Predicting Soil Erosion with Estimation of Saturated Hydraulic … · 2019. 10. 13. · World...

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( Received 20 September 2019; Accepted 12 October 2019; Date of Publication 13 October 2019 )

WSN 136 (2019) 194-225 EISSN 2392-2192

Predicting Soil Erosion with Estimation of Saturated Hydraulic Conductivity from Soil Porosity:

A Strategy for Meeting the SDG Goal Two and Six

M. S. Adiaha1,*, E. E. Oku2, V. O. Chude3, G. I. C. Nwaka2 and B. Ukem1

1Department of Planning, Research, Extension & Statistics, Nigeria Institute of Soil Science (NISS), 8 Abdullahi Ibrahim Street, Utako, Abuja, Nigeria

2Department of Soil Science, Faculty of Agriculture, University of Abuja, Along Airport Road, PMB 117, FCT, Abuja, Nigeria

3Nigeria Institute of Soil Science (NISS), 8 Abdullahi Ibrahim Street, Utako, Abuja, Nigeria

*E-mail address: [email protected] , [email protected]

ABSTRACT

For years now, the continual degradation of soils in the tropics, and around the globe has

continued to be one of the challenges facing humankind. Soil erosion is one of the factors gearing low

food production, environmental pollution and degradation, acting like an hindrance towards the

realization of the Sustainable Development Goals (SDGs) two (zero hunger) including SDG six (clean

water and sanitation). The importance of saturated hydraulic conductivity (Ks) of a soil to Agriculturist,

Environmentalist including Engineers cannot be exhausted, as this single hydro-physical soil property

controls many processes in the soil system. An experiment was conducted to access the vulnerability of

University of Abuja soils to erosion. Result of data analysis proves that the saturated hydraulic

conductivity of the soils is slow to extremely slow with value recorded at (0.89 – 4.50 mm hr-1). Field

data outcome presents a view that the soils of the area is mostly very compact to compact, with porosity

value ranging from (1 – 21%). Saturated hydraulic conductivity estimation was done using hydro-

physical models. The performance of the models were evaluated using Root Mean Square Error (RMSE)

statistics. Outcome of the model comparation proves the two model as been able to effectively estimate

the water flux of the area, presenting RMSE values at (5.67 and 2.41 respectively for the two models).

The study thus concluded that for loss of arable land to be minimized or avoided and for environmental

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World Scientific News 136 (2019) 194-225

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sustainability, ecological tool like planting of grasses including trees can be employed to salvage the

impending case of soil erosion in the area.

Keywords: SDG, Soil erosion, Hydraulic conductivity, Hydro-physical, Human development

1. INTRODUCTION

The continual decrease in soil productivity is a far cry to sustainable food production,

environmental development including economic sustainability. The SDG goal two (2) (zero

hunger) and goal six (6) (clean water and sanitation) is an important approach to follow for

humans to live productively and meet sustainability target.

Erosion has been described as one of the major cause of land degradation (Ahuju, 1973).

The impact of various forms of erosion has created a serious drawback to human survival, acting

like a hindrance to global development Najah, et al. (2009). Report of Ahuju, (1973) presented

a view that the total vegetated land area of the earth is about 11,500 hectare, of this about 14%

is degraded either by; water erosion, chemicals, wind erosion and other forms of physical

degradation. In most tropics water erosion is a major process of soil degradation (Ahuju, 1973).

Water erosion has been reported to have destroy many farmlands, apart from the huge

water contamination, inundation of materials and pollution of downstream due to the movement

of pollutant by the action of running water (Ahuju, 1973). Water erosion has been reported to

have destroyed soil structure, especially the functional topsoil and attributes of soil pores to

transmit and retain water, and to facilitate root growth (Najah, et al., 2009; Ahuju, 1973).

Climate, soil and topographic characteristics determine runoff and erosion potential from

agricultural lands (Ahuju, 1973; Oku et al., 2015). The main factors causing soil erosion is

divided into three groups: Thus:

a) Energy factors: Rainfall erosivity, runoff volume, wind strength, relief, slope angle,

slope length.

b) Protection factors: Population density, plant cover, amenity value (pressure for use) and

land management.

c) Resistance factors: soil erodibility, infiltration capacity and soil management.

The degree of soil erosion in a particular climate zone, with particular soils, landuse and

socioeconomic conditions will always result from a combination of the above mentioned

factors. It is not easy to isolate a single factor. Several report including the work of Oku et al.

(2015), Hume (1993) have presented soil hydrological and physical properties as been among

the determining factors to assess a soil or land for vulnerability to erosion. Their works further

stated that the physical properties of soils like its total porosity can determine to a large extent

the water intake or runoff on a particular soil. The deterioration of soil physical properties is

manifested though interrelated problems of surface sealing, crusting, soil compaction, poor

drainage, impeded root growth, excessive runoff and accelerated erosion (Ahuja et al., 1993,

2004; Najah, et al. (2009); Cresswell and Hamilton, 2002; Shanan et al., 1970). When an

unprotected soil surface is exposed to the direct impact of raindrops it can produce different

responses: production of smaller aggregate, dispersed particles, particles in suspension and

transfer and deposition of particles. When this has occurred, the material is reorganized at the


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location into a surface seal (Beven et al, 1993, Akamigbo, 1983; Najah, et al., 2009); Aggregate

breakdown under rainfall depends on soil strength and a certain threshold of kinetic energy is

needed to start detachment.

