inst/R_old/20211001_flow_net.R
In GJMeijer/soilmech: R functions and plots for Soil Mechanics teaching
#' Define flow net problem using grided domain system
#'
#' @description
#' Defines a geometry for a flow net problem. rectangular domains are defined
#' using a grid system. For each domain, horizontal and vertical permeabilities
#' may be defined seperately.
#'
#' Domains that are next to each other in the grid are automatically connected.
#' All boundary conditions are assumed impermeable, unless otherwise defined
#' using the inputs `bc_id`, `bc_edge`, `bc_type` and `bc_value`.
#'
#' @param x x-coordinates of boundary lines in the grid
#' @param y y-coordinates of boundary lines in the grid
#' @param ix x-index in grid of soil rectangle (length n)
#' @param iy y-index in grid of soil rectangle (length n)
#' @param kx,ky horizontal and vertical permeabilities. Either define as
#' arrays (with length n), or as scalars if the permeability is the same
#' in each domain
#' @param bc_id domain at which the boundary condition applies (array with
#' length m, the integers relate to the position in `ix`,`iy`)
#' @param bc_edge edge in domain at which the boundary condition applies (
#' array with length m). Edges are numbered clockwise: `1` for left
#' (negative x-face), `2` for top (positive y-face), `3` for right (
#' positive x-face) or `4` for bottom (negative y-face)
#' @param bc_type type of boundary condition (array with length m). Use `h`
#' for a known head, and `q` for a known flow (positive when flowing into
#' the domain)
#' @param bc_value Values for boundary conditions (array with length m). If
#' `bc_type == "h"`, it defines the known hydraulic head on the boundary.
#' If `bc_type == "q"`, it defines the fixed discharge into the domain on
#' this boundary.
#' @param grid_size the requested grid size. Actual sizes may be slightly
#' larger to ensure a regular number of nodes fits in each domain. Thus
#' grid sizes may be slightly different in each domain
#' @param node_min minimum number of nodes in each direction in each
#' domain. Set to at least 3 to ensure finite difference approximation
#' works properly
#' @importFrom rlang .data
#' @examples
#' flownet_geometry()
#' @export
flownet_geometry <- function(
x = c(0, 15, 20, 40),
y = c(0, 10, 12, 17.5, 20.0),
ix = c(1, 1, 1, 1, 2, 3, 3),
iy = c(4, 3, 2, 1, 1, 1, 2),
kx = 1e-6,
ky = 1e-6,
bc_id = c(1, 7),
bc_edge = c(2, 2),
bc_type = c("h", "h"),
bc_value = c(17.5, 15),
grid_size = 0.25,
node_min = 3
){
#generate tibble with all soil domains
dom <- tibble::tibble(
ix = ix,
iy = iy,
x0 = x[ix],
y0 = y[iy],
x1 = x[ix + 1],
y1 = y[iy + 1],
kx = kx,
ky = ky
)
#generate numbers of nodes
dom <- dplyr::mutate(
dom,
id = seq(dplyr::n()),
nx = pmax(node_min, 1 + ceiling((.data$x1 - .data$x0)/grid_size)),
ny = pmax(node_min, 1 + ceiling((.data$y1 - .data$y0)/grid_size)),
hx = (.data$x1 - .data$x0)/(.data$nx - 1),
hy = (.data$y1 - .data$y0)/(.data$ny - 1)
)
#add offsets for node numbering (both with and without ghost nodes)
dom <- dplyr::mutate(
dom,
n = nodes_total(.data$nx, .data$ny, real_only = FALSE),
n_real = nodes_total(.data$nx, .data$ny, real_only = TRUE),
i0 = cumsum(c(0, utils::head(.data$n, -1))),
i0_real = cumsum(c(0, utils::head(.data$n_real, -1))),
)
#generate tibble with all default boundary conditions (impermeable boundaries)
bc <- tibble::tibble(
id = rep(seq(nrow(dom)), each = 4),
edge = rep(seq(4), nrow(dom)),
type = "q",
value = 0
)
#add connecting boundary conditions
for (id in 1:nrow(dom)) {
#other domain connected at the right (positive x-side, edge 3)
id_next <- which((dom$ix == (dom$ix[id] + 1)) & (dom$iy == dom$iy[id]))
if (length(id_next) == 1) {
bc$edge[4*(id - 1) + 3] <- 3
bc$type[4*(id - 1) + 3] <- "c"
bc$value[4*(id - 1) + 3] <- id_next
bc$edge[4*(id_next - 1) + 1] <- 1
bc$type[4*(id_next - 1) + 1] <- "c"
bc$value[4*(id_next - 1) + 1] <- id
}
#other domain connected at the bottom (positive y-side, edge 2)
id_next <- which((dom$ix == dom$ix[id]) & (dom$iy == (dom$iy[id] + 1)))
if (length(id_next) == 1) {
bc$edge[4*(id - 1) + 2] <- 2
bc$type[4*(id - 1) + 2] <- "c"
bc$value[4*(id - 1) + 2] <- id_next
bc$edge[4*(id_next - 1) + 4] <- 4
bc$type[4*(id_next - 1) + 4] <- "c"
bc$value[4*(id_next - 1) + 4] <- id
}
}
#add boundary conditions for head or flow
bc$id[4*(bc_id - 1) + bc_edge] <- bc_id
bc$edge[4*(bc_id - 1) + bc_edge] <- bc_edge
bc$type[4*(bc_id - 1) + bc_edge] <- bc_type
bc$value[4*(bc_id - 1) + bc_edge] <- bc_value
#return
return(list(dom = dom, bc = bc))
}
#' get all sparse entries and lhs for boundary conditions
#'
#' @description
#' function to get sparse matrix element positions for flow net finite
#' difference boundary conditions (known head, known flow or connected to
#' another domain)
#'
#' @param df tibble describing flow problem. Generated by function
#' `generate_flownet_properties()`
#' @importFrom magrittr `%>%`
#' @importFrom rlang .data
#' @return a list with two fields: `mat` containing a tibble with sparse
#' row (`row`), column (`col`) and values (`val`) of finite difference
#' matrix elements related to boundary conditions; and `lhs` which is a
#' vector with all left-hand side of equation values
#' @examples
#' df <- flownet_geometry()
#' ds <- findiff_sparse_entries_bc(df)
#' @export
findiff_sparse_entries_bc <- function(df) {
#join domain properties onto boundary conditions
dbc <- dplyr::left_join(df$bc, df$dom, by = "id") %>%
dplyr::mutate(
k = ifelse((.data$edge %in% c(1, 3)), .data$kx, .data$ky),
h = ifelse((.data$edge %in% c(1, 3)), .data$hx, .data$hy)
)
#initiate list and left-hand sides of bx's
mlist <- vector(mode = "list", length = nrow(dbc))
lhs <- rep(0, sum(df$dom$n))
#initiate list of connecting nodes
clist <- vector(mode = "list", length = nrow(dbc))
#loop through all bcs
for (i in 1:nrow(dbc)) {
if (dbc$type[i] == "h") {
#Defined head
i1 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 0)
i2 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 1)
mlist[[i]] <- tibble::tibble(
row = i1,
col = i2,
val = 1
)
lhs[i1] <- dbc$value[i]
} else if (dbc$type[i] == "q") {
#Defined flow rate (positive into domain)
i1 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 0)
i2 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 2)
mlist[[i]] <- tibble::tibble(
row = rep(i1, 2),
col = c(i1, i2),
val = rep(c(0.5, -0.5)*dbc$k[i]/dbc$h[i], each = length(i1))
)
lhs[i1] <- dbc$value[i]
} else if (dbc$type[i] == "c") {
#connected to other domain (b)
#index in <dbc> of connecting edge
ib <- which((dbc$id == dbc$value[i]) & (dbc$edge == (1 + (dbc$edge[i] + 1)%%4)))
if (dbc$edge[i] %in% c(2, 3)) {
#other domain connected on positive side - same head
ia1 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 0)
ia2 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 1)
ib2 <- index_edge(dbc$nx[ib], dbc$ny[ib], dbc$edge[ib], i0 = dbc$i0[ib], offset = 1)
mlist[[i]] <- tibble::tibble(
row = rep(ia1, 2),
col = c(ia2, ib2),
val = rep(c(-1, 1), each = length(ia1))
)
#add connecting real nodes - real node indexing - used later for solving flow potential
clist[[i]] <- tibble::tibble(
i1 = index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0_real[i], offset = 0, real_only = TRUE),
i2 = index_edge(dbc$nx[ib], dbc$ny[ib], dbc$edge[ib], i0 = dbc$i0_real[ib], offset = 0, real_only = TRUE)
)
} else {
#other domain on negative side - same flow rate
ia1 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 0)
ia2 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 2)
ib1 <- index_edge(dbc$nx[ib], dbc$ny[ib], dbc$edge[ib], i0 = dbc$i0[ib], offset = 0)
ib2 <- index_edge(dbc$nx[ib], dbc$ny[ib], dbc$edge[ib], i0 = dbc$i0[ib], offset = 2)
