatest stressSlide38: Friction in rock masses All rock masses contain discontinuities such as bedding planes, joints, shear zones and faults. At shallow depth, where stresses are low, failure of the intact rock material is minimal and the behaviour of the rock mass is controlled by friction (sliding) on the discontinuities. Slide39: Friction in rock masses To determine the basic friction angle it is common to shear a sawn or ground surface. S N frSlide40: Friction in rock masses Natural discontinuity surfaces in hard rock are never as smooth as a sawn or ground surface The undulations and asperities on a natural joint surface have a significant influence on its shear behaviour At low N, At high N, shearing occurs through the teeth Slide41: Friction in rock masses Real data from tests on a discontinuity in slateSlide42: Friction in rock masses Barton has proposed an empirical expression to account for different joint roughnesses and different material strengths given by: JRC = joint roughness coefficient JCS = joint material compressive strength But joint roughness is scale dependentSlide43: Friction in rock masses The joint shear strength can be reduced drastically when part, or all, of the surface is covered by soft filling material such as clay gouge. For planar surfaces, such as bedding planes in sedimentary rock, a thin clay coating can result in a significant shear strength reduction. For a rough or undulating joint, the filling thickness has to be greater than the amplitude of the undulations before the shear strength is reduced to that of the filling material. It is important, as in lubrication of metals, that the soft filling is not squeezed out so that it allows rock to rock contact. You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.