Several experiment including the work of Oku and Aiyelari (2011); Najah, et al. (2009)

have presented a view that a minimum of kinetic energy that comes with the drop of rain is

able to detach soil particle of about 0.125mm with particle between 0.063 to 0.250mm being

the most vulnerable to detachment by the action of rain-drop kinetic energy. This means that

soils with high content of particles into vulnerable range for example silty loam, fine sand and

sandy loam are the most susceptible soils to detachment. Many aspect of soils behavior in the

field such as hydraulic conductivity including soil compaction are influential factors towards

the severity of soil erosion. Saturated hydraulic conductivity (Ks) is one of the most important

hydrologic properties of soils. Information derived from a soil Ks is useful for hydrologist, water

resources engineers including environmental soil scientist. The soil Saturated hydraulic

conductivity information is used to estimate internal drainage of soils, used in liquid waste

management, for assessing non-point source pollution including estimation and evaluation of

soil /land vulnerability to erosion. Field determination of Saturated hydraulic conductivity from

soil morphological properties have as been encouraged by King and Franzmeier (1981), while

Ruiz and Utset (1992) noted that the major factor contributing to high Saturated hydraulic

conductivity value and which can be observed during routine field soil survey are abundant

biopores. Ruiz and Utset (1992) finding further stated that using morphological field

observation is more convenience in coarser than loamy fine and strong fine to medium blocky

structure. Still with this mere observation it is not always possible to effectively evaluate the

hydro-physical behavior of soils, and if done may lead to inconsistency and misleading

conclusion. Field determination of saturated hydraulic conductivity is time consuming,

laborious and in many situation facilities to aid this kind of experiment is limited, especially in

the poor resource countries. Oku et al. (2005); Hume (1993) also reported time consuming and

the problem of water scarcity, scarcity of apparatus and limited technical know-how as been

associated with the field determination of saturated hydraulic conductivity.

Building upon the problem associated with in-situ determination of saturated hydraulic

conductivity Suleiman and Ritchie (2001) proposed an alternative route in the estimation of

saturated hydraulic conductivity (Ks). Their work presented that saturated hydraulic

conductivity is directly linked with how compact or porous the soil is, thus presenting a view

that Saturated hydraulic conductivity can be derived from Effective Porosity (Ne) and Relative

Porosity (Ner), where both Ne and Ne can be estimated from the bulk density field value. Against

the rapid increase in the trend of soil degradation due to the action of erosion, and as a gear

towards realizing the goal three (3) and six (6) of the SGDs (Sustainable Development Goals)

this work emerges. This experiment seeks to estimate saturated hydraulic conductivity from

Field Capacity (volumetric moisture content), Ne and Ner and Total Porosity in-order to evaluate

the tendency of occurrence of destructive erosion in the soils of University of Abuja.

2. MATERIALS AND METHOD

2. 1. Study Area

University of Abuja lies at Latitude 8°.95' 43'' and Longitude is 7°.07'47''. University of

Abuja is located in sub-locality of Gwagwalada. Gwagwalada a times can record extreme


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maximum temperature which varies from 37 °C in the south west (Bida) to about 30 °C in the

north-east (Jos). The two distinct season within the zone are rainy and dry season. The parent

material of the area is characterized by the presence of stones, gravel with ironstone and sand

to loamy texture.

Map 1. Extrapolated map of Abuja from the map of Nigeria

2. 2. Field Investigation

Twenty (20) soil sample were collected using a standard soil core with length of 7 cm and

diameter of the core was calculated thus:

Volume of core = 𝜋𝑟2ℎ − − − − − − − − − − − − − − − − − 𝐸𝑞𝑛. 1

22

7× 3.5𝑐𝑚 × 7𝑐𝑚

= 3.143 × 12.25 cm × 7 cm

= 269.43cm3


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2. 3. Laboratory Analysis

2. 3. 1. Volumetric Moisture Analysis of Soil Sample

A know weight of moisture can was used to weigh each of soil sample collected at a

twenty (20) replicate sampling point. The moisture can was perforated at the base to aid

gravitational drain of free water. Initial weight was recorded for each of the 20 replication.

The can was immerse in water to saturation, this was done to all the 20 sites soil sample

inside the perforated can. The weight was taken 6 hours after immersion in water for 1 day of

drainage. At day 2 the weight of the set-up was also taken at 6 hours and same was done at day

3. The various weight taken represents the volumetric water content in the soil after free

gravitational drainage.

2. 3. 2. Bulk Density Determination

The moist soil from the field was weigh into a known weight moisture can and oven dried

at 115 °C. After which the soil sample was reweighed. The oven dried weight was divided by

the volume of the soil, thus;

𝐵𝑢𝑙𝑘 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 = 𝑃𝑏 = 𝑂𝑣𝑒𝑛 𝑑𝑟𝑦 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔)

𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑠𝑜𝑖𝑙 𝑐𝑚3− − − − − − − − − − − − − 𝐸𝑞𝑛. 2

= Pb (g/cm-3)

2. 3. 3. Determination of Total Porosity

𝑃 = 1 −𝑃𝑏

𝑃𝑠− − − − − − − − − − − − − − − 𝐸𝑞𝑛. 3

where

Ps = constant at 2.65 g/cm3

.

Figure 1. Soil sample collection using the soil core


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Figure 2. Oven-dried soil sample used for bulk density and Porosity determination

2. 3. 4. Determination of Effective Porosity (Ne)

Effective porosity according to the definition presented by Suleiman and Ritchie (2001)

is total porosity minus field capacity (FC), thus;

𝑇𝑜𝑡𝑎𝑙 𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦 − 𝐹𝐶 − − − − − − − − − − − − − − 𝐸𝑞𝑛. 4

2. 3. 5. Determination of Relative Porosity (Ner)

Relative Porosity as presented in the work of Kozeny-Carman, modified by Suleiman and

Ritchie (2001) is defined as Effective Porosity (Ne) divided by Field Capacity, thus;

𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦 = 𝑁𝑒

𝐹𝐶− − − − − − − − − − − 𝐸𝑞𝑛. 5

2. 3. 6. Estimating Saturated Hydraulic Conductivity from Total Porosity, Ne, Ner and