mlist[[i]] <- tibble::tibble(
row = rep(ia1, 4),
col = c(ia1, ia2, ib1, ib2),
val = c(
rep(c(-0.5, 0.5)*dbc$k[i]/dbc$h[i], each = length(ia1)),
rep(c(-0.5, 0.5)*dbc$k[ib]/dbc$h[ib], each = length(ib1))
)
)
}
}
}
#return
return(list(
mat = dplyr::bind_rows(mlist),
lhs = lhs,
conn = dplyr::bind_rows(clist)
))
}
#' Solve flow net head problem for concatenated rectangular domains
#'
#' @description
#' Solves a flow net problem for a problem consisting of connected rectangular
#' grids. This function solves the hydraulic head using boundary conditions and
#' a finite difference approach, and also calculates the flow potential psi
#'
#' @param df tibble with problem description, generated by function
#' `flownet_geometry()`
#' @return a tibble with heads (field `h`), flow rates in x and y-direction
#' (`qx`, `qy`) and flow potential (`psi`) for each real point in the finite
#' difference grid. Each point is characterised by a position (`x`, `y`)
#' and an index `id` indicating which domain the point belongs to
#' @importFrom magrittr `%>%`
#' @importFrom rlang .data
#' @examples
#' df <- flownet_geometry()
#' dp <- solve_flownet(df)
#' @export
solve_flownet <- function(df) {
## SOLVE FOR HEAD
#get sparse matrix elements and left-hand side for boundary conditions
Mbc <- findiff_sparse_entries_bc(df)
#get sparse matrix elements for Poissons equation for each real node
M2x <- df$dom %>%
dplyr::select(.data$nx, .data$ny, .data$kx, .data$hx, .data$i0) %>%
purrr::pmap_dfr(
function(nx, ny, kx, hx, i0) findiff_sparse_entries(nx, ny, order = 2, h = hx, direction = "x", multiplier = kx, i0_row = i0, i0_col = i0)
)
M2y <- df$dom %>%
dplyr::select(.data$nx, .data$ny, .data$ky, .data$hy, .data$i0) %>%
purrr::pmap_dfr(
function(nx, ny, ky, hy, i0) findiff_sparse_entries(nx, ny, order = 2, h = hy, direction = "y", multiplier = ky, i0_row = i0, i0_col = i0)
)
#create sparse matrix
mat <- Matrix::sparseMatrix(
i = c(Mbc$mat$row, M2x$row, M2y$row),
j = c(Mbc$mat$col, M2x$col, M2y$col),
x = c(Mbc$mat$val, M2x$val, M2y$val),
dims = rep(sum(df$dom$n), 2)
)
#bind together, and solve system
h = as.vector(Matrix::solve(mat, Mbc$lhs))
## CALCULATE FLOW FROM HEAD
#flow in x-direction
M1qx <- df$dom %>%
dplyr::select(.data$nx, .data$ny, .data$kx, .data$hx, .data$i0) %>%
purrr::pmap_dfr(
function(nx, ny, kx, hx, i0) findiff_sparse_entries(nx, ny, order = 1, h = hx, direction = "x", multiplier = -kx, i0_row = i0, i0_col = i0)
)
qx <- as.vector(
Matrix::sparseMatrix(
i = M1qx$row,
j = M1qx$col,
x = M1qx$val,
dims = rep(sum(df$dom$n), 2)
) %*% h
)
#flow in y-direction
M1qy <- df$dom %>%
dplyr::select(.data$nx, .data$ny, .data$ky, .data$hy, .data$i0) %>%
purrr::pmap_dfr(
function(nx, ny, ky, hy, i0) findiff_sparse_entries(nx, ny, order = 1, h = hy, direction = "y", multiplier = -ky, i0_row = i0, i0_col = i0)
)
qy <- as.vector(
Matrix::sparseMatrix(
i = M1qy$row,
j = M1qy$col,
x = M1qy$val,
dims = rep(sum(df$dom$n), 2)
) %*% h
)
## ASSIGN SOLUTIONS AND POSITIONS (real nodes only)
#indices of real nodes
i_real <- purrr::pmap(df$dom, index_real) %>% unlist()
#generate positions for all solution object for all nodes
dp <- df$dom %>%
dplyr::summarise(
nodal_coordinates_real(
.data$nx,
.data$ny,
x0 = .data$x0,
x1 = .data$x1,
y0 = .data$y0,
y1 = .data$y1,
id = .data$id
)
)
#add head and flow for all real points
dp <- dplyr::mutate(
dp,
h = h[i_real],
qx = qx[i_real],
qy = qy[i_real]
)
## GET FLOW POTENTIAL FROM FLOW
#x-direction elements - first order differentiation - real nodes only
M1x_el <- df$dom %>%
dplyr::select(.data$nx, .data$ny, .data$kx, .data$hx, .data$i0_real) %>%
purrr::pmap_dfr(
function(nx, ny, kx, hx, i0_real) findiff_sparse_entries(nx, ny, order = 1, h = hx, direction = "x", i0_row = i0_real, i0_col = i0_real, real_only = TRUE)
)
#x-direction elements - first order differentiation - real nodes only
M1y_el <- df$dom %>%
dplyr::select(.data$nx, .data$ny, .data$ky, .data$hy, .data$i0_real) %>%
purrr::pmap_dfr(
function(nx, ny, ky, hy, i0_real) findiff_sparse_entries(nx, ny, order = 1, h = hy, direction = "y", i0_row = i0_real, i0_col = i0_real, real_only = TRUE)
)
#flow potential must match on each of the connecting segments
Mc <- Mbc$conn
Mc_el <- tibble::tibble(
row = rep(seq(nrow(Mc)), 2),
col = c(Mc$i1, Mc$i2),
val = rep(c(-1, 1), each = nrow(Mc))
)
#notal number of real nodes
ntreal <- sum(df$dom$n_real)
#crate single matrix and left-hand side for flow potential solving
mat_fp <- Matrix::sparseMatrix(
i = c(M1x_el$row, M1y_el$row + ntreal, Mc_el$row + 2*ntreal),
j = c(M1x_el$col, M1y_el$col, Mc_el$col),
x = c(M1x_el$val, M1y_el$val, Mc_el$val),
dims = c(2*ntreal + nrow(Mc), ntreal)
)
lhs_fp <- c(dp$qy, -dp$qx, rep(0, nrow(Mc)))
#solve for flow potential
psi <- as.vector(
Matrix::solve(
(Matrix::t(mat_fp) %*% mat_fp),
(Matrix::t(mat_fp) %*% lhs_fp)
)
)
#scale so flow potential ranges between 0 and Q_total, and assign
dp$psi <- psi - min(psi)
## RETURN
#return
return(dp)
}
#' Decide on number of equipotential intervals
#'
#' @description
#' This function takes a finite difference solution for both head `h` and flow
#' potential function `psi` to get the best number of equipotential intervals
#' `Nd` based on a given number of flow channels `Nf`. This function assumes
#' the permeabilities in all domains is the same
#'
#' @param df tibble with information about domain
#' @param dp tibble with head and flow potential results for each node
#' @param Nf number of requested flow channels
#' @return the optimal number of equipotential intervals `Nd`
#' @importFrom magrittr `%>%`
#' @importFrom rlang .data
#' @examples
#' df <- flownet_geometry()
#' dp <- solve_flownet(df)
#' amount_equipotentialintervals(df, dp, Nf = 5)
#' @export
amount_equipotentialintervals <- function(df, dp, Nf = 5) {
#total head difference
dh <- max(dp$h) - min(dp$h)
#total flow per second
Q <- max(dp$psi) - min(dp$psi)
#k_avg
k_avg <- df$dom %>%
dplyr::summarize(k = mean(sqrt(.data$kx*.data$ky))) %>%
dplyr::pull(.data$k)
#Nd
Nd <- round(k_avg*dh*Nf/Q)
#return
return(Nd)
}
#' Add flownet to an existing ggplot
#'
#' @description
#' Function to add a flow net to an existing ggplot. If the plot does not
#' exist yet, a new one if created
#'
#' @param df tibble with domains/problem description
#' @param dp flow net solution tibble. If not specified, it is calculated
#' using `df`
#' @param Nf number of requested flow paths
#' @param line_width line thickness for all lines
#' @param colour_flowline colour of flow lines
#' @param colour_equipotentialline colour of equipotential lines
#' @param fill fill colour for (saturated) soil
#' @param plt a ggplot object. If not defined, a new plot is generated
#' @param xlab,ylab x and y-axis label - if `plt` not defined
#' @param xlim,ylim user-defined axis limits - if `plt` not defined
#' @param axes if `FALSE` no axes are plotted - if `plt` not defined
#' @return a ggplot object
#' @importFrom magrittr `%>%`
#' @importFrom rlang .data
#' @examples
#' df <- flownet_geometry()
#' ggplot_add_flownet(df, axes = FALSE)
#' ggplot_add_flownet(df, axes = TRUE, fill = NA)
#' @export
ggplot_add_flownet <- function(
df,
dp = NULL,
Nf = 5,
linewidth = 0.5,
colour_flowline = "black",
colour_equipotentialline = "black",
fill = "#aebab7",
plt = NULL,
xlab = "x [m]",
ylab = "z [m]",
xlim = c(NA, NA),
ylim = c(NA, NA),
axes = TRUE
){
#if dp not provided, calculate heads and flow potential
if (is.null(dp)) {
dp <- solve_flownet(df)
}
#calculate number of equipotential intervals
Nd <- amount_equipotentialintervals(df, dp, Nf = Nf)
Nd_levels <- seq(min(dp$h), max(dp$h), l = (Nd + 1))[2:Nd]
Nf_levels <- seq(min(dp$psi), max(dp$psi), l = (Nf + 1))
#if plot does not exist, generate a new one
