Replicate the R code

Install the packages

Note: If you wish to replicate the R code below, then you will need to copy and paste the following commands in R first to make sure you have all the packages and their dependencies installed:

install.packages(c("install.load", "import", "ggplot2", "data.table", "pander", "units",
    "remotes"))
# install the packages and their dependencies


# As geotech is currently archived,
remotes::install_version("geotech", version = "1.0")
# Source 1



Load the packages

Note: If you wish to replicate the R code below, then you will need to copy and paste the following commands in R first to make sure you have all the packages loaded:

install.load::load_package("geotech", "ggplot2", "data.table", "pander", "units")
# load needed packages using the load_package function from the install.load
# package (it is assumed that you have already installed these packages)


import::from(pracma, semilogx, std)
# import semilogx and std from the pracma package


panderOptions("missing", "")
# set pander options to have missing values in the tables as blank cells



Sand Gradation Analysis Examples from Tennessee State University (TSU) Structural Testing Laboratory undergraduate-level course, Fall 2014 and Fall 2016

Fall 2014

# Example 1 from Fall 2014 Group 1

# create a numeric vector with the units of inch
value_in <- set_units(3/8, "in")

# create a numeric vector to convert from inch to centimeter
value_mm <- value_in

# create a numeric vector with the units of millimeter
units(value_mm) <- make_units(mm)

# make numeric
value_mmnum <- drop_units(value_mm)


sand_grad_1a <- data.table(Sieve = c("3/8”", "4", "8", "16", "30", "50", "Pan"),
    Size = c(value_mmnum, 4.75, 2.36, 1.18, 0.6, 0.3, NA), Mass_Sieve = c(0.516,
        0.734, 0.46, 0.408, 0.39, 0.344, 0.362), Mass_SievePlus = c(0.516, 0.766,
        0.566, 0.532, 0.618, 0.76, 0.45))
sand_grad_1a <- sand_grad_1a[, V2 := Mass_SievePlus - Mass_Sieve]
sand_grad_1a <- sand_grad_1a[, V3 := cumsum(V2)]
sand_grad_1a <- sand_grad_1a[, V4 := round(V3/sum(V2) * 100, digits = 0)]
sand_grad_1a <- sand_grad_1a[, V5 := round(100 - V4, digits = 0)]
set(sand_grad_1a, i = 7L, j = c(5L:8L), value = NA)
setnames(sand_grad_1a, c("Sieve #", "Size (mm)", "Mass Sieve (kg)", "Mass Retained + Sieve (kg)",
    "Mass Retained (kg)", "Cumulative Mass Retained (kg)", "Cumulative % Retained",
    "% Passing"))

sand_grad_1a <- setDF(sand_grad_1a)
sand_grad_1a[, 7:8] <- round(sand_grad_1a[, 7:8], digits = 3)


pander(sand_grad_1a, caption = "Fall 2014 Group 1 Sieve Analysis Table", round = c(c(2,
    2), c(3, 3), c(4, 3), c(5, 3), c(6, 3)))
Sieve # Size (mm) Mass Sieve (kg) Mass Retained + Sieve (kg)
3/8” 9.53 0.516 0.516
4 4.75 0.734 0.766
8 2.36 0.46 0.566
16 1.18 0.408 0.532
30 0.6 0.39 0.618
50 0.3 0.344 0.76
Pan 0.362 0.45

Fall 2014 Group 1 Sieve Analysis Table (continued below)

Mass Retained (kg) Cumulative Mass Retained (kg) Cumulative % Retained
0 0 0
0.032 0.032 3
0.106 0.138 14
0.124 0.262 26
0.228 0.49 49
0.416 0.906 91
% Passing
100
97
86
74
51
9 
# calculate the Fineness Modulus
FM_1a <- sum(sand_grad_1a[, 7], na.rm = TRUE)/100

FM_1a
## [1] 1.83
op <- par(mar = c(5, 4, 8, 2))  # set margins
semilogx(sand_grad_1a[, 2], (sand_grad_1a[, 8] - 1L), xlab = "Sieve size (mm)", ylab = "% Passing",
    type = "b", axes = FALSE, pch = 19, xlim = c(0.075, 50), ylim = c(0, 100))
x1 <- c(0.075, 0.15, 0.3, 0.6, 1.18, 2.36, 4.75, 9.5, 12.5, 19, 25, 37.5, 50)
x2 <- c("No. 200", "No. 100", "No. 50", "No. 30", "No. 16", "No. 8", "No. 4", "3/8 in.",
    "1/2 in.", "3/4 in.", "1 in.", "1 1/2 in.", "2 in.")
y <- seq(0, 100, 10)
axis(1, at = x1, labels = NULL, tck = 0, las = 2)
axis(3, at = x1, labels = x2, tck = 0, las = 2)
abline(h = seq(0, 100, 5), v = x1)
axis(2, at = y, labels = y, tck = 0)
box()  # Source 3
mtext("Sieve size", side = 3, line = 4, cex.lab = 0.8, las = 0)
mtext("Group 1 Sand Gradation Results (ASTM C136)", side = 3, line = 5, cex.lab = 0.8,
    las = 0)