FC

Based on the relationship between saturated hydraulic conductivity (Ks) and effective

porosity (Ne) as developed in the a model by Ahuja et al. (1984) derived from the generalized

Kozeny-Carman equation; thus

𝐾𝑠 = 𝐵𝜙𝑒𝑥 − − − − − − − − − − − − (cm 𝑑−1 ) 𝐸𝑞𝑛. 6


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where:

B and x are empirical constant

[B = Intercept]

φe = total porosity-volumetric soil water content at field capacity [assumed to be the content at

a suction of 33Kpa]

Building upon the concept of Ahuja et al. (1984), Sulieman and Ritchie (2001) modified

the model of Ahuja et al. (1984) to fit into variation that may exist in an experiment, thus the

model;

𝐾𝑠 = 75 (𝜙𝑒𝑟)2 (𝑐𝑚𝑑−1) − − − − − − − − − − − 𝐸𝑞𝑛. 7

Was derived.

where

Ks = Saturated hydraulic Conductivity

75 = model constant

(φer)2 = total porosity – Volumetric moisture content at 1 day, 2 days and 3 days [taken at 6

hours after immersion in water, assume to be at 33 KPa]

3. RESULT AND DISCUSSION

3. 1. Estimation of Saturated Hydraulic Conductivity form Total Porosity

3. 1. 1. Determination of Volumetric water

From the model of Ahuja et al. (1984):

𝐾𝑠 = Β𝜙𝑒𝑥 − − − − − − − − − 𝐸𝑞𝑛. 8

Volumetric water analysis showed that (site 5) had the highest free gravitational drain, at

a value of 20.09 at day one (1) of free drain, this was followed closely by (site 3) was presented

a value at 19.57. The least observed free drainage was recorded in site 18 as presented in (Table

1). At day two (2) of free drainage site 5 also recorded a high value of 30.13 taken at an

atmospheric assumption of (33 kpa).

However, it was observed that at day 3 of free gravitational drainage that site 2 produce

value of 32.6, but with an overriding figure of 33.7 recorded for site 5 which stands over all

other sites free drain at 3 days of volumetric experiment. Findings of this experiment confirms

the study of Ahuja et al. (1984), which stated that free drainage due to gravity is continuous

until the soil reaches the point at which the force that holds the limited moisture in the soil

sample is higher than the force of free drainage, that at this point the soil reaches it volumetric

water threshold.

B = Intercept x = Slope

1.5737 2


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Table 1. Analysis of Volumetric Water Content, Total Porosity, Effective Porosity and

Relative Porosity.

(Volumetric Moisture

Content) (per days)

Tp-FC Ne/FC

Site

USDA

Textural

Class

vo

lum

etri

c so

il

mo

istu

re

con

ten

t R

atin

g

(at

33

KP

a)

φ φ2 φ3 FC mean

Total

Porosity

(%)

Effective

Porosity

(Ne)

Relative

Porosity

(Ner)

1 Loamy

Sand

15 to 25%

for sandy

soils

18.72 28.51 32.11 19.84 21 1.16 0.0585

2 Loamy

Sand

15 to 25%

for sandy

soils

19.29 28.39 31.99 19.92 25 5.08 0.255

3 Loamy

Sand

15 to 25%

for sandy

soils

19.57 28.25 31.85 19.92 17 2.92 0.1466

4 Sandy

Loam

15 to 25%

for sandy

soils

19.18 29.49 33.09 20.44 38 17.56 0.8591

5 Loam

35 to 45%

for loam

soils

20.09 30.13 33.73 20.99 38 17.01 0.8104

6 Sandy

Loam

15 to 25%

for sandy

soils

18.58 27.79 31.39 19.44 14 5.44 0.2798

7 Sandy

Loam

15 to 25%

for sandy

soils

19.76 29.3 32.9 20.49 9 11.49 0.5608

8 Loamy

Sand

15 to 25%

for sandy

soils

19.06 29.53 33.13 20.43 18 2.43 0.1189

9 Sandy

Loam

15 to 25%

for sandy

soils

19.77 29.07 32.67 20.38 22 1.62 0.0795

10 Sandy

Loam

15 to 25%

for sandy

soils

18.97 28.91 32.51 20.1 15 5.1 0.2537

1 Loamy

Sand

15 to 25%

for sandy

soils

19.12 28.57 32.17 19.97 35 15.03 0.7526


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12 Loamy

Sand

15 to 25%

for sandy

soils

19.43 28.65 32.25 20.08 17 3.08 0.1534

13 Sandy

Loam

15 to 25%

for sandy

soils

19.2 28.03 31.63 19.72 1 18.72 0.9493

14 Sandy

Loam

15 to 25%

for sandy

soils

19.16 29.05 32.65 20.22 7 13.22 0.6538

15 Sandy

Loam

15 to 25%

for sandy

soils

18.82 28.11 31.71 19.66 41 21.34 1.0855

16 Sandy

Loam

15 to 25%

for sandy

soils

18.96 28.35 31.95 19.82 18 1.82 0.0916

17 Loamy

Sand

15 to 25%

for sandy

soils

19.04 28.22 31.82 19.77 2 17.77 0.8988

18 Loam

35 to 45%

for loam

soils

17.73 27.56 31.16 19.11 13 6.11 0.3198

19 Sandy

Loam

15 to 25%

for sandy

soils

19.77 29.12 32.72 20.4 12 8.4 0.4118

20 Sandy

Loam

15 to 25%

for sandy

soils

18.96 29 32.6 20.14 14 6.14 0.3049

X 19.159 28.702 32.302 20.042 18.85 9.072 0.452

STD 0.503 0.629 0.629 0.411 11.244 6.573 0.328

CV (%) 3 2 2 2 60 72 73

SE 0.112 0.141 0.141 0.092 2.514 1.47 0.073

X = mean, SD = Standard deviation, CV = coefficient of variability, SE = Standard error,

FC = field capacity

3. 2. Determination of Effective Porosity (Ne)

Effective Porosity (Ne) has been defined as total porosity (TP) minus Filed Capacity (FC).