if (is.null(plt)) {
plt <- ggplot_geometry(xlim = xlim, ylim = ylim, axes = axes, xlab = xlab, ylab = ylab)
}
#plot rectangular soil elements
plt <- plt + ggplot2::geom_rect(
data = df$dom,
ggplot2::aes(xmin = .data$x0, xmax = .data$x1, ymin = .data$y0, ymax = .data$y1),
fill = fill,
color = NA
)
#add flow and equipotential lines using contour lines
plt <- plt +
ggplot2::geom_contour(
data = dp,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$h),
breaks = Nd_levels,
color = colour_equipotentialline,
size = line_width
) +
ggplot2::geom_contour(
data = dp,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$psi),
breaks = Nf_levels,
color = colour_flowline,
size = line_width
)
#return
return(plt)
}
#' Plot flow net and soil geometry for a dam/sheet pile problem
#'
#' @param df tibble with domains/problem description, generated by function
#' `generate_flownet_properties()`.#'
#' @param dp solution for heads and flow potential for each node. If not
#' defined, it is calculated in this plotting function
#' @param Nf number of requested flow paths
#' @param xlab,ylab x and y-axis label
#' @param fill_soilwet fill colour for saturated soil
#' @param fill_soildry fill colour for dry soil,
#' @param colour_soil line colour for soil
#' @param colour_flowline colour of flow lines
#' @param colour_equipotentialline colour of equipotential lines
#' @param fill_water fill colour for water
#' @param colour_water line colour for water
#' @param fill_impermeable fill colour for impermeable parts of the domain
#' @param fill_air fill colour for air on top of soil/water
#' @param line_water line type for water edges (defined head)
#' @param line_width line thickness for all lines
#' @param xlim,ylim user-defined axis limits
#' @param axes if `FALSE` no axes are plotted
#' @param thickness_impermeable thickness of impermeable border around the
#' entire problem. Defined as an array for all edges (left, top, right,
#' bottom), or single value for all edges
#' @param scale_soilmarker size of soil marker, in fraction of height
#' @param scale_watermarker size of water table marker, in fraction of height
#' @return a ggplot object
#' @importFrom magrittr `%>%`
#' @examples
#' #default example
#' df <- flownet_geometry()
#' ggplot_flownet_dam(df)
#'
#' #anisotropic permeability - with 6 flow channels
#' df <- flownet_geometry(kx = 4e-6, ky = 1e-6)
#' ggplot_flownet_dam(df, Nf = 6)
#'
#' #deep excavation example
#' df <- flownet_geometry(
#' x = c(0, 5, 5.25, 30),
#' y = c(0, 5, 7.5, 15, 20),
#' ix = c(1, 1, 2, 3, 3, 3, 3),
#' iy = c(2, 1, 1, 1, 2, 3, 4),
#' bc_id = c(1, 6),
#' bc_edge = c(2, 2),
#' bc_type = c("h", "h"),
#' bc_value = c(7.5, 15),
#' dry = c(rep(FALSE, 6), TRUE)
#' )
#' ggplot_flownet_dam(df)
#' @export
ggplot_flownet_dam <- function(
df,
dp = NULL,
Nf = 5,
xlab = "x [m]",
ylab = "z [m]",
fill_soilwet = "#aebab7",
fill_soildry = "#d3bc5f",
colour_soil = "#65571d",
colour_flowline = "black",
colour_equipotentialline = "black",
fill_water = "#2a7fff",
colour_water = "#000080",
fill_impermeable = "#333333",
fill_air = "white",
line_water = 2,
line_width = 0.5,
xlim = c(NA, NA),
ylim = c(NA, NA),
axes = TRUE,
thickness_impermeable = c(0, 1, 0, 1),
scale_soilmarker = 0.075,
scale_watermarker = 0.050
){
#if dp not provided, calculate heads and flow potential
if (is.null(dp)) {
dp <- solve_flownet(df)
}
#calculate number of equipotential intervals
Nd <- amount_equipotentialintervals(df, dp, Nf = Nf)
Nd_levels <- seq(min(dp$h), max(dp$h), l = (Nd + 1))[2:Nd]
Nf_levels <- seq(min(dp$psi), max(dp$psi), l = (Nf + 1))
#impermeable thickness
if (length(thickness_impermeable) == 1) {
thickness_impermeable <- rep(thickness_impermeable, 4)
}
#get head edges
dedge <- df$bc %>%
dplyr::filter(.data$type == "h") %>%
dplyr::left_join(df$dom, by = "id") %>%
dplyr::mutate(
x = ifelse(.data$edge == 3, .data$x1, .data$x0),
xend = ifelse(.data$edge == 1, .data$x0, .data$x1),
y = ifelse(.data$edge == 2, .data$y1, .data$y0),
yend = ifelse(.data$edge == 4, .data$y0, .data$y1)
)
#plot limits
if (is.na(xlim[1])) {
xlim[1] <- min(df$dom$x0) - thickness_impermeable[1]
}
if (is.na(xlim[2])) {
xlim[2] <- max(df$dom$x1) + thickness_impermeable[3]
}
if (is.na(ylim[1])) {
ylim[1] <- min(df$dom$y0) - thickness_impermeable[4]
}
if (is.na(ylim[2])) {
ylim[2] <- max(c(df$dom$y1, dedge$yend)) + thickness_impermeable[2]
}
#initiate plot
plt <- ggplot2::ggplot() +
ggplot2::coord_equal(ratio = 1, xlim = xlim, ylim = ylim, expand = FALSE)
#impermeable background
plt <- plt +
ggplot2::annotate(
"polygon",
x = c(rep(xlim[1], 2), rep(xlim[2], 2)),
y = c(ylim[1], rep(ylim[2], 2), ylim[1]),
color = NA,
fill = fill_impermeable
)
#plot rectangles for ponding water
plt <- plt +
ggplot2::geom_rect(
data = dedge,
ggplot2::aes(xmin = .data$x, xmax = .data$xend, ymin = .data$y0, ymax = .data$value),
fill = fill_water,
color = NA
)
#plot air
plt <- plt +
ggplot2::geom_rect(
data = dedge,
ggplot2::aes(xmin = .data$x, xmax = .data$xend, ymin = .data$value, ymax = ylim[2]),
fill = fill_air,
colour = NA
)
#plot rectangles for dry soil
plt <- plt +
ggplot2::geom_rect(
data = dplyr::filter(df$dom, .data$dry == TRUE),
ggplot2::aes(xmin = .data$x0, xmax = .data$x1, ymin = .data$y0, ymax = .data$y1),
fill = fill_soildry,
colour = NA
)
#plot rectangles for saturated soil
plt <- plt +
ggplot2::geom_rect(
data = dplyr::filter(df$dom, .data$dry == FALSE),
ggplot2::aes(xmin = .data$x0, xmax = .data$x1, ymin = .data$y0, ymax = .data$y1),
fill = fill_soilwet,
colour = NA
)
#plot soil surface lines
dsurf <- dplyr::left_join(
dedge %>%
dplyr::select(.data$ix, .data$x, .data$xend, .data$y, .data$yend),
df$dom %>%
dplyr::filter(.data$dry == TRUE) %>%
dplyr::select(.data$ix, .data$y1),
by = "ix"
) %>%
dplyr::mutate(
y = pmax(.data$y, .data$y1, na.rm = TRUE),
yend = pmax(.data$yend, .data$y1, na.rm = TRUE)
)
plt <- plt +
ggplot2::geom_segment(
data = dsurf,
ggplot2::aes(x = .data$x, xend = .data$xend, y = .data$y, yend = .data$yend),
color = colour_soil,
size = line_width
)
#plot water table lines
plt <- plt +
ggplot2::geom_segment(
data = dedge,
ggplot2::aes(x = .data$x, xend = .data$xend, y = .data$value, yend = .data$value),
color = colour_water,
linetype = line_water,
size = line_width
)
#plot soil surface marker
if (!is.na(scale_soilmarker)) {
for (i in 1:nrow(dsurf)) {
if ((dsurf$xend[i] > xlim[1]) & (dsurf$x[i] <= xlim[2])) {
plt <- ggplot_add_soilmarker(
plt,
1/3*max(xlim[1], dsurf$x[i]) + 2/3*min(xlim[2], dsurf$xend[i]),
dsurf$y[i],
scale = scale_soilmarker*diff(ylim)
)
}
}
}
#plot water table markers
if (!is.na(scale_watermarker)) {
for (i in 1:nrow(dedge)) {
if ((dedge$xend[i] > xlim[1]) & (dedge$x[i] <= xlim[2])) {
plt <- ggplot_add_watermarker(
plt,
2/3*max(xlim[1], dedge$x[i]) + 1/3*min(xlim[2], dedge$xend[i]),
dedge$value[i],
scale = scale_watermarker*diff(ylim)
)
}
}
}
#switch axes off if requested
if (axes == FALSE) {
plt <- plt + ggplot2::theme_void()
} else {
plt <- plt +
theme_soilmech() +
ggplot2::theme(
panel.background = ggplot2::element_blank(),
panel.border = ggplot2::element_blank()
) +
ggplot2::xlab(xlab) +
ggplot2::ylab(ylab)
}
#add flow and equipotential lines using contour lines
plt <- plt +
ggplot2::geom_contour(
data = dp,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$h),
breaks = Nd_levels,
color = colour_equipotentialline,
size = line_width
) +
ggplot2::geom_contour(
data = dp,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$psi),
breaks = Nf_levels,
color = colour_flowline,
size = line_width
)
#return
return(plt)
}
#' ggplot 2D map of hydraulic heads and pressures
#'
#' @description
#' Plots a 2D map of the pressure or head distributions in a flow net problem.
