I/O format for 2D Steady Seepage Flow Analysis

Size: px

Start display at page:

Download "I/O format for 2D Steady Seepage Flow Analysis"

Ralph Dennis
6 years ago
Views:

1 I/O format for 2D Steady Seepage Flow Analysis (f90 FEM SEEP.f90) December 2, Outline of a program f90 FEM SEEP.f90 This is a program for 2D Steady Seepage Flow Analysis. This program can not treat unsteady problem. This program can do the saturated-unsaturated seepage flow analysis in the vertical section, and saturated seepage flow analysis in the horizontal and vertical section. Von Genuchten model is used as a unsaturated ground model. In this program, 3 node element or 4 node element can be used. Mixed model of 3 node elements and 4 node elements can not be solved. User of this program needs to choose either 3 node model or 4 node model. Linear triangular element is used as a 3 node element. 1 node has 2 degrees of freedom in horizontal direction and vertical direction. 4 node isoparametric element with 4 Gauss points is used as a 4 node element. 1 node has 2 degrees of freedom in horizontal direction and vertical direction. Thickness of the element is unit thickness and it is not changeable. As boundary conditions, impervious boundary, given total head boundary, given discharge boundary and saturation point boundary can be considered. In coordinate system, x-direction is defined as right direction and z-direction is defined as upward direction. Only an isotropic material can be treated. Nodal head must be inputted as total head and solution of simultaneous equations is described as total head. Pressure head is calculated as the difference between total head and position head. Simultaneous linear equations are solved using Cholesky method for banded matrix. Convergence criterion is that the case change of pressure head becomes less than Upper limit of iteration is set to 100 times. Input/Output file name can be defined arbitrarily with the format of csv and those are inputted from command line of MS-Windows. Used language for program is Fortran 90 and used compiler is MinGW gfortran. 1

2 2. Format of input file ( csv format) Items for input nod,nodt,nelt,matel,koh,koq,kou,idan Ak0,alpha,em...(1 MATEL)... node-1,node-2,node-3(,node-4),matno...(1 MATEL)... x,z,hvec...(1 NODT)... nokh,hinp...(1 KOH)... nokq,qinp...(1 KOQ)... noku...(1 KOU)... basic values for analysis Material properties Remarks Element-nodes relationship, material set number (counterclockwise order of node numbers) Node coordinate, initial value of total head (x: right-direction, z: upward-direction) Node number of given total head boundary, total head of node (Omit data input if KOH=0) Node number of given discharge boundary, discharge of node (Omit data input if KOQ=0) Node number of saturation point (Omit data input if KOU=0) nod : Number of nodes of each element (3 or 4) nokh : Node number with given total head NODT : Number of nodes nokq : Node number with given discharge NELT : Number of elements noqu : Node number with saturation point MATEL : Number of material sets Hinp : Total head at specified node KOH : Number of nodes with given total head Qinp : Discharge at specified node KOQ : Number of nodes with given discharge (positive: in-flow, negative: out-flow) KOU : Number of nodes with saturation point Ak0 : Permeability coefficient of element (saturated) idan : Section (0: Vertical, 1: horizontal) alpha : Unsaturated property (α) of element matno : Material set number em : Unsaturated property (m) of element Notice Unsaturated properties are α and m on van Genuchten model. { } m 1 S e = 1 + (α h s ) n n = 1 (0 < m < 1) 1 m { ( ) m} 2 K r = (S e ) 0.5 1/m 1 1 S e (0 S r, K r 1) K = K r K 0 K : Permeability coefficient S e : Degree of saturation K 0 : Saturated permeability coefficient h s : Suction head K r : Relative hydraulic conductivity function α : Scaling parameter m : Non-dimensional parameter Condition of node at which noting is inputted is no discharge. (in-flow discharge + out-flow discharge = 0) If input of in-flow or out-flow discharge is wanted especially, the values of KOQ, nokq and Qinp should be inputted. The discharge is known if total head is unknown at a node, and total head is known if discharge is unknown at a node. This condition is maintained except the node with saturation point. Nodes which have the possibility becoming saturation point such as downstream slope of embankment dam shall be specified as saturation point boundary with input of KOU and noku. It is necessary to input initial total heads for all nodes for iterative process of saturates-unsaturated analysis. It is better to input minimum total head in the domain. If proper initial total heads are not inputted, unsuitable results may be obtained. 2