Value recorded for Effective Porosity (Ne) presented a view that site 13 has a high soil

compartment at a recorded value of (18.72%) which stands above all other sites. This was

closely followed by value of 17.77 observed for (site 17). Using the soil porosity ranking table,

it could be stated that site 1, 3, 8, 9, 12 and 16 soils is very compact. Site 4, site 2, 6, 18, 10, 19,


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20 soils is compact. Site 5, 7,11, 13, 14, 15, 17 soils is moderately porous. Based upon the fact

that soil porosity status gives the ability of water intake into the soil, it could be said that point

observed with high compaction could be an evidence for the low infiltration observed in some

of the sampled points. Findings observed in this experiment confirms the study of Oku et al.,

(2015) which stated soil compaction been a problem to soil water absorption in Northern Ghana.

Findings of this experiment also confirms the work of Suleiman and Ritchie (2001) which

presented soil effective porosity as been an indicator of soil-water flux, while acting as an

important parameter for estimating the saturated hydraulic conductivity in soils

3. 3. Determination of Relative Porosity (Ner)

Value observed for Relative Porosity (Ner) indicated that site 15 differed in the relative

porosity at a value of (1.0855) which stands over all other sites. Using the Porosity ranking as

presented by Pagliai (1988) it could be stated that all the sites are very compact since all the

values obtained for the Ner value is ˂5%. This view can be interpreted that for such location as

this, extensive ecological or engineering manipulation is required for sustainability of soils and

water resources. Findings obtained from the relative porosity calculation confirms the work of

Suleiman and Ritchie (2001), which stated that relative porosity is always a very detail survey

into the compactness of soils. Further, for such soil to be put into agricultural uses then proper

tillage is required. It could be also stated that for such soils to serve as a sponge or tank for

increase water intake then ecological remedy like planting of trees and grasses is of high

importance.

3. 4. Estimating Saturated Hydraulic Conductivity form Total Porosity

Applying the equation;

𝐾𝑠 = Β𝜙𝑒𝑥 (𝑐𝑚𝑑−1) − −𝐸𝑞𝑛. 7 and 𝐾𝑠 = 75 (𝜙𝑒𝑟) 2(𝑐𝑚𝑑−1) - - - - Eqn. 8

Saturated Hydraulic Conductivity was estimated.

3. 5. Relationship of saturated hydraulic conductivity (Ks) with 2 days relative effective

porosity (φer2), 3 days relative effective porosity (φer3), and relative effective porosity

(φer)

The data presented in (Figure 1) presented a strong correlation between saturated

hydraulic conductivity and relative effective porosity with a value of (1.0) which signifies a

strong linkage. Analysis of the estimation proves that there is a relationship between log (Ks )

and log (φer), this was observed as there was a high value (1.0 - 0.8 between Ks and relative

effective porosity), presenting a view that saturated hydraulic conductivity is greatly influenced

by the force to which a soil is able to transmit water down its profile. This force is evident in

the soil volumetric water content, especially for dry soils with less porosity value. The result of

this findings further presented a view that with the high value of r2 (1.0 - 0.8 respectively) a

good and strong relationship between Ks and relative effective porosity exist in the soils, and

can be stated that the relative effective porosity influences the flow of water into the soil profile,

thereby confirming the experiment of Suleiman and Ritchie (2001).


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Figure 1. Relationship of saturated hydraulic conductivity (Ks) with 2 days relative effective

porosity (φer2), 3 days relative effective porosity (φer3), and relative effective porosity (φer)

3. 6. Relationship of 2 d effective porosity (φer2) and 3 d effective Porosity (φer3) with

effective porosity (φe) of the Soils of University of Abuja

Figure 2. Relationship of 2 d effective porosity (φer2) and 3 d effective Porosity with effective

porosity (φer3) with effective porosity (φe) of University of Abuja Soils

y = 0,5x - 0,9375R² = 1

y = 0.0661x + 0.8513R² = 0.865

y = -0.0566x + 1.3143R² = 0.829

-0,2000

0,0000

0,2000

0,4000

0,6000

0,8000

1,0000

1,2000

1,4000

1,6000

0,0000 0,5000 1,0000 1,5000 2,0000 2,5000 3,0000 3,5000 4,0000 4,5000 5,0000

Log

Ks (c

m d

-1)

Log (φer, φer2, φer3)

Log φer Log φer2 Log φer3

Liniowy (Log φer) Liniowy (Log φer2) Liniowy (Log φer3)

φer2 or φer3 (cm 3 cm-3)

y = 1.164x - 0.0415

R² = 0.9809

φe (cm 3 cm-3)

y = 0.3551x + 3.9992R² = 0.1063

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30

φer

2o

r φ

er3

φe

φer3 φe Liniowy (φer3)Liniowy (φe) Liniowy (φe) Liniowy (φe)


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Analysis of data presented in (Figure 2) proofs that there exist a strong correlation (where

r2 = 0.9 and 0.10) between effective porosity at the different days of volumetric water content

in the soils, presenting a view that at 2 days of free drainage by gravity in soils, the threshold

to which the soil will hold water will be influential in estimation of water quantity by hydraulic

force, this view supports the work of Suleiman and Ritchie (2001).

