sma07 - Flow Nets for Anisotropic Materials Layered soil...

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Flow Nets for Anisotropic Materials
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d 1 d 2 k=k 2 Layered soil deposit
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Horizontal flow in a layered soil deposit d 1 d 2 v = v 2 L h h = 0 h h h = - 0
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Horizontal flow in a layered soil deposit d 1 d 2 v = v 2 L h h = 0 h h h = - 0 v k h L Q k h L d 1 1 1 1 1 = = ; For layer 1 (1a)
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Horizontal flow in a layered soil deposit d 1 d 2 v = v 2 L (1b) h h = 0 h h h = - 0 and v k h L Q k h L d 1 1 1 1 1 = = ; v k h L Q k h L d 2 2 2 2 2 = = ; For layer 1 For layer 2 (1a)
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Horizontal flow in a layered soil deposit Q k h L d Q k h L d 1 1 1 2 2 2 = = d 1 d 2 v = v 2 L
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(2a) Horizontal flow in a layered soil deposit now the average velocity, v, can be determined as v Q Q d d k h L H 1 2 1 2 = + + = Q k h L d Q k h L d 1 1 1 2 2 2 = = d 1 d 2 v = v 2 L
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(2a) Horizontal flow in a layered soil deposit now the average velocity, v, can be determined as v Q Q d d k h L where H 1 2 1 2 = + + = k k d k d d H 1 1 d 2 2 1 2 = + + Q k h L d Q k h L d 1 1 1 2 2 2 = = (2b) d 1 d 2 v = v 2 L
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Vertical flow in a layered soil deposit d 1 d 2 v v L h h h h = - - 0 1 2 h h h = - 0 1 h h = 0
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(3a) Vertical flow in a layered soil deposit d 1 d 2 v v L v k h d = 1 1 1 h v d k = 1 1 1 For layer 1 hence h h h h = - - 0 1 2 h h h = - 0 1 h h = 0
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(3a) (3b) Vertical flow in a layered soil deposit d 1 d 2 v v L v k h d = 1 1 1 h v d k = 1 1 1 For layer 1 For layer 2 hence v k h d = 2 2 2 h v d k = 2 2 2 hence h h h h = - - 0 1 2 h h h = - 0 1 h h = 0
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Vertical flow in a layered soil deposit h d h h d 1 + d 2 1 2 = + The hydraulic gradient for the layered system is given by
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(3c) Vertical flow in a layered soil deposit vd k vd k d d 1 1 2 2 1 2 h d h h d 1 + d 2 1 2 = + = + + The hydraulic gradient for the layered system is given by
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(3c) Vertical flow in a layered soil deposit vd k vd k d d v k h d 1 1 2 2 1 2 V h d h h d 1 + d 2 1 2 = + = + + = The hydraulic gradient for the layered system is given by Now applying Darcy’s law to the layered system gives (3d)
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(3c) Vertical flow in a layered soil deposit vd k vd k d d v k h d and hence 1 1 2 2 1 2 V h d h h d 1 + d 2 1 2 = + = + + = The hydraulic gradient for the layered system is given by Now applying Darcy’s law to the layered system gives k d k d k V 1 1 2 2 = + d 1 + d 2 (3e) (3d)
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d 1 = d 0 k = k 2 = 10 -10 m/s d 2 = d 0 Example: permeability in a layered soil deposit
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d 1 = d 0 k = k 2 = 10 -10 m/s d 2 = d 0 Example: permeability in a layered soil deposit k k d k d d H 1 1 d 2 2 1
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