Soil Erosion Homework Solution
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Purdue University *
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325
Subject
Geography
Date
Dec 6, 2023
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Pages
5
Uploaded by AdmiralWasp3805
Soil Erosion Homework Solution
September 26, 2021
Question 1
What is the soil loss for up and downslope farming in Indianapolis, IN with a slope length of 180
m? What will be the soil loss if the field is terraced with a horizontal spacing of 24 m, assuming
the cover management conditions remain unchanged? Assume and the soil is a Lewisburg soil and
a continuous corn/soybean rotation with spring conservation tillage and a slope of four percent.
Solution
Part 1 - Erosion from hillslope with minimal conservation practices
First solve for the hillslope with no conservation practices in place.
Use these variables to estimate missing values required for USLE, $ A = R K L S C P $.
The
variables R, K and P are already defined, but we will need to estimate L, S and C, using the
following equations:
L
=
(
l
22
)
b
(1)
b
=
sin
θ
sin
θ
+ 0
.
269(
sin
θ
)
0
.
8
+ 0
.
05
(2)
So
b
= 0.36, and
L
= 2.14.
For slopes greater than 4 m long, and steepness less than 9% use equation 7.8a:
S
= 10
.
8
sin
θ
+ 0
.
03
(3)
So
S
= 0.46.
Answer:
The annual erosion from this hill slope is
29.87 Mg/ha
Part 2 - Impact of terracing on erosion {-}
In the second part of the problem, we consider the
same hill slope but with 24 m terraces. One of the effects of terraces is that the slope length is
shortened to the terrace spacing. This means that we need to recompute the L factor, though not
the b exponent since the angle of the overall slope does not change. Additionally the P factor will
change to reflect terracing.
So L = 1.03 for the terraced field.
Answer:
The annual erosion from the terraced hill slope is
4.75 Mg/ha
.
1
Question 2
Use the Forest Service Internet site (
forest.moscowfsl.wsu.edu/fswepp/
) to estimate the road
erosion and sediment delivery for a road located near Flagstaff, Arizona, for a graveled road segment
that is 250 m long, with a gradient of 5%, a 4-m long fillslope with a steepness of 50%, and a 35-m
long buffer with a steepness of 40%. The width of the road is 5 m and the soil is a sandy loam.
Compare the runoff and erosion from a rutted road to a road that is maintained to be outsloped.
Solution
Compare results: rutted, unmaintained road should have more erosion and more sediment leaving
the buffer. Actual numbers will depend on what parameters they picked for the final submission.
Two sample results are provided for reference.
Maintained Road
Rutted Road
2
Question 3
On a 60-m long slope, what is the relative difference in water erosion between slopes of 2 and 10%,
assuming other factors are constant (compare USLE equations and WEPP Internet interfaces;
milford.nserl.purdue.edu
)?
Solution
From USLE:
The factors L and S are affected when slope changes, but all other factors are constant.
Variable
Low Slope
High Slope
Comment
Slope Length
60 m
60 m
given
Slope (percent)
2
10
given
Slope (m/m)
0.02
0.10
converted from given slope
Slope Angle (rad)
0.020
0.100
computed from given slope
Slope Factor
0.246
1.172
From Eqn 7.8b or 7.8c depending on
slope angle
b
0.245
0.518
From Eqn 7.7b, assuming similar rill and
interrill erosion
Length Factor
1.278
1.682
From Eqn 7.7a
A (Mg/ha)
0.31
1.97
Assume all other factors = 1, since they
will not change
Change in erosion
∆
A = 1.66 increase ton/acre/year.
Answer:
So erosion increases by a factor of 6.4.
From WEPP
3
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Note:
Actual answer will vary based on what factors are selected for the base case, changing the
slope should lead to an increase in erosion.
Example for a 2% slope:
• Annual average soil loss = 0.7 ton/acre/year
Example for a 10% slope, all other factors stay the same:
4
• Total soil loss 1.3 ton/acre/year
Change in erosion
∆
A = 0.6 ton/acre/year.
Answer:
So erosion increases by a factor of 1.8.
5