3. 7. Relationship of 2 d relative effective Porosity (φer2) and 3 d Relative Effective

Porosity (φer3) with Relative Effective Porosity (φer) for Soil of University of Abuja

The relationship between φer2, φer3 and φer has been statistically proven to be of strong

correlation, presenting a value of (0.8809 and 0.1011 respectively), this gives an indication that

at 2 and 3 days relative effective porosity is influenced by its original first day of free gravitation

drain, which can adversely affect the modelling or estimation of saturated hydraulic conductive

from the relative effective porosity, this view is supported the wok of Suleiman and Ritchie

(2001). Further, experiment conducted by Oku et al. (2015) presented a view that with total

porosity of a soil, valid estimating of that soil bulk density is proven authoritative, and can be

used to make strong management policy regarding the useland decision on the soil in question.

Looking at the analysis outcome presented in (Figure 3) it could be said that φer2, φer3 and φer

intercepted at point (5.0) which strongly proves the work of Suleiman and Ritchie (2001) as

been valid regardless of soil type and locations. Thus this follows that for effective and accurate

computation of estimation of Saturated hydraulic conductivity (Ks) extensive observation of

free drainage is imperative, in addition to the inferred porosity from the determination of bulk

density, this view supports the work of Oyegun R. O (2010).

Figure 3. Relationship of 2 d relative effective Porosity (φer2) and 3 d Relative Effective

Porosity (φer3) with Relative Effective Porosity (φer) for Soil of University of Abuja

φer2 or φe3

y = 1.164x - 0.0415

R² = 0.8809

φer

y = 0.3494x + 4.1207

R² = 0.1011

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30

φer

2 o

r φ

e 3

φer

φer3 φer Liniowy (φer3) Liniowy (φer) Liniowy (φer)


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3. 8. Estimation of Saturated Hydraulic Conductivity form Total Porosity using equation

of Suleiman and Ritchie (2001)

Analysis of saturated hydraulic conductivity form the Total Porosity proves effective and

presents a reliable means of determining saturated hydraulic conductivity outside the in-situ

field determination, this view is validated by the data analysis as presented in (Figure 4 and

Table 1). It was observed that data obtained at day 1 of free drain was similar to the 3 days

drain, presenting a correlation co-efficient value of (r2 = 0.2108 for day 1 and day 3 respectively)

as presented in (Figure 4), presenting a view that the saturated hydraulic conductivity of the

area is constant, and that the model Ks = 75 (φ)2 (cmd-1) is able to effectively estimate the water

flux of the area, this finding supports the work of Suleiman and Ritchie (2001) who developed

the model. The outcome of this finding recorded similar water flux between day I and day 3 of

saturated hydraulic conductivity, which proves the steady state flow theory of Green and Ampt

(1911) as valid. The study further validates the experiment of Shrestha et al. (2008); Lal (1990)

including Oku et al. (2010) where their various experiment stated constant flow (steady state

flow) as water in soil reaches point of saturation. It could also be stated that at a certain threshold

in the soil the water constant keeps moving at points which the force of absorption and adhesion

is constant resulting in the steady water flux observed in this experiment, validating the work

of Ouyang et al. (2006).

Table 2. Estimation of Saturated Hydraulic Conductivity form Total Porosity using equation


Ks = 75 (φ)2 (cmd-1)

φer (K=75 *φ2 )