#' The plot shows both a heat map and contour lines.
#'
#' @inheritParams ggplot_flownet_dam
#' @param type parameter to plot. `type = "h"` for hydraulic heads,
#' `type = "hz"` for elevation head, `type = `hb` for pressure head
#' or `type = "u"` for pore water pressures
#' @param binwidth contour line distance
#' @param label_size contour line text label size
#' @param label_n number of times contour label appears on each line
#' @param gamma_w unit weight of water, in kN/m3 (required for calculating
#' pore water pressures)
#' @param palette RColorBrewer color map for shading
#' @param palette_direction RColorBrewer color map direction (`1` or `-1`)
#' @param colour_contour colour of contour lines
#' @return a ggplot object
#' @examples
#' #generate flow net geometry
#' df <- flownet_geometry()
#'
#' #solve flow net problem
#' dp <- solve_flownet(df)
#'
#' #plot heads
#' ggplot_hydraulichead_dam(df, dp = dp, type = "h", binwidth = 0.25)
#'
#' #plot elevation head
#' ggplot_hydraulichead_dam(df, dp = dp, type = "hz", binwidth = 2.5)
#'
#' #plot pressure head
#' ggplot_hydraulichead_dam(df, dp = dp, type = "hb", binwidth = 2.5)
#'
#' #plot pore water pressure
#' ggplot_hydraulichead_dam(df, dp = dp, type = "u", binwidth = 25)
#' @export
ggplot_hydraulichead_dam <- function(
df,
dp = NULL,
type = "h", #h, hz, hb, u
binwidth = 0.25,
gamma_w = 10,
label_size = 3,
label_n = 1,
xlab = "x [m]",
ylab = "z [m]",
palette = "Blues", #YlGnBu
palette_direction = 1,
fill_soilwet = "white",
fill_soildry = "white",
colour_soil = "#65571d",
colour_contour = "black",
fill_water = "white",
colour_water = "#000080",
fill_impermeable = "#333333",
fill_air = "white",
line_water = 2,
line_width = 0.5,
xlim = c(NA, NA),
ylim = c(NA, NA),
axes = TRUE,
thickness_impermeable = c(0, 1, 0, 1),
scale_soilmarker = 0.075,
scale_watermarker = 0.050
){
#if dp not provided, calculate heads and flow potential
if (is.null(dp)) {
dp <- solve_flownet(df)
}
#impermeable thickness
if (length(thickness_impermeable) == 1) {
thickness_impermeable <- rep(thickness_impermeable, 4)
}
#get head edges
dedge <- df$bc %>%
dplyr::filter(.data$type == "h") %>%
dplyr::left_join(df$dom, by = "id") %>%
dplyr::mutate(
x = ifelse(.data$edge == 3, .data$x1, .data$x0),
xend = ifelse(.data$edge == 1, .data$x0, .data$x1),
y = ifelse(.data$edge == 2, .data$y1, .data$y0),
yend = ifelse(.data$edge == 4, .data$y0, .data$y1)
)
#plot limits
if (is.na(xlim[1])) {
xlim[1] <- min(df$dom$x0) - thickness_impermeable[1]
}
if (is.na(xlim[2])) {
xlim[2] <- max(df$dom$x1) + thickness_impermeable[3]
}
if (is.na(ylim[1])) {
ylim[1] <- min(df$dom$y0) - thickness_impermeable[4]
}
if (is.na(ylim[2])) {
ylim[2] <- max(c(df$dom$y1, dedge$yend)) + thickness_impermeable[2]
}
#initiate plot
plt <- ggplot2::ggplot() +
ggplot2::coord_equal(ratio = 1, xlim = xlim, ylim = ylim, expand = FALSE)
#impermeable background
plt <- plt +
ggplot2::annotate(
"polygon",
x = c(rep(xlim[1], 2), rep(xlim[2], 2)),
y = c(ylim[1], rep(ylim[2], 2), ylim[1]),
color = NA,
fill = fill_impermeable
)
#plot rectangles for ponding water
plt <- plt +
ggplot2::geom_rect(
data = dedge,
ggplot2::aes(xmin = .data$x, xmax = .data$xend, ymin = .data$y0, ymax = .data$value),
fill = fill_water,
color = NA
)
#plot air
plt <- plt +
ggplot2::geom_rect(
data = dedge,
ggplot2::aes(xmin = .data$x, xmax = .data$xend, ymin = .data$value, ymax = ylim[2]),
fill = fill_air,
colour = NA
)
#plot rectangles for dry soil
plt <- plt +
ggplot2::geom_rect(
data = dplyr::filter(df$dom, .data$dry == TRUE),
ggplot2::aes(xmin = .data$x0, xmax = .data$x1, ymin = .data$y0, ymax = .data$y1),
fill = fill_soildry,
colour = NA
)
#plot rectangles for saturated soil
plt <- plt +
ggplot2::geom_rect(
data = dplyr::filter(df$dom, .data$dry == FALSE),
ggplot2::aes(xmin = .data$x0, xmax = .data$x1, ymin = .data$y0, ymax = .data$y1),
fill = fill_soilwet,
colour = NA
)
#plot hydraulic head profiles
if (type == "h") {
dp$val <- dp$h
label <- expression(h~"[m]")
} else if (type == "hz") {
dp$val <- dp$y
label <- expression(h[z]~"[m]")
} else if (type == "hb") {
dp$val <- dp$h - dp$y
label <- expression(h[b]~"[m]")
} else if (type == "u") {
dp$val <- (dp$h - dp$y)*gamma_w
label <- expression(u~"[kPa]")
}
plt <- plt +
ggplot2::stat_summary_2d(
data = dp,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$val),
binwidth = min(c(df$dom$hx, df$dom$hy))
) +
ggplot2::geom_contour(
data = dp,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$val),
binwidth = binwidth,
color = colour_contour,
size = line_width
) +
ggplot2::scale_fill_distiller(
name = label,
palette = palette,
direction = palette_direction
) +
metR::geom_text_contour(
data = dp,
binwidth = binwidth,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$val),
label.placement = metR::label_placement_n(label_n),
size = label_size
)
#plot soil surface lines
dsurf <- dplyr::left_join(
dedge %>%
dplyr::select(.data$ix, .data$x, .data$xend, .data$y, .data$yend),
df$dom %>%
dplyr::filter(.data$dry == TRUE) %>%
dplyr::select(.data$ix, .data$y1),
by = "ix"
) %>%
dplyr::mutate(
y = pmax(.data$y, .data$y1, na.rm = TRUE),
yend = pmax(.data$yend, .data$y1, na.rm = TRUE)
)
plt <- plt +
ggplot2::geom_segment(
data = dsurf,
ggplot2::aes(x = .data$x, xend = .data$xend, y = .data$y, yend = .data$yend),
color = colour_soil,
size = line_width
)
#plot water table lines
plt <- plt +
ggplot2::geom_segment(
data = dedge,
ggplot2::aes(x = .data$x, xend = .data$xend, y = .data$value, yend = .data$value),
color = colour_water,
linetype = line_water,
size = line_width
)
#plot soil surface marker
if (!is.na(scale_soilmarker)) {
for (i in 1:nrow(dsurf)) {
if ((dsurf$xend[i] > xlim[1]) & (dsurf$x[i] <= xlim[2])) {
plt <- ggplot_add_soilmarker(
plt,
1/3*max(xlim[1], dsurf$x[i]) + 2/3*min(xlim[2], dsurf$xend[i]),
dsurf$y[i],
scale = scale_soilmarker*diff(ylim)
)
}
}
}
#plot water table markers
if (!is.na(scale_watermarker)) {
for (i in 1:nrow(dedge)) {
if ((dedge$xend[i] > xlim[1]) & (dedge$x[i] <= xlim[2])) {
plt <- ggplot_add_watermarker(
plt,
2/3*max(xlim[1], dedge$x[i]) + 1/3*min(xlim[2], dedge$xend[i]),
dedge$value[i],
scale = scale_watermarker*diff(ylim)
)
}
}
}
#switch axes off if requested
if (axes == FALSE) {
plt <- plt + ggplot2::theme_void()
} else {
plt <- plt +
theme_soilmech() +
ggplot2::theme(
panel.background = ggplot2::element_blank(),
panel.border = ggplot2::element_blank()
) +
ggplot2::xlab(xlab) +
ggplot2::ylab(ylab)
}
#return
return(plt)
}
GJMeijer/soilmech documentation built on May 22, 2022, 10:39 a.m.