3 2.1 Format of output file ( csv format) nod,nodt,nelt,matel,koh,koq,kou,idan (Each value of above items) *node characteristics node,x,z,koh,koq,kou,hinp,qinp node : Node number x,z : (x,z) Coordinate of node KOH : Node with given total head (1: yes, 0: no) KOQ : Node with given discharge (1: yes, 0: no) KOU : Node with saturation point (1: yes, 0: no) Hinp : Given total head (if KOH=0, value=0) Qinp : Given discharge (if KOQ=0, value=0)...(1 NODT)... *element characteristics element,node-1,node-2,node-3(,node-4),ak0,alpha,em,matno element : Element number node-1,node-2,node-3(,node-4) : Element-nodes relationship Ak0 : Permeability coefficient of element (saturated) alpha : Unsaturated property α em : Unsaturated property m matno : material set number...(1 NELT)... *node value node,x,z,hvec,qvec,pvec node : Node number x : x-coordinate of node z : z-coordinate of node hvec : Total head of node qvec : Discharge of node pvec : Pressure head of node (total head position head)...(1 NODT)... *element value element,xg,zg,vx,vz,vm,ak0,akr,matno element : Element number xg : x-coordinate of COG of element zg : z-coordinate of COG of element vx : x-direction mean velocity in global coordinate system vz : z-direction mean velocity in global coordinate system vm : Combined mean velocity in global coordinate system Ak0 : Permeability coefficient (saturated) Akr : Relative hydraulic conductivity function of element matno : Material set number...(1 NELT)... #,Summary #,item,qti,qto #,discharge,sum total of in-flow,sum total of out-flow #,item,ne,vmax,xg,zg #,vmmax,element number,max.velocity in all elements,x-coordinate of COG,,z-coordinate of COG #,vimax,element number,max.velocity in in-flow elements,x-coordinate of COG,,z-coordinate of COG #,vomax,element number,max.velocity in out-flow elements,x-coordinate of COG,,z-coordinate of COG #,NELT=(Number of elements), NODT=(Number of nodes), nt=(nt), mm=(mm), ib=(ib) #,nnn=(number of iteration), icount=(number of converged degrees of freedom) #,Calculation time=(calculation time) #,Date time=(date of execution) nt mm ib : Total degrees of freedom of FE equation : Dimension of reduced FE equation : band width of reduced FE equation 3

4 3. Sample model analysis 3.1 Outline of model Consider rectangular saturated area with 10m-length and 4m-width. Total heads of 10m are given at left side nodes and total heads of 0m are given at right side nodes. Permeability coefficients of all elements are m/s y distance (m) x distance (m) 3.2 Input data sample Seepage-test1 4,18,10,1,6,0,0,1 nod,nodt,nelt,matel,koh,koq,kou,idan 1e-7,0.1,0.7 Material properties (k,alpha,m) for material set No.1 1, 2, 8, 7,1 Element-nodes relationship for element No.1, Material set number (No.1) 2, 3, 9, 8,1 Element-nodes relationship for element No.2, Material set number (No.1) 3, 4,10, 9,1 Element-nodes relationship for element No.3, Material set number (No.1) 4, 5,11,10,1 Element-nodes relationship for element No.4, Material set number (No.1) 5, 6,12,11,1 Element-nodes relationship for element No.5, Material set number (No.1) 7, 8,14,13,1 Element-nodes relationship for element No.6, Material set number (No.1) 8, 9,15,14,1 Element-nodes relationship for element No.7, Material set number (No.1) 9,10,16,15,1 Element-nodes relationship for element No.8, Material set number (No.1) 10,11,17,16,1 Element-nodes relationship for element No.9, Material set number (No.1) 11,12,18,17,1 Element-nodes relationship for element No.10, Material set number (No.1) 0,0,0 Coordinates (x,z) and initial total head for node No.1 2,0,0 Coordinates (x,z) and initial total head for node No.2 4,0,0 Coordinates (x,z) and initial total head for node No.3 6,0,0 Coordinates (x,z) and initial total head for node No.4 8,0,0 Coordinates (x,z) and initial total head for node No.5 10,0,0 Coordinates (x,z) and initial total head for node No.6 0,2,0 Coordinates (x,z) and initial total head for node No.7 2,2,0 Coordinates (x,z) and initial total head for node No.8 4,2,0 Coordinates (x,z) and initial total head for node No.9 6,2,0 Coordinates (x,z) and initial total head for node No.10 8,2,0 Coordinates (x,z) and initial total head for node No.11 10,2,0 Coordinates (x,z) and initial total head for node No.12 0,4,0 Coordinates (x,z) and initial total head for node No.13 2,4,0 Coordinates (x,z) and initial total head for node No.14 4,4,0 Coordinates (x,z) and initial total head for node No.15 6,4,0 Coordinates (x,z) and initial total head for node No.16 8,4,0 Coordinates (x,z) and initial total head for node No.17 10,4,0 Coordinates (x,z) and initial total head for node No.18 1,10 Node number and given total head (Node No. 1, total head 10m) 7,10 Node number and given total head (Node No. 7, total head 10m) 13,10 Node number and given total head (Node No.10, total head 10m) 6, 0 Node number and given total head (Node No. 6, total head 0m) 12, 0 Node number and given total head (Node No.12, total head 0m) 18, 0 Node number and given total head (Node No.18, total head 0m) 4