φer Log

φer φer2

Log

φer2 φer3

Log

φer3 75 * φ2

Log 75 *

φ2 75 *φ2

2 Log 75

*φ22

75

φ32

Log 75

*φ32

2.2

8

0.3

579

7.5

1

0.8

756

11

.11

1.0

457

38

9.8

8

2.5

909

42

30

.00

75

3.6

263

92

57

.40

75

3.9

665

5.7

1

0.7

566

3.3

9

0.5

302

6.9

9

0.8

445

24

45

.30

75

3.3

883

86

1.9

07

5

2.9

355

36

64

.50

75

3.5

64

2.5

7

0.4

099

11

.25

1.0

512

14

.85

1.1

717

49

5.3

67

5

2.6

949

94

92

.18

75

3.9

774

16

539

.187

5

4.2

185

18

.82

1.2

746

8.5

1

0.9

299

4.9

1

0.6

911

26

564

.43

4.4

243

54

31

.50

75

3.7

349

18

08

.10

75

3.2

572


-207-

17

.91

1.2

531

7.8

7

0.8

96

4.2

7

0.6

304

24

057

.607

5

4.3

813

46

45

.26

75

3.6

67

13

67

.46

75

3.1

359

4.5

8

0.6

609

13

.79

1.1

396

17

.39

1.2

403

15

73

.23

3.1

968

14

262

.307

5

4.1

542

22

680

.907

5

4.3

557

10

.76

1.0

318

20

.3

1.3

075

23

.9

1.3

784

86

83

.32

3.9

387

30

906

.75

4.4

901

42

840

.75

4.6

319

1.0

6

0.0

253

11

.53

1.0

618

15

.13

1.1

798

84

.27

1.9

257

99

70

.56

75

3.9

987

17

168

.767

5

4.2

347

2.2

3

0.3

483

7.0

7

0.8

494

10

.67

1.0

282

37

2.9

67

5

2.5

717

37

48

.86

75

3.5

739

85

38

.66

75

3.9

314

3.9

7

0.5

988

13

.91

1.1

433

17

.51

1.2

433

11

82

.06

75

3.0

726

14

511

.607

5

4.1

617

22

995

.007

5

4.3

616

15

.88

1.2

009

6.4

3

0.8

082

2.8

3

0.4

518

18

913

.08

4.2

768

31

00

.86

75

3.4

915

60

0.6

67

5

2.7

786

2.4

3

0.3

856

11

.65

1.0

663

15

.25

1.1

833

44

2.8

67

5

2.6

463

10

179

.187

5

4.0

077

17

442

.187

5

4.2

416

18

.2

1.2

601

27

.03

1.4

318

30

.63

1.4

861

24

843

4.3

952

54

796

.567

5

4.7

388

70

364

.767

5

4.8

474

12

.16

1.0

849

22

.05

1.3

434

25

.65

1.4

091

11

089

.92

4.0

449

36

465

.187

5

4.5

619

49

344

.187

5

4.6

932


-208-

22

.18

1.3

46

12

.89

1.1

103

9.2

9

0.9

68

36

896

.43

4.5

67

12

461

.407

5

4.0

956

64

72

.80

75

3.8

111

0.9

6

-0.0

17

7

10

.35

1.0

149

13

.95

1.1

446

69

.12

1.8

396

80

34

.18

75

3.9

049

14

595

.187

5

4.1

642

17

.04

1.2

315

26

.22

1.4

186

29

.82

1.4

745

21

777

.12

4.3

38

51

561

.63

4.7

123

66

692

.43

4.8

241

4.7

3

0.6

749

14

.56

1.1

632

18

.16

1.2

591

16

77

.96

75

3.2

248

15

899

.52

4.2

014

24

733

.92

4.3

933

7.7

7

0.8

904

17

.12

1.2

335

20

.72

1.3

164

45

27

.96

75

3.6

559

21

982

.08

4.3

421

32

198

.88

4.5

078

4.9

6

0.6

955

15

1.1

761

18

.6

1.2

695

18

45

.12

3.2

66

16

875

4.2

272

25

947

4.4

141

Figure 4. Estimation of Saturated Hydraulic Conductivity form Total Porosity using equation


Ks at day 1 free driany = 0.0543x + 3.501

R² = 0.2108

Ks at day 2 free drain

y = 0.0326x + 2.0522

R² = 0.192

Ks at day 3 free drain

y = 0.0543x + 1.8228

R² = 0.2108

0,0000

1,0000

2,0000

3,0000

4,0000

5,0000

6,0000

0 5 10 15 20 25

Ks

= 7

5 (

φ)2

(cm

d-1

)

Site of Investigation

Ks = 75 (φ)2 (cmd-1)

Log 75 *φ2 Log B x φe 2^ 2 Log B x φe3^ 2


-209-

3. 9. Estimation of Saturated Hydraulic Conductivity form Total Porosity using the

Generalized Equation of Kozeny-Carman as modified by Suleiman and Ritchie

(2001)

Data presented in (Figure 5) indicated that the equation Ks = Bφex is effective in estimating

the saturated hydraulic conductivity of the soil of University of Abuja, this was validated as the

r2 (coefficient of variation) value obtained at day 1 of free drainage, day 2 of free drainage and

day 3 of free drainage is closely related, thus: (0.2002, 0.3398 and 0.015 for day 1, 2 and 3

respectively). Although one may quickly noticed that the value slidely differed when compare

to the value of saturated hydraulic conductivity obtained using the equation: Ks = 75 (φ)2. The

outcome presented in this report agrees with the work of Ahuja et al. (1993) which stated

variation in the hydraulic behavior of soils at different locations. Sojka and Upchurch (1999);

Delgado and Lopez (1998); Larson and Larson (1988); Murphy et al.(1977b); Oku et al. (2015)

recorded similar experience in working in tropical soils, presenting a view that variation in soils

causes differences water flux.

Table 3. Estimation of Saturated Hydraulic Conductivity form Total Porosity using the

Generalized Equation of Kozeny-Carman as modified by Suleiman and Ritchie (2001)