R Package Documentation
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#' Define flow net problem using grided domain system
#'
#' @description
#' Defines a geometry for a flow net problem. rectangular domains are defined
#' using a grid system. For each domain, horizontal and vertical permeabilities
#' may be defined seperately.
#'
#' Domains that are next to each other in the grid are automatically connected.
#' All boundary conditions are assumed impermeable, unless otherwise defined
#' using the inputs `bc_id`, `bc_edge`, `bc_type` and `bc_value`.
#'
#' @param x x-coordinates of boundary lines in the grid
#' @param y y-coordinates of boundary lines in the grid
#' @param ix x-index in grid of soil rectangle (length n)
#' @param iy y-index in grid of soil rectangle (length n)
#' @param kx,ky horizontal and vertical permeabilities. Either define as
#' arrays (with length n), or as scalars if the permeability is the same
#' in each domain
#' @param bc_id domain at which the boundary condition applies (array with
#' length m, the integers relate to the position in `ix`,`iy`)
#' @param bc_edge edge in domain at which the boundary condition applies (
#' array with length m). Edges are numbered clockwise: `1` for left
#' (negative x-face), `2` for top (positive y-face), `3` for right (
#' positive x-face) or `4` for bottom (negative y-face)
#' @param bc_type type of boundary condition (array with length m). Use `h`
#' for a known head, and `q` for a known flow (positive when flowing into
#' the domain)
#' @param bc_value Values for boundary conditions (array with length m). If
#' `bc_type == "h"`, it defines the known hydraulic head on the boundary.
#' If `bc_type == "q"`, it defines the fixed discharge into the domain on
#' this boundary.
#' @param grid_size the requested grid size. Actual sizes may be slightly
#' larger to ensure a regular number of nodes fits in each domain. Thus
#' grid sizes may be slightly different in each domain
#' @param node_min minimum number of nodes in each direction in each
#' domain. Set to at least 3 to ensure finite difference approximation
#' works properly
#' @importFrom rlang .data
#' @examples
#' flownet_geometry()
#' @export
flownet_geometry <- function(
x = c(0, 15, 20, 40),
y = c(0, 10, 12, 17.5, 20.0),
ix = c(1, 1, 1, 1, 2, 3, 3),
iy = c(4, 3, 2, 1, 1, 1, 2),
kx = 1e-6,
ky = 1e-6,
bc_id = c(1, 7),
bc_edge = c(2, 2),
bc_type = c("h", "h"),
bc_value = c(17.5, 15),
grid_size = 0.25,
node_min = 3
){
#generate tibble with all soil domains
dom <- tibble::tibble(
ix = ix,
iy = iy,
x0 = x[ix],
y0 = y[iy],
x1 = x[ix + 1],
y1 = y[iy + 1],
kx = kx,
ky = ky
)
#generate numbers of nodes
dom <- dplyr::mutate(
dom,
id = seq(dplyr::n()),
nx = pmax(node_min, 1 + ceiling((.data$x1 - .data$x0)/grid_size)),
ny = pmax(node_min, 1 + ceiling((.data$y1 - .data$y0)/grid_size)),
hx = (.data$x1 - .data$x0)/(.data$nx - 1),
hy = (.data$y1 - .data$y0)/(.data$ny - 1)
)
#add offsets for node numbering (both with and without ghost nodes)
dom <- dplyr::mutate(
dom,
n = nodes_total(.data$nx, .data$ny, real_only = FALSE),
n_real = nodes_total(.data$nx, .data$ny, real_only = TRUE),
i0 = cumsum(c(0, utils::head(.data$n, -1))),
i0_real = cumsum(c(0, utils::head(.data$n_real, -1))),
)
#generate tibble with all default boundary conditions (impermeable boundaries)
bc <- tibble::tibble(
id = rep(seq(nrow(dom)), each = 4),
edge = rep(seq(4), nrow(dom)),
type = "q",
value = 0
)
#add connecting boundary conditions
for (id in 1:nrow(dom)) {
#other domain connected at the right (positive x-side, edge 3)
id_next <- which((dom$ix == (dom$ix[id] + 1)) & (dom$iy == dom$iy[id]))
if (length(id_next) == 1) {
bc$edge[4*(id - 1) + 3] <- 3
bc$type[4*(id - 1) + 3] <- "c"
bc$value[4*(id - 1) + 3] <- id_next
bc$edge[4*(id_next - 1) + 1] <- 1
bc$type[4*(id_next - 1) + 1] <- "c"
bc$value[4*(id_next - 1) + 1] <- id
}
#other domain connected at the bottom (positive y-side, edge 2)
id_next <- which((dom$ix == dom$ix[id]) & (dom$iy == (dom$iy[id] + 1)))
if (length(id_next) == 1) {
bc$edge[4*(id - 1) + 2] <- 2
bc$type[4*(id - 1) + 2] <- "c"
bc$value[4*(id - 1) + 2] <- id_next
bc$edge[4*(id_next - 1) + 4] <- 4
bc$type[4*(id_next - 1) + 4] <- "c"
bc$value[4*(id_next - 1) + 4] <- id
}
}
#add boundary conditions for head or flow
bc$id[4*(bc_id - 1) + bc_edge] <- bc_id
bc$edge[4*(bc_id - 1) + bc_edge] <- bc_edge
bc$type[4*(bc_id - 1) + bc_edge] <- bc_type
bc$value[4*(bc_id - 1) + bc_edge] <- bc_value
#return
return(list(dom = dom, bc = bc))
}
#' get all sparse entries and lhs for boundary conditions
#'
#' @description
#' function to get sparse matrix element positions for flow net finite
#' difference boundary conditions (known head, known flow or connected to
#' another domain)
#'
#' @param df tibble describing flow problem. Generated by function
#' `generate_flownet_properties()`
#' @importFrom magrittr `%>%`
#' @importFrom rlang .data
#' @return a list with two fields: `mat` containing a tibble with sparse
#' row (`row`), column (`col`) and values (`val`) of finite difference
#' matrix elements related to boundary conditions; and `lhs` which is a
#' vector with all left-hand side of equation values
#' @examples
#' df <- flownet_geometry()
#' ds <- findiff_sparse_entries_bc(df)
#' @export
findiff_sparse_entries_bc <- function(df) {
#join domain properties onto boundary conditions
dbc <- dplyr::left_join(df$bc, df$dom, by = "id") %>%
dplyr::mutate(
k = ifelse((.data$edge %in% c(1, 3)), .data$kx, .data$ky),
h = ifelse((.data$edge %in% c(1, 3)), .data$hx, .data$hy)
)
#initiate list and left-hand sides of bx's
mlist <- vector(mode = "list", length = nrow(dbc))
lhs <- rep(0, sum(df$dom$n))
#initiate list of connecting nodes
clist <- vector(mode = "list", length = nrow(dbc))
#loop through all bcs
for (i in 1:nrow(dbc)) {
if (dbc$type[i] == "h") {
#Defined head
i1 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 0)
i2 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 1)
mlist[[i]] <- tibble::tibble(
row = i1,
col = i2,
val = 1
)
lhs[i1] <- dbc$value[i]
} else if (dbc$type[i] == "q") {
#Defined flow rate (positive into domain)
i1 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 0)
i2 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 2)
mlist[[i]] <- tibble::tibble(
row = rep(i1, 2),
col = c(i1, i2),
val = rep(c(0.5, -0.5)*dbc$k[i]/dbc$h[i], each = length(i1))
)
lhs[i1] <- dbc$value[i]
} else if (dbc$type[i] == "c") {
#connected to other domain (b)
#index in <dbc> of connecting edge
ib <- which((dbc$id == dbc$value[i]) & (dbc$edge == (1 + (dbc$edge[i] + 1)%%4)))
if (dbc$edge[i] %in% c(2, 3)) {
#other domain connected on positive side - same head
ia1 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 0)
ia2 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 1)
ib2 <- index_edge(dbc$nx[ib], dbc$ny[ib], dbc$edge[ib], i0 = dbc$i0[ib], offset = 1)
mlist[[i]] <- tibble::tibble(
row = rep(ia1, 2),
col = c(ia2, ib2),
val = rep(c(-1, 1), each = length(ia1))
)
#add connecting real nodes - real node indexing - used later for solving flow potential
clist[[i]] <- tibble::tibble(
i1 = index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0_real[i], offset = 0, real_only = TRUE),
i2 = index_edge(dbc$nx[ib], dbc$ny[ib], dbc$edge[ib], i0 = dbc$i0_real[ib], offset = 0, real_only = TRUE)
)
} else {
#other domain on negative side - same flow rate
ia1 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 0)
ia2 <- index_edge(dbc$nx[i], dbc$ny[i], dbc$edge[i], i0 = dbc$i0[i], offset = 2)
ib1 <- index_edge(dbc$nx[ib], dbc$ny[ib], dbc$edge[ib], i0 = dbc$i0[ib], offset = 0)
ib2 <- index_edge(dbc$nx[ib], dbc$ny[ib], dbc$edge[ib], i0 = dbc$i0[ib], offset = 2)