par(op)  # reset to previous settings


sieve <- c(3/8, 4, 8, 16, 30, 50)

# Modified Example 1 from the grainSize function of the geotech package Plot
# grain-size distribution
grainSize.plot(sieve = sieve, percent = (sand_grad_1a[(1:nrow(sand_grad_1a) - 1L),
    8] - 1L), metric = TRUE)

# Group 2

sand_grad_2a <- data.table(Sieve = c("3/8”", "4", "8", "16", "30", "50", "Pan"),
    Size = c(value_mmnum, 4.75, 2.36, 1.18, 0.6, 0.3, NA), Mass_Sieve = c(0.516,
        0.508, 0.462, 0.406, 0.38, 0.348, 0.366), Mass_SievePlus = c(0.516, 0.538,
        0.558, 0.522, 0.606, 0.77, 0.466))
sand_grad_2a <- sand_grad_2a[, V2 := Mass_SievePlus - Mass_Sieve]
sand_grad_2a <- sand_grad_2a[, V3 := cumsum(V2)]
sand_grad_2a <- sand_grad_2a[, V4 := round(V3/sum(V2) * 100, digits = 0)]
sand_grad_2a <- sand_grad_2a[, V5 := round(100 - V4, digits = 0)]
set(sand_grad_2a, i = 7L, j = c(5L:8L), value = NA)
setnames(sand_grad_2a, c("Sieve #", "Size (mm)", "Mass Sieve (kg)", "Mass Retained + Sieve (kg)",
    "Mass Retained (kg)", "Cumulative Mass Retained (kg)", "Cumulative % Retained",
    "% Passing"))

sand_grad_2a <- setDF(sand_grad_2a)
sand_grad_2a[, 7:8] <- round(sand_grad_2a[, 7:8], digits = 3)


pander(sand_grad_2a, caption = "Fall 2014 Group 2 Sieve Analysis Table", round = c(c(2,
    2), c(3, 3), c(4, 3), c(5, 3), c(6, 3)))
Sieve # Size (mm) Mass Sieve (kg) Mass Retained + Sieve (kg)
3/8” 9.53 0.516 0.516
4 4.75 0.508 0.538
8 2.36 0.462 0.558
16 1.18 0.406 0.522
30 0.6 0.38 0.606
50 0.3 0.348 0.77
Pan 0.366 0.466

Fall 2014 Group 2 Sieve Analysis Table (continued below)

Mass Retained (kg) Cumulative Mass Retained (kg) Cumulative % Retained
0 0 0
0.03 0.03 3
0.096 0.126 13
0.116 0.242 24
0.226 0.468 47
0.422 0.89 90
% Passing
100
97
87
76
53
10 
# calculate the Fineness Modulus
FM_2a <- sum(sand_grad_2a[, 7], na.rm = TRUE)/100

FM_2a
## [1] 1.77
# mean, standard deviation, and variance of the Fineness Modulus (Group 1 and
# 2)
FM_2014 <- c(FM_1a, FM_2a)

mean(FM_2014)
## [1] 1.8
std(FM_2014)
## [1] 0.04242641
var(FM_2014)
## [1] 0.0018
op <- par(mar = c(5, 4, 8, 2))  # set margins
semilogx(sand_grad_2a[, 2], sand_grad_2a[, 8], xlab = "Sieve size (mm)", ylab = "% Passing",
    type = "b", axes = FALSE, pch = 19, xlim = c(0.075, 50), ylim = c(0, 100))
axis(1, at = x1, labels = NULL, tck = 0, las = 2)
axis(3, at = x1, labels = x2, tck = 0, las = 2)
axis(2, at = y, labels = y, tck = 0)
abline(h = seq(0, 100, 5), v = x1)
box()  # Source 3
mtext("Sieve size", side = 3, line = 4, cex.lab = 0.8, las = 0)
mtext("Group 2 Sand Gradation Results (ASTM C136)", side = 3, line = 5, cex.lab = 0.8,
    las = 0)