5 3.3 Output data sample Output data sample is shown below. The significant figure is set to 3 due to space arrangement. *node value node, coord-x, coord-z, hvec, qvec, pvec 1, 0.000E+00, 0.000E+00, 0.100E+02, 0.100E-06, 0.100E+02 2, 0.200E+01, 0.000E+00, 0.800E+01, 0.000E+00, 0.800E+01 3, 0.400E+01, 0.000E+00, 0.600E+01, 0.000E+00, 0.600E+01 4, 0.600E+01, 0.000E+00, 0.400E+01, 0.000E+00, 0.400E+01 5, 0.800E+01, 0.000E+00, 0.200E+01, 0.000E+00, 0.200E+01 6, 0.100E+02, 0.000E+00, 0.000E+00,-0.100E-06, 0.000E+00 7, 0.000E+00, 0.200E+01, 0.100E+02, 0.200E-06, 0.100E+02 8, 0.200E+01, 0.200E+01, 0.800E+01, 0.000E+00, 0.800E+01 9, 0.400E+01, 0.200E+01, 0.600E+01, 0.000E+00, 0.600E+01 10, 0.600E+01, 0.200E+01, 0.400E+01, 0.000E+00, 0.400E+01 11, 0.800E+01, 0.200E+01, 0.200E+01, 0.000E+00, 0.200E+01 12, 0.100E+02, 0.200E+01, 0.000E+00,-0.200E-06, 0.000E+00 13, 0.000E+00, 0.400E+01, 0.100E+02, 0.100E-06, 0.100E+02 14, 0.200E+01, 0.400E+01, 0.800E+01, 0.000E+00, 0.800E+01 15, 0.400E+01, 0.400E+01, 0.600E+01, 0.000E+00, 0.600E+01 16, 0.600E+01, 0.400E+01, 0.400E+01, 0.000E+00, 0.400E+01 17, 0.800E+01, 0.400E+01, 0.200E+01, 0.000E+00, 0.200E+01 18, 0.100E+02, 0.400E+01, 0.000E+00,-0.100E-06, 0.000E+00 *element value elem, xg, zg, vx, vz, vm, Ak0, Akr, matno 1, 0.100E+01, 0.100E+01, 0.100E-06, 0.638E-22, 0.100E-06, 0.100E-06, 0.100E+01, 1 2, 0.300E+01, 0.100E+01, 0.100E-06, 0.277E-22, 0.100E-06, 0.100E-06, 0.100E+01, 1 3, 0.500E+01, 0.100E+01, 0.100E-06,-0.249E-22, 0.100E-06, 0.100E-06, 0.100E+01, 1 4, 0.700E+01, 0.100E+01, 0.100E-06,-0.277E-23, 0.100E-06, 0.100E-06, 0.100E+01, 1 5, 0.900E+01, 0.100E+01, 0.100E-06,-0.277E-23, 0.100E-06, 0.100E-06, 0.100E+01, 1 6, 0.100E+01, 0.300E+01, 0.100E-06,-0.360E-22, 0.100E-06, 0.100E-06, 0.100E+01, 1 7, 0.300E+01, 0.300E+01, 0.100E-06,-0.555E-22, 0.100E-06, 0.100E-06, 0.100E+01, 1 8, 0.500E+01, 0.300E+01, 0.100E-06, 0.277E-23, 0.100E-06, 0.100E-06, 0.100E+01, 1 9, 0.700E+01, 0.300E+01, 0.100E-06, 0.360E-22, 0.100E-06, 0.100E-06, 0.100E+01, 1 10, 0.900E+01, 0.300E+01, 0.100E-06, 0.416E-23, 0.100E-06, 0.100E-06, 0.100E+01, 1 #,Summary #,item, QTi, QTo #,discharge, 0.400E-06, E-06 #,item, ne, vmax, xg, zg #,vmmax, 1, 0.100E-06, 0.100E+01, 0.100E+01 #,vimax, 1, 0.100E-06, 0.100E+01, 0.100E+01 #,vomax, 5, 0.100E-06, 0.900E+01, 0.100E+01 #,NELT=10 NODT=18 nt=18 mm=12 ib=6 #,Convergence nnn=2 icount=18 #,Calculation time= 0.000(sec) #,Date_time= _20:16:51_(gfortran) 5

I/O data format for 2D Unsteady Heat Conduction Analysis

December 2, 2012 I/O data format for 2D Unsteady Heat Conduction Analysis (f90 FEM HEAT.f90) 1. Outline of a program f90 FEM HEAT.f90 This is a program for 2D Unsteady Heat Conduction Analysis. This program