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ENV-2E1Y: Fluvial Geomorphology: Slope Stability and Geotechnics Landslide Hazards River Bank Stability Section 2 - Water Flow in Soils N.K. Tovey Н.К.Тови М.А., д-р технических наук Landslide on Main Highway at km 365 west of Sao Paulo: August 2002 Lecture 5 Lecture 6

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2.1 Introduction Three component parts to the water pressure:- – pressure arising from a static head ( w Z) –excess pore water pressure (pressure head differential which actually causes water flow. (u ) –a velocity head = total = position + pressure + velocity head head head head total pore water pressure (pwp ) =

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Fig. 2.1 Flow of water in a simple channel section 2.2Hydraulic Gradient Pressure at A is w h 1 and at B is w h 2 hydraulic gradient = Water In Soil Sample P1h1P1h1 Standpipes h2h2 Water Out A B more generally NOTE: The hydraulic gradient as defined above is dimensionless (i.e. has no units). some other disciplines.....(kNm -3 ) P2P2

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Water IN z h 2.3The Permeameter - (Constant Head) Q - flow rate A t - cross section area Darcys Law

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2.5Results from Permeameter Quicksand occurs Medium Dense e=0.620 k=2.93 mm/s Loose Dense e=0.744 k=5.89 mm/s

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2.5Results from Permeameter m - total mass of sand A - cross section of sand column L - length (height) of column of sand Volume occupied = A.L Volume of Sand grains =

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Falling Head Permeameter is used for clays - in constant head permeameter, flow rate is far to small to get meaningful readings Formation of a Quicksand - Piping occurs when upward seepage force = downward force from self weight Further Comments about Permeability

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Analogies in Heat Flow and Electricity –In HEAT FLOW - (ENV-2D02) 2.10 Flow of Water in Soils –In the FLOW of ELECTRICTY Where Q is the heat flow rate 1 is the internal temperature 2 is the external temperature A is the cross-section area k is the thermal conductivity is the path length Where I is the current E 1 is the inlet voltage E 2 is the outlet voltage A is the cross-section area k is the electrical conductivity is the path length

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In the FLOW of WATER in SOILS 2.10 Flow of Water in Soils (continued) Where Q is the water flow rate h 1 is the inlet head h 2 is the outlet head A is the cross-section area k is the permeability is the path length 1)Mathematical solutions a) exact solutions for certain simple situations b) solutions by successive approximate - e.g. relaxation methods 2)Graphical solutions 3)Solutions using the electrical analogue 4)Solutions using models Only graphical methods will be used in this course

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1) 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 equal head drops between the equipotentials are also equal Graphical Solutions - Flow Nets Equi- potentials Flow Lines Water IN

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2.12 Asymetric Flow

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Intersections are at right angles approximate to curvilinear square A B C D

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2.12 Asymetric Flow Intersections are at right angles approximate to curvilinear square A B C D n d pressure drops a

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pressure drop between AB and CD is H and let there be n d pressure drops and n f flow lines Asymetric Flow (continued) where q f is the flow per unit cross-section and a x 1 is the cross- section between flow lines. the total seepage =

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Summary of Flow Nets Solutions are relatively straightforward. 1)draw the appropriate flow net 2)count the number of pressure drops in the flow net (over the relevant distance) 3)count the number of flow lines 4)do a simple calculation –work out total flow – work out pressure at any given point – etc.

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2.13 Seepage around an obstruction H A B

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upward seepage force = 2.13 Seepage around an obstruction downward force of the soil = A quicksand will occur if but very approximately ' = w so actual downward force of the soil Factor of safety = downwards force required to resist seepage force In the above example, n d = 10 and N ab ~ 3.5 i.e. the distance must exceed 0.35 times the difference in head of water.

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Rules for drawing flow nets:- 1) All impervious boundaries are flow lines. 2) All permeable boundaries are equipotentials 3) Phreatic surface - pressure is atmospheric, i.e. excess pressure is zero Flow nets Summary h h h h h h Water table 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 lines 5) 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.

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Uplift arises the total water pressure exerted on the base. Static head (constant for flat based obstruction) excess head Uplift on Obstructions Distance under obstruction (m) Head of Water (m) 6 m 3 m 4 m 2

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If total uplift force > the self weight downward object will be displaced downstream. Draw flow net Plot graph of uplift pressure (Y –axis) against distance along base (X-axis). Uplift pressure is estimate from flownet head at the upstream head is ~0.75 of total head head at the down stream end it is ~0.25 of the total head Uplift on Obstructions

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Base of the obstruction is 2m below the surface uplift force from the static head is 2 w multiplied by width (i.e. 6 w kN per metre length). the upward force is the area under the curve multiplied by w. In this example upward force = 6 w kN per metre length, i.e. in this case it equals the static head uplift. total uplift = 12 w kN m-1. Uplift reduces ability of the obstruction to resist movement through the pressure of water potential boulder blockages in a river man-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 Uplift on Obstructions

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Water IN z h 2.3The Permeameter - (Constant Head)

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