mlist[[i]] <- tibble::tibble(
row = rep(ia1, 4),
col = c(ia1, ia2, ib1, ib2),
val = c(
rep(c(-0.5, 0.5)*dbc$k[i]/dbc$h[i], each = length(ia1)),
rep(c(-0.5, 0.5)*dbc$k[ib]/dbc$h[ib], each = length(ib1))
)
)
}
}
}
#return
return(list(
mat = dplyr::bind_rows(mlist),
lhs = lhs,
conn = dplyr::bind_rows(clist)
))
}
#' Solve flow net head problem for concatenated rectangular domains
#'
#' @description
#' Solves a flow net problem for a problem consisting of connected rectangular
#' grids. This function solves the hydraulic head using boundary conditions and
#' a finite difference approach, and also calculates the flow potential psi
#'
#' @param df tibble with problem description, generated by function
#' `flownet_geometry()`
#' @return a tibble with heads (field `h`), flow rates in x and y-direction
#' (`qx`, `qy`) and flow potential (`psi`) for each real point in the finite
#' difference grid. Each point is characterised by a position (`x`, `y`)
#' and an index `id` indicating which domain the point belongs to
#' @importFrom magrittr `%>%`
#' @importFrom rlang .data
#' @examples
#' df <- flownet_geometry()
#' dp <- solve_flownet(df)
#' @export
solve_flownet <- function(df) {
## SOLVE FOR HEAD
#get sparse matrix elements and left-hand side for boundary conditions
Mbc <- findiff_sparse_entries_bc(df)
#get sparse matrix elements for Poissons equation for each real node
M2x <- df$dom %>%
dplyr::select(.data$nx, .data$ny, .data$kx, .data$hx, .data$i0) %>%
purrr::pmap_dfr(
function(nx, ny, kx, hx, i0) findiff_sparse_entries(nx, ny, order = 2, h = hx, direction = "x", multiplier = kx, i0_row = i0, i0_col = i0)
)
M2y <- df$dom %>%
dplyr::select(.data$nx, .data$ny, .data$ky, .data$hy, .data$i0) %>%
purrr::pmap_dfr(
function(nx, ny, ky, hy, i0) findiff_sparse_entries(nx, ny, order = 2, h = hy, direction = "y", multiplier = ky, i0_row = i0, i0_col = i0)
)
#create sparse matrix
mat <- Matrix::sparseMatrix(
i = c(Mbc$mat$row, M2x$row, M2y$row),
j = c(Mbc$mat$col, M2x$col, M2y$col),
x = c(Mbc$mat$val, M2x$val, M2y$val),
dims = rep(sum(df$dom$n), 2)
)
#bind together, and solve system
h = as.vector(Matrix::solve(mat, Mbc$lhs))
## CALCULATE FLOW FROM HEAD
#flow in x-direction
M1qx <- df$dom %>%
dplyr::select(.data$nx, .data$ny, .data$kx, .data$hx, .data$i0) %>%
purrr::pmap_dfr(
function(nx, ny, kx, hx, i0) findiff_sparse_entries(nx, ny, order = 1, h = hx, direction = "x", multiplier = -kx, i0_row = i0, i0_col = i0)
)
qx <- as.vector(
Matrix::sparseMatrix(
i = M1qx$row,
j = M1qx$col,
x = M1qx$val,
dims = rep(sum(df$dom$n), 2)
) %*% h
)
#flow in y-direction
M1qy <- df$dom %>%
dplyr::select(.data$nx, .data$ny, .data$ky, .data$hy, .data$i0) %>%
purrr::pmap_dfr(
function(nx, ny, ky, hy, i0) findiff_sparse_entries(nx, ny, order = 1, h = hy, direction = "y", multiplier = -ky, i0_row = i0, i0_col = i0)
)
qy <- as.vector(
Matrix::sparseMatrix(
i = M1qy$row,
j = M1qy$col,
x = M1qy$val,
dims = rep(sum(df$dom$n), 2)
) %*% h
)
## ASSIGN SOLUTIONS AND POSITIONS (real nodes only)
#indices of real nodes
i_real <- purrr::pmap(df$dom, index_real) %>% unlist()
#generate positions for all solution object for all nodes
dp <- df$dom %>%
dplyr::summarise(
nodal_coordinates_real(
.data$nx,
.data$ny,
x0 = .data$x0,
x1 = .data$x1,
y0 = .data$y0,
y1 = .data$y1,
id = .data$id
)
)
#add head and flow for all real points
dp <- dplyr::mutate(
dp,
h = h[i_real],
qx = qx[i_real],
qy = qy[i_real]
)
## GET FLOW POTENTIAL FROM FLOW
#x-direction elements - first order differentiation - real nodes only
M1x_el <- df$dom %>%
dplyr::select(.data$nx, .data$ny, .data$kx, .data$hx, .data$i0_real) %>%
purrr::pmap_dfr(
function(nx, ny, kx, hx, i0_real) findiff_sparse_entries(nx, ny, order = 1, h = hx, direction = "x", i0_row = i0_real, i0_col = i0_real, real_only = TRUE)
)
#x-direction elements - first order differentiation - real nodes only
M1y_el <- df$dom %>%
dplyr::select(.data$nx, .data$ny, .data$ky, .data$hy, .data$i0_real) %>%
purrr::pmap_dfr(
function(nx, ny, ky, hy, i0_real) findiff_sparse_entries(nx, ny, order = 1, h = hy, direction = "y", i0_row = i0_real, i0_col = i0_real, real_only = TRUE)
)
#flow potential must match on each of the connecting segments
Mc <- Mbc$conn
Mc_el <- tibble::tibble(
row = rep(seq(nrow(Mc)), 2),
col = c(Mc$i1, Mc$i2),
val = rep(c(-1, 1), each = nrow(Mc))
)
#notal number of real nodes
ntreal <- sum(df$dom$n_real)
#crate single matrix and left-hand side for flow potential solving
mat_fp <- Matrix::sparseMatrix(
i = c(M1x_el$row, M1y_el$row + ntreal, Mc_el$row + 2*ntreal),
j = c(M1x_el$col, M1y_el$col, Mc_el$col),
x = c(M1x_el$val, M1y_el$val, Mc_el$val),
dims = c(2*ntreal + nrow(Mc), ntreal)
)
lhs_fp <- c(dp$qy, -dp$qx, rep(0, nrow(Mc)))
#solve for flow potential
psi <- as.vector(
Matrix::solve(
(Matrix::t(mat_fp) %*% mat_fp),
(Matrix::t(mat_fp) %*% lhs_fp)
)
)
#scale so flow potential ranges between 0 and Q_total, and assign
dp$psi <- psi - min(psi)
## RETURN
#return
return(dp)
}
#' Decide on number of equipotential intervals
#'
#' @description
#' This function takes a finite difference solution for both head `h` and flow
#' potential function `psi` to get the best number of equipotential intervals
#' `Nd` based on a given number of flow channels `Nf`. This function assumes
#' the permeabilities in all domains is the same
#'
#' @param df tibble with information about domain
#' @param dp tibble with head and flow potential results for each node
#' @param Nf number of requested flow channels
#' @return the optimal number of equipotential intervals `Nd`
#' @importFrom magrittr `%>%`
#' @importFrom rlang .data
#' @examples
#' df <- flownet_geometry()
#' dp <- solve_flownet(df)
#' amount_equipotentialintervals(df, dp, Nf = 5)
#' @export
amount_equipotentialintervals <- function(df, dp, Nf = 5) {
#total head difference
dh <- max(dp$h) - min(dp$h)
#total flow per second
Q <- max(dp$psi) - min(dp$psi)
#k_avg
k_avg <- df$dom %>%
dplyr::summarize(k = mean(sqrt(.data$kx*.data$ky))) %>%
dplyr::pull(.data$k)
#Nd
Nd <- round(k_avg*dh*Nf/Q)
#return
return(Nd)
}
#' Add flownet to an existing ggplot
#'
#' @description
#' Function to add a flow net to an existing ggplot. If the plot does not
#' exist yet, a new one if created
#'
#' @param df tibble with domains/problem description
#' @param dp flow net solution tibble. If not specified, it is calculated
#' using `df`
#' @param Nf number of requested flow paths
#' @param line_width line thickness for all lines
#' @param colour_flowline colour of flow lines
#' @param colour_equipotentialline colour of equipotential lines
#' @param fill fill colour for (saturated) soil
#' @param plt a ggplot object. If not defined, a new plot is generated
#' @param xlab,ylab x and y-axis label - if `plt` not defined
#' @param xlim,ylim user-defined axis limits - if `plt` not defined
#' @param axes if `FALSE` no axes are plotted - if `plt` not defined
#' @return a ggplot object
#' @importFrom magrittr `%>%`
#' @importFrom rlang .data
#' @examples
#' df <- flownet_geometry()
#' ggplot_add_flownet(df, axes = FALSE)
#' ggplot_add_flownet(df, axes = TRUE, fill = NA)
#' @export
ggplot_add_flownet <- function(
df,
dp = NULL,
Nf = 5,
linewidth = 0.5,
colour_flowline = "black",
colour_equipotentialline = "black",
fill = "#aebab7",
plt = NULL,
xlab = "x [m]",
ylab = "z [m]",
xlim = c(NA, NA),
ylim = c(NA, NA),
axes = TRUE
){
#if dp not provided, calculate heads and flow potential
if (is.null(dp)) {
dp <- solve_flownet(df)
}
#calculate number of equipotential intervals
Nd <- amount_equipotentialintervals(df, dp, Nf = Nf)
Nd_levels <- seq(min(dp$h), max(dp$h), l = (Nd + 1))[2:Nd]
Nf_levels <- seq(min(dp$psi), max(dp$psi), l = (Nf + 1))
#if plot does not exist, generate a new one
