Presentation on theme: "ENV-2E1Y: Fluvial Geomorphology:"— Presentation transcript:
1 ENV-2E1Y: Fluvial Geomorphology: 2004 - 5 Slope Stability and GeotechnicsLandslide HazardsRiver Bank StabilitySection 2 - Water Flow in SoilsN.K. ToveyН.К.Тови М.А., д-р технических наукLecture 5Lecture 6Landslide on Main Highway at km 365 west of Sao Paulo: August 2002
2 pressure arising from a static head (wZ) 2.1 IntroductionThree component parts to the water pressure:-pressure arising from a static head (wZ)excess pore water pressure (pressure head differential which actually causes water flow. (u )a velocity head =total pore water pressure (pwp) =total = position + pressure velocityhead head head head
3 2.2 Hydraulic Gradient Standpipes P1 h1 h2 P2 Water In Water Out A B Pressure at A is w h1and at B is w h2hydraulic gradient =StandpipesP1h1more generallyh2P2Water InWater OutNOTE: The hydraulic gradient as defined above is dimensionless (i.e. has no units).some other disciplinesABSoil Sample.....(kNm-3)Fig Flow of water in a simple channel section
4 2.3 The Permeameter - (Constant Head) Water INQ - flow rateAt - cross section areaDarcy’s Lawhz
6 2.5 Results from Permeameter m - total mass of sandA - cross section of sand columnL - length (height) of column of sandVolume occupied = A.LVolume of Sand grains =
7 Further Comments about Permeability Falling Head Permeameter is used for clays- in constant head permeameter, flow rate is far to small to get meaningful readingsFormation of a Quicksand - Pipingoccurs when upward seepage force= downward force from self weight
8 Analogies in Heat Flow and Electricity 2.10 Flow of Water in SoilsAnalogies in Heat Flow and ElectricityIn HEAT FLOW - (ENV-2D02)Where Q is the heat flow rate1 is the internal temperature2 is the external temperatureA is the cross-section areak is the thermal conductivityis the path lengthIn the FLOW of ELECTRICTYWhere I is the currentE1 is the inlet voltageE2 is the outlet voltageA is the cross-section areak is the electrical conductivityis the path length
9 2.10 Flow of Water in Soils (continued) In the FLOW of WATER in SOILSWhere Q is the water flow rateh1 is the inlet headh2 is the outlet headA is the cross-section areak is the permeabilityis the path length1) Mathematical solutionsa) exact solutions for certain simple situationsb) solutions by successive approximate e.g. relaxation methods2) Graphical solutions3) Solutions using the electrical analogue4) Solutions using modelsOnly graphical methods will be used in this course
10 2.12 Graphical Solutions - Flow Nets Flow Lines1) flow lines and equipotentials are at right angles to one another.2) the cylinder walls are also flow lines.3) distances between the equipotentials are equalhead drops between the equipotentials are also equal.Equi-potentialsWater IN
12 2.12 Asymetric Flow C A B Intersections are at right angles approximate to curvilinear squareD
13 2.12 Asymetric Flow nd pressure drops C a A B Intersections are at right anglesapproximate to curvilinear squareD
14 2.12 Asymetric Flow (continued) pressure drop between AB and CD is Hand let there be nd pressure drops and nf flow lines.where qf is the flow per unit cross-section anda x 1 is the cross- section between flow lines.the total seepage =
15 Solutions are relatively straightforward. Summary of Flow NetsSolutions are relatively straightforward.1) draw the appropriate flow net2) count the number of pressure drops in the flow net(over the relevant distance)3) count the number of flow lines4) do a simple calculationwork out total flowwork out pressure at any given pointetc.
17 2.13 Seepage around an obstruction upward seepage force =downward force of the soil =A quicksand will occur ifactual downward force of the soilFactor of safety =downwards force required to resist seepage forceIn the above example, nd = 10 and Nab ~ 3.5but very approximately ' = w soi.e. the distance must exceed 0.35 times the difference in head of water.
18 2.14 Flow nets Summary Rules for drawing flow nets:- Water table 1) All impervious boundaries are flow lines.2) All permeable boundaries are equipotentials3) Phreatic surface - pressure is atmospheric, i.e. excess pressure is zero.Change in head between adjacent equipotentials equals the vertical distance between the points on the phreatic surface.4) All equipotentials are at right angles to flow lines5) All parts of the flow net must have the same geometric proportions(e.g. square or similarly shaped rectangles).6) Good approximations can be obtained with flow channels. More accurate results are possible with higher numbers of flow channels, but the time taken goes up in proportion to the number of channels.The extra precision is usually not worth the extra effort.Water tablehhhhhh
19 2.17 Uplift on Obstructions Uplift arises the total water pressure exerted on the base.Static head (constant for flat based obstruction)excess head.3 m4 m6 m4321Head of Water (m)Distance under obstruction (m)2
20 2.17 Uplift on Obstructions If total uplift force > the self weight downwardobject will be displaced downstream.Draw flow netPlot graph of uplift pressure (Y –axis) against distance along base (X-axis). Uplift pressure is estimate from flownethead at the upstream head is ~0.75 of total headhead at the down stream end it is ~0.25 of the total head.
21 2.17 Uplift on Obstructions Base of the obstruction is 2m below the surfaceuplift force from the static head is 2w multiplied by width(i.e. 6w kN per metre length).the upward force is the area under the curve multiplied by w.In this example upward force = 6w kN per metre length,i.e. in this case it equals the static head uplift.total uplift = 12w kN m-1.Uplift reduces ability of the obstruction to resist movement through the pressure of waterpotential boulder blockages in a riverman-made drop structure built in river engineering works to dissipate energy (see RDH's part of the Course).quicksand might form at the down stream end of the obstruction.
22 2.3 The Permeameter - (Constant Head) Water INhz