Ks = Bφex

φe Ks

φe Log

φe φe2 Logφe2 φe3 Logφe3

B x

φe ^

2

Log B

x φe ^

2

B x

φe2 ^

2

Log B x

φe 2^ 2

B x φe3

^2

Log B x

φe3^ 2

2.2

8

0.3

579

7.5

1

0.8

756

11

.11

1.0

457

8.1

81

0.9

13

88

.757

1.9

48

19

4.2

45

1

2.2

884

5.7

1

0.7

566

3.3

9

0.5

302

6.9

9

0.8

445

51

.309

1.7

1

18

.085

1.2

57

76

.891

1

1.8

859

2.5

7

0.4

099

11

.25

1.0

512

14

.85

1.1

717

10

.394

1.0

17

19

9.1

71

2.2

99

34

7.0

36

3

2.5

404

17

.91

1.2

531

8.5

1

0.9

299

4.9

1

0.6

911

50

4.7

93

2.7

03

11

3.9

68

2.0

57

37

.938

9

1.5

791

17

.91

1.2

531

7.8

7

0.8

96

4.2

7

0.6

304

50

4.7

93

2.7

03

97

.47

1.9

89

28

.693

1

1.4

578


-210-

4.5

8

0.6

609

13

.79

1.1

396

17

.39

1.2

403

33

.011

1.5

19

29

9.2

61

2.4

76

47

5.9

05

9

2.6

775

10

.76

1.0

318

20

.3

1.3

075

23

.9

1.3

784

18

2.1

99

2.2

61

64

8.5

06

2.8

12

89

8.9

13

2

2.9

537

1.0

6

0.0

253

11

.53

1.0

618

15

.13

1.1

798

1.7

68

0.2

48

20

9.2

09

2.3

21

36

0.2

46

5

2.5

566

2.2

3

0.3

483

7.0

7

0.8

494

10

.67

1.0

282

7.8

26

0.8

94

78

.661

1.8

96

17

9.1

64

2.2

533

3.9

7

0.5

988

13

.91

1.1

433

17

.51

1.2

433

24

.803

1.3

95

30

4.4

92

2.4

84

48

2.4

96

6

2.6

835

15

.88

1.2

009

6.4

3

0.8

082

2.8

3

0.4

518

39

6.8

47

2.5

99

65

.064

1.8

13

12

.603

6

1.1

005

2.4

3

0.3

856

11

.65

1.0

663

15

.25

1.1

833

9.2

93

0.9

68

21

3.5

86

2.3

3

36

5.9

83

6

2.5

635

18

.2

1.2

601

27

.03

1.4

318

30

.63

1.4

861

52

1.2

72

2.7

17

11

49

.77

8

3.0

61

14

76

.44

05

3.1

692

12

.16

1.0

849

22

.05

1.3

434

25

.65

1.4

091

23

2.6

96

2.3

67

76

5.1

37

2.8

84

10

35

.37

26

3.0

151

22

.18

1.3

46

12

.89

1.1

103

9.2

9

0.9

68

77

4.1

85

2.8

89

26

1.4

74

2.4

17

13

5.8

16

8

2.1

33

0.9

6

-0.0

17

7

10

.35

1.0

149

13

.95

1.1

446

1.4

5

0.1

61

16

8.5

79

2.2

27

30

6.2

46

2.4

861


-211-

17

.04

1.2

315

26

.22

1.4

186

29

.82

1.4

745

45

6.9

42

2.6

6

10

81

.9

3.0

34

13

99

.38

5

3.1

459

4.7

3

0.6

749

14

.56

1.1

632

18

.16

1.2

591

35

.208

1.5

47

33

3.6

14

2.5

23

51

8.9

83

6

2.7

152

7.7

7

0.8

904

17

.12

1.2

335

20

.72

1.3

164

95

.009

1.9

78

46

1.2

43

2.6

64

67

5.6

18

4

2.8

297

4.9

6

0.6

955

15

1.1

761

18

.6

1.2

695

38

.716

1.5

88

35

4.0

83

2.5

49

54

4.4

37

3

2.7

359

Figure 5. Estimation of Saturated Hydraulic Conductivity form Total Porosity using the

Generalized Equation of Kozeny-Carman as modified by Suleiman and Ritchie (2001)

3. 9. 1. Root Mean Square Error (RMSE)

Result analysis output from Suleiman and Ritchie (2001) model and Ahuja et al. (1984)

model was compared using RMSE (Root Mean Square Error), is presented in (Figure 6 and

7).

Ks = Bφex at day 3 of free drain

y = 0.0178x + 1.555

R² = 0.0151


y = 0.0438x + 1.8916

R² = 0.3398


y = 0.0427x + 1.9902

R² = 0.2002

0,0000

0,5000

1,0000

1,5000

2,0000

2,5000

3,0000

3,5000

0 5 10 15 20 25

Ks=

Bφ

ex

Site of Investigation

Ks = Bφex (cm3cm-3)

Log B x φe ^ 2 Log B x φe 2^ 2 Log B x φe3^ 2


-212-

Figure 6. Root Mean Square Error (RMSE) analysis using Suleiman and Ritchie (2001)

model

Figure 7. Root Mean Square Error (RMSE) analysis using Ahuja et al. (1984) model

K=75 *φ2

y = -0.1118x - 10.462R² = 0.0157

K=75 *φ32

y = -0.3206x - 11.986R² = 0.3327

K=75 *φ22

y = -0.3235x - 12.732R² = 0.2175

-25,00

-20,00

-15,00

-10,00

-5,00

0,00

0 5 10 15 20 25

RM

SE

val

ue

No of site of field observation

RMSE Comparation between field data and model output for Suleiman and Ritchie Ks

model

RMSE K=75 *φ2 RMSE K=75 *φ22 RMSE K=75 *φ32

Ks=Bφexy = -0.0556x - 2.3726

R² = 0.0182

Ks=Bφexy = -0.1735x - 2.8213

R² = 0.3236

Ks=Bφexy = -0.1802x - 3.2364

R² = 0.2303

-9,0000

-8,0000

-7,0000

-6,0000

-5,0000

-4,0000

-3,0000

-2,0000

-1,0000

0,0000

0 5 10 15 20 25

RM

SE

val

ue

No of site of field observation

RMSE Comparation between field data and model output for Kozeny-Carman Ks model

Log B x φe ^ 2 Log B x φe2^ 2 Log B x φe3 ^ 2

Liniowy (Log B x φe ^ 2) Liniowy (Log B x φe2^ 2) Liniowy (Log B x φe3 ^ 2)


-213-

Table 4. RMSE Comperation of the strength to estimate Ks of the two model used.

Model RMSE from Expected and observed

value

Ks = 75φ2 5.67

Ks = Bφex 2.41

Ks = saturated hydraulic conductivity

Outcome of the RMSE analysis proves that the model Ks = Bφex produced small value of

RMSE which validated this experiment, and further confirms the experiment of Ahuja et al.

(1984) which stated that the model can effectively estimate Ks behavior of soils.

However, it could be stated that though the RMSE value obtained for Ks = Bφex (Ahuja et

al., 1984) model gave a small RMSE value. Model built by Suleiman and Ritchie (2001) (Ks =

75φ2) also effectively estimated the Ks of the soils, presenting a value of (5.67). Thus it could

be stated that the two model productively estimated the saturated hydraulic conductivity of the

soils of University of Abuja.

3. 9. 2. Raking of the Saturated Hydraulic Conductivity of University of Abuja Soils to

Predict Erosion and other Land disturbances

Result of the model analysis of the estimated saturated hydraulic Conductivity was rated

with a standardized value of saturated hydraulic Conductivity as presented in (Table 5)

Table 5. Water transmission ability of soils of University of Abuja.

Saturated hydraulic

Conductivity (mm hr-1) *Rating *Interpretation

< 0.5 Extremely slow Liable to water log

0.7-7 Very slow

Poor infiltration may cause

overland flow, flood under

rainfall

7.75-8.18 Slow Poor infiltration

Source: *Hazelton and Murphy (2007)


-214-

Table 6. Ks Value for 1 day of free gravitational drain using Ks = Bφex for

University of Abuja Soils.