if (is.null(plt)) {
plt <- ggplot_geometry(xlim = xlim, ylim = ylim, axes = axes, xlab = xlab, ylab = ylab)
}
#plot rectangular soil elements
plt <- plt + ggplot2::geom_rect(
data = df$dom,
ggplot2::aes(xmin = .data$x0, xmax = .data$x1, ymin = .data$y0, ymax = .data$y1),
fill = fill,
color = NA
)
#add flow and equipotential lines using contour lines
plt <- plt +
ggplot2::geom_contour(
data = dp,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$h),
breaks = Nd_levels,
color = colour_equipotentialline,
size = line_width
) +
ggplot2::geom_contour(
data = dp,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$psi),
breaks = Nf_levels,
color = colour_flowline,
size = line_width
)
#return
return(plt)
}
#' Plot flow net and soil geometry for a dam/sheet pile problem
#'
#' @param df tibble with domains/problem description, generated by function
#' `generate_flownet_properties()`.#'
#' @param dp solution for heads and flow potential for each node. If not
#' defined, it is calculated in this plotting function
#' @param Nf number of requested flow paths
#' @param xlab,ylab x and y-axis label
#' @param fill_soilwet fill colour for saturated soil
#' @param fill_soildry fill colour for dry soil,
#' @param colour_soil line colour for soil
#' @param colour_flowline colour of flow lines
#' @param colour_equipotentialline colour of equipotential lines
#' @param fill_water fill colour for water
#' @param colour_water line colour for water
#' @param fill_impermeable fill colour for impermeable parts of the domain
#' @param fill_air fill colour for air on top of soil/water
#' @param line_water line type for water edges (defined head)
#' @param line_width line thickness for all lines
#' @param xlim,ylim user-defined axis limits
#' @param axes if `FALSE` no axes are plotted
#' @param thickness_impermeable thickness of impermeable border around the
#' entire problem. Defined as an array for all edges (left, top, right,
#' bottom), or single value for all edges
#' @param scale_soilmarker size of soil marker, in fraction of height
#' @param scale_watermarker size of water table marker, in fraction of height
#' @return a ggplot object
#' @importFrom magrittr `%>%`
#' @examples
#' #default example
#' df <- flownet_geometry()
#' ggplot_flownet_dam(df)
#'
#' #anisotropic permeability - with 6 flow channels
#' df <- flownet_geometry(kx = 4e-6, ky = 1e-6)
#' ggplot_flownet_dam(df, Nf = 6)
#'
#' #deep excavation example
#' df <- flownet_geometry(
#' x = c(0, 5, 5.25, 30),
#' y = c(0, 5, 7.5, 15, 20),
#' ix = c(1, 1, 2, 3, 3, 3, 3),
#' iy = c(2, 1, 1, 1, 2, 3, 4),
#' bc_id = c(1, 6),
#' bc_edge = c(2, 2),
#' bc_type = c("h", "h"),
#' bc_value = c(7.5, 15),
#' dry = c(rep(FALSE, 6), TRUE)
#' )
#' ggplot_flownet_dam(df)
#' @export
ggplot_flownet_dam <- function(
df,
dp = NULL,
Nf = 5,
xlab = "x [m]",
ylab = "z [m]",
fill_soilwet = "#aebab7",
fill_soildry = "#d3bc5f",
colour_soil = "#65571d",
colour_flowline = "black",
colour_equipotentialline = "black",
fill_water = "#2a7fff",
colour_water = "#000080",
fill_impermeable = "#333333",
fill_air = "white",
line_water = 2,
line_width = 0.5,
xlim = c(NA, NA),
ylim = c(NA, NA),
axes = TRUE,
thickness_impermeable = c(0, 1, 0, 1),
scale_soilmarker = 0.075,
scale_watermarker = 0.050
){
#if dp not provided, calculate heads and flow potential
if (is.null(dp)) {
dp <- solve_flownet(df)
}
#calculate number of equipotential intervals
Nd <- amount_equipotentialintervals(df, dp, Nf = Nf)
Nd_levels <- seq(min(dp$h), max(dp$h), l = (Nd + 1))[2:Nd]
Nf_levels <- seq(min(dp$psi), max(dp$psi), l = (Nf + 1))
#impermeable thickness
if (length(thickness_impermeable) == 1) {
thickness_impermeable <- rep(thickness_impermeable, 4)
}
#get head edges
dedge <- df$bc %>%
dplyr::filter(.data$type == "h") %>%
dplyr::left_join(df$dom, by = "id") %>%
dplyr::mutate(
x = ifelse(.data$edge == 3, .data$x1, .data$x0),
xend = ifelse(.data$edge == 1, .data$x0, .data$x1),
y = ifelse(.data$edge == 2, .data$y1, .data$y0),
yend = ifelse(.data$edge == 4, .data$y0, .data$y1)
)
#plot limits
if (is.na(xlim[1])) {
xlim[1] <- min(df$dom$x0) - thickness_impermeable[1]
}
if (is.na(xlim[2])) {
xlim[2] <- max(df$dom$x1) + thickness_impermeable[3]
}
if (is.na(ylim[1])) {
ylim[1] <- min(df$dom$y0) - thickness_impermeable[4]
}
if (is.na(ylim[2])) {
ylim[2] <- max(c(df$dom$y1, dedge$yend)) + thickness_impermeable[2]
}
#initiate plot
plt <- ggplot2::ggplot() +
ggplot2::coord_equal(ratio = 1, xlim = xlim, ylim = ylim, expand = FALSE)
#impermeable background
plt <- plt +
ggplot2::annotate(
"polygon",
x = c(rep(xlim[1], 2), rep(xlim[2], 2)),
y = c(ylim[1], rep(ylim[2], 2), ylim[1]),
color = NA,
fill = fill_impermeable
)
#plot rectangles for ponding water
plt <- plt +
ggplot2::geom_rect(
data = dedge,
ggplot2::aes(xmin = .data$x, xmax = .data$xend, ymin = .data$y0, ymax = .data$value),
fill = fill_water,
color = NA
)
#plot air
plt <- plt +
ggplot2::geom_rect(
data = dedge,
ggplot2::aes(xmin = .data$x, xmax = .data$xend, ymin = .data$value, ymax = ylim[2]),
fill = fill_air,
colour = NA
)
#plot rectangles for dry soil
plt <- plt +
ggplot2::geom_rect(
data = dplyr::filter(df$dom, .data$dry == TRUE),
ggplot2::aes(xmin = .data$x0, xmax = .data$x1, ymin = .data$y0, ymax = .data$y1),
fill = fill_soildry,
colour = NA
)
#plot rectangles for saturated soil
plt <- plt +
ggplot2::geom_rect(
data = dplyr::filter(df$dom, .data$dry == FALSE),
ggplot2::aes(xmin = .data$x0, xmax = .data$x1, ymin = .data$y0, ymax = .data$y1),
fill = fill_soilwet,
colour = NA
)
#plot soil surface lines
dsurf <- dplyr::left_join(
dedge %>%
dplyr::select(.data$ix, .data$x, .data$xend, .data$y, .data$yend),
df$dom %>%
dplyr::filter(.data$dry == TRUE) %>%
dplyr::select(.data$ix, .data$y1),
by = "ix"
) %>%
dplyr::mutate(
y = pmax(.data$y, .data$y1, na.rm = TRUE),
yend = pmax(.data$yend, .data$y1, na.rm = TRUE)
)
plt <- plt +
ggplot2::geom_segment(
data = dsurf,
ggplot2::aes(x = .data$x, xend = .data$xend, y = .data$y, yend = .data$yend),
color = colour_soil,
size = line_width
)
#plot water table lines
plt <- plt +
ggplot2::geom_segment(
data = dedge,
ggplot2::aes(x = .data$x, xend = .data$xend, y = .data$value, yend = .data$value),
color = colour_water,
linetype = line_water,
size = line_width
)
#plot soil surface marker
if (!is.na(scale_soilmarker)) {
for (i in 1:nrow(dsurf)) {
if ((dsurf$xend[i] > xlim[1]) & (dsurf$x[i] <= xlim[2])) {
plt <- ggplot_add_soilmarker(
plt,
1/3*max(xlim[1], dsurf$x[i]) + 2/3*min(xlim[2], dsurf$xend[i]),
dsurf$y[i],
scale = scale_soilmarker*diff(ylim)
)
}
}
}
#plot water table markers
if (!is.na(scale_watermarker)) {
for (i in 1:nrow(dedge)) {
if ((dedge$xend[i] > xlim[1]) & (dedge$x[i] <= xlim[2])) {
plt <- ggplot_add_watermarker(
plt,
2/3*max(xlim[1], dedge$x[i]) + 1/3*min(xlim[2], dedge$xend[i]),
dedge$value[i],
scale = scale_watermarker*diff(ylim)
)
}
}
}
#switch axes off if requested
if (axes == FALSE) {
plt <- plt + ggplot2::theme_void()
} else {
plt <- plt +
theme_soilmech() +
ggplot2::theme(
panel.background = ggplot2::element_blank(),
panel.border = ggplot2::element_blank()
) +
ggplot2::xlab(xlab) +
ggplot2::ylab(ylab)
}
#add flow and equipotential lines using contour lines
plt <- plt +
ggplot2::geom_contour(
data = dp,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$h),
breaks = Nd_levels,
color = colour_equipotentialline,
size = line_width
) +
ggplot2::geom_contour(
data = dp,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$psi),
breaks = Nf_levels,
color = colour_flowline,
size = line_width
)
#return
return(plt)
}
#' ggplot 2D map of hydraulic heads and pressures
#'
#' @description
#' Plots a 2D map of the pressure or head distributions in a flow net problem.
