土壤力学土壤力学英文 (10).ppt

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1、Outline of the lectureFlow NetInterpretation of Flow Net Laplaces Equation1.Laplaces equationAssumptions:Darcys law is valid.The fluid is incompressibleInflow:Inflow:OutflowOutflow:Inflow=OutflowInflow=Outflow:(1)(2)(3)1.Laplaces equationInflow=OutflowInflow=Outflow:For isotropic soilFor isotropic s

2、oil(1)(2)(3)(4)(5)1.Laplaces equationIt represents an infinite number of mutually perpendicular curves.One group of curves shows paths/channels of water and called flow lines.Total head gradually decreases along a flow line.Another group represents lines on which the total head is constant and calle

3、d equipotential lines.These lines are contours of constant total head.Flow lines and equipotential lines are orthogonal.A selected number of flow lines and equipotential lines constructs a flow net.2.Flow NetA flow net is a graphical representation of a flow field that satisfies Laplaces equation an

4、d comprises a family of flow lines and equipotential lines.Flow nets are constructed for the calculation of groundwater flow and the evaluation of heads in the soil mass.2.Flow NetFlow lines or streamlines represent flow paths of water particles.The area between two flow lines is called a flow chann

5、el or stream tubeThe rate of flow in a flow channel is constant.Flow cannot occur across flow lines.Flow lineFlow lineFlow channel2.Flow NetAn equipotential line is a line along which the total head at all points is equal.Flow lines and equipotential lines are perpendicular to each other.The differe

6、nce between two equipotential lines is called the potential drop or head loss.The head drop between two adjacent equipotential lines is the same.Equipotential linesEquipotential linesHH-DhH-2DhH-3DhH-4Dh2.Flow NetDraw the structure and soil mass to a suitable scale.Establish boundary conditions and

7、draw flow and equipotential lines near the boundaries.Constant head boundaries(water levels)represent initial or final equipotential linesImpermeable(no-flow)boundaries are flow linesSketch flow lines by smooth curves(3 to 5 flow lines).Flow net sketching for isotropic soilFlow net sketching for iso

8、tropic soil2.Flow NetDraw equipotential lines by smooth curves adhering to right angle intersections and square grids conditions(aspect ratio=1).Continue sketching and re-adjusting until you get squares almost everywhere.Successive trials will result in a reasonably consistent flow net.In most cases

9、,5 to 10 flow lines are usually sufficient.Depending on the number of flow lines selected,the number of equipotential line will automatically be fixed by geometry and grid layout.Flow net sketching for isotropic soilFlow net sketching for isotropic soil2.Flow NetFlow net sketching for isotropic soil

10、Flow net sketching for isotropic soilSteps in construction a flow net(a)Cross-section pervious stratum(b)result of first attempt to construct flow net;(c)result of adjusting flow net constructed in(b);(d)final flow net3.Interpretation of Flow Net h Head loss h between each consecutive pair of equipo

11、tential lines is:N Nd d is the Number of equipotential drops;H H head difference between the upstream and downstream sides(1)3.Interpretation of Flow Net h By construction,B1/L1=B2/L2=1If the number of flow channels in a flow net is equal to Nf,Q -flow per unit length in yQ -flow per unit length in

12、y(1)(2)3.Interpretation of Flow Net 1.Select a datum2.Calculate the total heads at the upstream&downstream HU&HD3.Calculate the total head drop between each consecutive pair of equipotential linesh=H/Nd=(HU-HD)/Nd4.Calculate the total head at j j Hj=HU (Nd)j hwhere(Nd)j is the number of equipotentia

13、l drops at point j;(Nd)j can be fractional.5.Calculate the pressure head at j by subtracting the elevation head from the total head(hp)j=Hj (he)j6.Calculate the pore water pressure uj=w(hp)jPore water Pore water Pressure DistributionPressure Distribution(1)(2)(3)2.Interpretation of Flow Net A sheet

14、pile wall supporting 6 m of water is shown in the figure opposite.(a)Draw the flow net.(b)Determine the flow rate if k=0.0019 cm/s.(c)Determine the pore water pressure distributions on the upstream and downstream faces of the wall.2.Interpretation of Flow Net Step 1:Draw the structure and soil mass to a suitable scale.Step 2:Calculate the flow.Select the downstream end as the datum.Nf=4Nd=10H=6mk=0.0019 cm/s(1)2.Interpretation of Flow Net Step Step 3:3:Determine the pore water pressure under the base of the dam.