Ks Value for 1 day of free gravitational drain using Ks = Bφex

Site Ks

Value

Interpretation

Rating Problem associated with the site

1 0.9128 Very slow Poor infiltration may cause overland and erosional flow, flood

under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall

8 0.2475 Extremely

slow Liable to water logging


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall

16 0.1615 Extremely

slow Liable to water logging


under rainfall


under rainfall


-215-


under rainfall


under rainfall





Site Ks

Value

Interpretation



under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


-216-


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall





Site Ks

Value

Interpretation



under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


-217-


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


Table 9. Ks Value for 1 day of free gravitational drain using Ks = 75 (φer)2 for


Ks Value for 1 day of free gravitational drain using Ks = 75 (φer)2

Site Ks

Value

Interpretation



under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


-218-


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall




Ks Value for 2 day of free gravitational drain using Ks = 75 (φer)2

Site Ks Value Interpretation

Rating

Problem associated with

the site

1 3.6263 Very slow

Poor infiltration may

cause overland and

erosional flow, flood

under rainfall


-219-

2 2.9355 Very slow


cause overland and


under rainfall

3 3.9774 Very slow


cause overland and


under rainfall

4 3.7349 Very slow


cause overland and


under rainfall

5 3.6670 Very slow


cause overland and


under rainfall

6 4.1542 Very slow


cause overland and


under rainfall

7 4.4901 Very slow


cause overland and


under rainfall

8 3.9987 Very slow


cause overland and


under rainfall

9 3.5739 Very slow


cause overland and


under rainfall

10 4.1617 Very slow


cause overland and


under rainfall

11 3.4915 Very slow


cause overland and


under rainfall

12 4.0077 Very slow


cause overland and


under rainfall

13 4.7388 Very slow Poor infiltration may

cause overland and


-220-


under rainfall

14 4.5619 Very slow


cause overland and


under rainfall

15 4.0956 Very slow


cause overland and


under rainfall

16 3.9049 Very slow


cause overland and


under rainfall

17 4.7123 Very slow


cause overland and


under rainfall

18 4.2014 Very slow


cause overland and


under rainfall

19 4.3421 Very slow


cause overland and


under rainfall

20 4.2272 Very slow


cause overland and


under rainfall




Ks Value for 3 day of free gravutatioanl drain using Ks = 75 (φer)2

Site Ks

Value

Interpretation



under rainfall


under rainfall


-221-


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


under rainfall


Table 12. Soil Analysis of the Physical and hydrological Properties affecting Ks

Site Bulk density

(gcm-1) Porosity (%)

USDA Textural

Class

1 2.1 21 Loamy Sand


-222-

2 2 25 Sand

3 2.19 17 Sand

4 1.64 38 Loamy Sand



7 2.41 9 Sandy Loam




1 1.73 35 Sand





16 2.18 18 Sandy Loam


18 2.31 13 Sandy Loam



Outcome of the estimated saturated hydraulic conductivity presented a view that the soil

has a slow to extremely slow hydraulic conductivity rate, this outcome confirms the work of

Oku et al., (2010) who reported slow hydraulic conductivity rate on most tropical soils with

low porosity rate. Experiment of Ahmed and Duru (1985) also validate this experiment where

the Scientist reported poor hydraulic conductivity rate in soils of Nigeria due to physical and

hydro-physical limitations, especially the low porosity and high bulk density values in addition

to surface sealing due to human, animal and machinery traffic. Building upon the hydro-

physical behavior of the soils of University of Abuja, it could be stated that the soils are

vulnerable to erosion, as almost all the investigated sites showed a slow to extremely slow

hydraulic conductivity rating, this outcome further validates the experiment of Lal (1989); Lal,

et al., (1989); Mbagwu (1989); Mbagwu (1989 b); Kureve (1995) who reported poor water

intake characteristics of savanna soils. Thus, presenting a view that the soils of University of


-223-

Abuja is physical and hydrologically weak in its water transmissivity status, which could

influence rapid and severe erosion cases in the area.

4. CONCLUSION AND RECOMMENDATION

Following the outcome of the ability of the two model used in the study to estimate the

saturated hydraulic conductivity (Ks) behavior of the University of Abuja soils, and further

rating, which presented the soils of the area to be slow to extremely slow in water (moisture)

transmissivity through its profile, it is thereby concluded that the soils of University of Abuja

is physically and hydro-physically sick and stands a chance of been affected by serve erosion

including flooding. This work hereby recommends that the areas (points) investigated should

be put into agroforestry or planted or replanted to grasses (vetiver grass) or any vegetation

cover, as this could serve as an ecological tool to salvage the impending severe erosion case.

These stated remedy could go a long way in improving crop production including creating good

area sanitation which stands as a sustainable approach towards environmental protection and

food security.

Acknowledgment

This work was supported by Prof. (Dr.) Effiom E. Oku, with facilities and laboratory for field investigation

provided by the Department of Soil Science, University of Abuja.

The Nigeria Institute of Soil Science (NISS) provided the internet facilities which aided the literature survey and

type-setting of this experimental report through Prof (Dr.) V. O. Chude.

Prof. G. 1. C Nwaka provided a geo-technical flow and direction on the use of the study area map including

interpretation of the terrain of University of Abuja. Prof. (Dr.) Ewa Ubi was contacted for statistical flow and

presentation.

References

[1] Ahmed, A and Duru, J. O (1985). Predicting infiltration rates and Determing hydrologic

grouping of soils near Samaru, Kaduna State. Nigeria. Samaru Journal of Agricultural

Research 13 (1 &2), 51-60.

[2] Lal, R. (1990). Tropical Soil Distribution Properties and Management. Resource

Management and Optimization Vol. (7), 39-52.

[3] Najah, A., Elshafie, A., Karima, O.A. and Jaffar, O. (2009). Prediction of Johor river

water quality parameters using artificial neural networks. European Journal of Science

Research 28(3), 422-435.

[4] Oku, E and Aiyelari, A. (2011). Predictability of Philip and Kostiakov Infiltration

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