#' The plot shows both a heat map and contour lines.
#'
#' @inheritParams ggplot_flownet_dam
#' @param type parameter to plot. `type = "h"` for hydraulic heads,
#' `type = "hz"` for elevation head, `type = `hb` for pressure head
#' or `type = "u"` for pore water pressures
#' @param binwidth contour line distance
#' @param label_size contour line text label size
#' @param label_n number of times contour label appears on each line
#' @param gamma_w unit weight of water, in kN/m3 (required for calculating
#' pore water pressures)
#' @param palette RColorBrewer color map for shading
#' @param palette_direction RColorBrewer color map direction (`1` or `-1`)
#' @param colour_contour colour of contour lines
#' @return a ggplot object
#' @examples
#' #generate flow net geometry
#' df <- flownet_geometry()
#'
#' #solve flow net problem
#' dp <- solve_flownet(df)
#'
#' #plot heads
#' ggplot_hydraulichead_dam(df, dp = dp, type = "h", binwidth = 0.25)
#'
#' #plot elevation head
#' ggplot_hydraulichead_dam(df, dp = dp, type = "hz", binwidth = 2.5)
#'
#' #plot pressure head
#' ggplot_hydraulichead_dam(df, dp = dp, type = "hb", binwidth = 2.5)
#'
#' #plot pore water pressure
#' ggplot_hydraulichead_dam(df, dp = dp, type = "u", binwidth = 25)
#' @export
ggplot_hydraulichead_dam <- function(
df,
dp = NULL,
type = "h", #h, hz, hb, u
binwidth = 0.25,
gamma_w = 10,
label_size = 3,
label_n = 1,
xlab = "x [m]",
ylab = "z [m]",
palette = "Blues", #YlGnBu
palette_direction = 1,
fill_soilwet = "white",
fill_soildry = "white",
colour_soil = "#65571d",
colour_contour = "black",
fill_water = "white",
colour_water = "#000080",
fill_impermeable = "#333333",
fill_air = "white",
line_water = 2,
line_width = 0.5,
xlim = c(NA, NA),
ylim = c(NA, NA),
axes = TRUE,
thickness_impermeable = c(0, 1, 0, 1),
scale_soilmarker = 0.075,
scale_watermarker = 0.050
){
#if dp not provided, calculate heads and flow potential
if (is.null(dp)) {
dp <- solve_flownet(df)
}
#impermeable thickness
if (length(thickness_impermeable) == 1) {
thickness_impermeable <- rep(thickness_impermeable, 4)
}
#get head edges
dedge <- df$bc %>%
dplyr::filter(.data$type == "h") %>%
dplyr::left_join(df$dom, by = "id") %>%
dplyr::mutate(
x = ifelse(.data$edge == 3, .data$x1, .data$x0),
xend = ifelse(.data$edge == 1, .data$x0, .data$x1),
y = ifelse(.data$edge == 2, .data$y1, .data$y0),
yend = ifelse(.data$edge == 4, .data$y0, .data$y1)
)
#plot limits
if (is.na(xlim[1])) {
xlim[1] <- min(df$dom$x0) - thickness_impermeable[1]
}
if (is.na(xlim[2])) {
xlim[2] <- max(df$dom$x1) + thickness_impermeable[3]
}
if (is.na(ylim[1])) {
ylim[1] <- min(df$dom$y0) - thickness_impermeable[4]
}
if (is.na(ylim[2])) {
ylim[2] <- max(c(df$dom$y1, dedge$yend)) + thickness_impermeable[2]
}
#initiate plot
plt <- ggplot2::ggplot() +
ggplot2::coord_equal(ratio = 1, xlim = xlim, ylim = ylim, expand = FALSE)
#impermeable background
plt <- plt +
ggplot2::annotate(
"polygon",
x = c(rep(xlim[1], 2), rep(xlim[2], 2)),
y = c(ylim[1], rep(ylim[2], 2), ylim[1]),
color = NA,
fill = fill_impermeable
)
#plot rectangles for ponding water
plt <- plt +
ggplot2::geom_rect(
data = dedge,
ggplot2::aes(xmin = .data$x, xmax = .data$xend, ymin = .data$y0, ymax = .data$value),
fill = fill_water,
color = NA
)
#plot air
plt <- plt +
ggplot2::geom_rect(
data = dedge,
ggplot2::aes(xmin = .data$x, xmax = .data$xend, ymin = .data$value, ymax = ylim[2]),
fill = fill_air,
colour = NA
)
#plot rectangles for dry soil
plt <- plt +
ggplot2::geom_rect(
data = dplyr::filter(df$dom, .data$dry == TRUE),
ggplot2::aes(xmin = .data$x0, xmax = .data$x1, ymin = .data$y0, ymax = .data$y1),
fill = fill_soildry,
colour = NA
)
#plot rectangles for saturated soil
plt <- plt +
ggplot2::geom_rect(
data = dplyr::filter(df$dom, .data$dry == FALSE),
ggplot2::aes(xmin = .data$x0, xmax = .data$x1, ymin = .data$y0, ymax = .data$y1),
fill = fill_soilwet,
colour = NA
)
#plot hydraulic head profiles
if (type == "h") {
dp$val <- dp$h
label <- expression(h~"[m]")
} else if (type == "hz") {
dp$val <- dp$y
label <- expression(h[z]~"[m]")
} else if (type == "hb") {
dp$val <- dp$h - dp$y
label <- expression(h[b]~"[m]")
} else if (type == "u") {
dp$val <- (dp$h - dp$y)*gamma_w
label <- expression(u~"[kPa]")
}
plt <- plt +
ggplot2::stat_summary_2d(
data = dp,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$val),
binwidth = min(c(df$dom$hx, df$dom$hy))
) +
ggplot2::geom_contour(
data = dp,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$val),
binwidth = binwidth,
color = colour_contour,
size = line_width
) +
ggplot2::scale_fill_distiller(
name = label,
palette = palette,
direction = palette_direction
) +
metR::geom_text_contour(
data = dp,
binwidth = binwidth,
ggplot2::aes(x = .data$x, y = .data$y, z = .data$val),
label.placement = metR::label_placement_n(label_n),
size = label_size
)
#plot soil surface lines
dsurf <- dplyr::left_join(
dedge %>%
dplyr::select(.data$ix, .data$x, .data$xend, .data$y, .data$yend),
df$dom %>%
dplyr::filter(.data$dry == TRUE) %>%
dplyr::select(.data$ix, .data$y1),
by = "ix"
) %>%
dplyr::mutate(
y = pmax(.data$y, .data$y1, na.rm = TRUE),
yend = pmax(.data$yend, .data$y1, na.rm = TRUE)
)
plt <- plt +
ggplot2::geom_segment(
data = dsurf,
ggplot2::aes(x = .data$x, xend = .data$xend, y = .data$y, yend = .data$yend),
color = colour_soil,
size = line_width
)
#plot water table lines
plt <- plt +
ggplot2::geom_segment(
data = dedge,
ggplot2::aes(x = .data$x, xend = .data$xend, y = .data$value, yend = .data$value),
color = colour_water,
linetype = line_water,
size = line_width
)
#plot soil surface marker
if (!is.na(scale_soilmarker)) {
for (i in 1:nrow(dsurf)) {
if ((dsurf$xend[i] > xlim[1]) & (dsurf$x[i] <= xlim[2])) {
plt <- ggplot_add_soilmarker(
plt,
1/3*max(xlim[1], dsurf$x[i]) + 2/3*min(xlim[2], dsurf$xend[i]),
dsurf$y[i],
scale = scale_soilmarker*diff(ylim)
)
}
}
}
#plot water table markers
if (!is.na(scale_watermarker)) {
for (i in 1:nrow(dedge)) {
if ((dedge$xend[i] > xlim[1]) & (dedge$x[i] <= xlim[2])) {
plt <- ggplot_add_watermarker(
plt,
2/3*max(xlim[1], dedge$x[i]) + 1/3*min(xlim[2], dedge$xend[i]),
dedge$value[i],
scale = scale_watermarker*diff(ylim)
)
}
}
}
#switch axes off if requested
if (axes == FALSE) {
plt <- plt + ggplot2::theme_void()
} else {
plt <- plt +
theme_soilmech() +
ggplot2::theme(
panel.background = ggplot2::element_blank(),
panel.border = ggplot2::element_blank()
) +
ggplot2::xlab(xlab) +
ggplot2::ylab(ylab)
}
#return
return(plt)
}
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