Investigation of Geotechnical Parameters of Sandstone in Banda, Kogi State, Nigeria Using Regression

www.mwe‐journal.org Journal of Mining World Express, Volume 3 2014 doi: 10.14355/mwe.2014.0302.03

Investigation of Geotechnical Parameters of Sandstone in Banda, Kogi State, Nigeria Using Regression Model LAWAL, Abiodun Ismail*1 and ANIKOH, Godwin Ateiza2 Department of Mining Engineering, the Federal University Technology, Akure, Ondo State, Nigeria Department of Mineral Resources, Kogi State Ministry of Science and Technology, Lokoja, Nigeria

1 2

E‐mail: abiodunismail18@yahoo.com; anikohgodwin@yahoo.com

Received 21 November 2013; Accepted 10 December 2013; Published 16 April 2014 © 2014 Science and Engineering Publishing Company

Abstract The study investigated geotechnical parameters of sandstone in Banda, Kogi State, Nigeria using regression model. To achieve the set objectives, in‐ situ tests were carried out by Schmidt hammer and laboratory tests were conducted on the sandstone samples collected from the study area. Five rock samples were prepared for the determination of density and porosity. The results obtained from the Schmidt hammer tests and those of density determined from laboratory tests were used to estimate the uniaxial compressive strength of the investigated rock. Point load index and tensile strength were determined from the laboratory tests and the relationship established by Brook, (1993) respectively. The results of the analyses reveal that the average density of sandstones is 2.08 g/cm3, the average porosity of the tested sandstones is 13.0% while the average uniaxial compressive strength value is 26.3 MPa. The average point load index and that of the tensile strength value are 1.17 MPa and 1.76 MPa respectively. The determined density, porosity, uniaxial compressive strength, point load index and tensile strength were analyzed statistically. From the statistical analysis mathematical models were established. The regression coefficients obtained from the analysis show that there are strong relationships between the physical and mechanical properties of sandstone.

Keywords In Situ Test; Geotechnical Parameters; Regression Coefficient; Mathematical Models; Density; Porosity; Mmechanical Properties

Introduction Rocks are important geotechnical materials that have been found usage in virtually all aspects of human’s technological development. Rocks form the essential part of the earth crust. They are usually discontinuous, inhomogeneous, anisotropic and non‐elastic (Saliu and

Akande, 2011). Sandstone is a sedimentary rock composed of sand‐sized grains of quartz and feldspar.

The spaces between grains may be empty or filled with either a chemical cement of silica or calcium carbonate or a fine‐grained matrix of silt and clay particles (Pettijohn, 2002). Sandstones often form in layers in environments where large amounts of sands can accumulate as beaches, deserts, flood plains, or deltas. Sandstone forms when sand is buried under successive layers of sediment (Scholle and Spearing, 1982). During burial the sand is compacted, and a binding agent such as quartz, calcite, or iron oxide is precipitated from ground water which moves through passageways between grains. Sandstones grade upward in grain size into conglomerates and breccias; they grade downward in size into siltstones and shales.

When the proportion of fossil fragments or carbonate grains is greater than 50%, sandstones grade into clastic limestones. Sandstones are often used as building stones, and have importance to geologists as indicators of erosional and depositional processes (Dottʹs, 1996). Definitely physical and mechanical properties of sandstone have direct impact on its permanence as building materials. The properties like density, porosity, Rebound hardness value, uniaxial compressive strength, point load index, and tensile strength. These various measures were then correlated to see what influence, if any, one property had on another. Those properties which had the most significant influence upon others were considered the most useful index properties as far as sandstones were concerned and could perhaps be used as a basis of an engineering classification of such rocks.

According to Hudson (1991), rock presents the designer the unique problems, unlike other

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engineering material. First of all, rock is a complex material varying widely in its properties and in most mining as well as Civil Engineering situations, not one but a number of rock types will be presented. Each rock formation has a unique feature that does not bear the imprints of its geological history but also controls the future behavior in engineering works.

using regression applications.

models

for

its

engineering

Geology of Kogi State The geological setting of Kogi State is unique for having the three major Nigerian geological formations; the basement complex (Precambrian and Upper Paleozoic), sedimentary basins and volcanic rock, the younger Granite. Half of the State (Western Flank) is covered by crystalline basement complex formation and older/younger granite province, While the remaining half (Easter Flank) is of sedimentary Formation with cretaceous to recent sediments. The Western Flank of the state West and central senatorial Districts is majorly underlain by crystalline basement and Ancient hard rocks. This formation is made up of gneiss, migmatite (crystalline basement rocks) schist’s, quartzite’s, marble and calc‐silicate (older meta‐ sediments) as well as the Pan African granite/older granites. This basement rocks contained some economic minerals such as iron ore, gemstone, quartz, feldspar and other associated minerals of economic resource such as cassiterite, tantalite, columbite, gemstones other related minerals are contained in the Pan‐African granite/older granite.

The performance of any rock under the action of load, water, and temperature and tectonic of the earth crust depends on the physical and mechanical properties (strength) of those materials. Application of rock mechanics principles in Mining Engineering therefore involves the selection of a tentative design and prediction of expected behavior. Hence, the validity of this prediction not greater than the validity of the physical and mechanical properties which is used (Cristescu and Hunsche, 1998). Daemen (1983) stated that comparative analysis of rocks properties involves thorough, detailed and comprehensive examination of already determined value for the properties of the rocks under consideration. Mathematical techniques such as correlation and regression play a very vital role in this analysis. This research work therefore investigates the geotechnical parameters of sandstone

FIG. 1 GEOLOGICAL MAP OF THE STUDY AREA

Banda Sandstone

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The eastern part of the state is on alluvium and is made up of the younger and most recent sedimentary formation as well as others sedimentary rocks forming part of the Nigerian cretaceous to recent sediments.

The geological setting of this flank is similar to that of Lower Benue trough in the South of Benue river. It is principally made up of different formations: Mamu, Ajali and Nsukka. These formations are normally interbedded with siltstones, carboniferous shale’s, coal, sandstones (of fluvial marine nature with distinct cross beddings) and laterite. The formations control the localization of economic minerals such as coal, kaolin, clay, sandstones, limestone, slate, gemstones, phosphate and other associated sedimentary minerals (Ayodele, 2010). Fig. 1 shows the geological map of the study. Banda is in Lokoja Local Government Area of the western flank of Kogi State, Nigeria. The town is located at 006045ʹE longitude and 07051ʹN latitude. The altitude of Banda is between 62m and 85m above sea level.

Determination of Porosity of Sandstone A representative sample comprising at least 5 lumps of irregular geometry, each having either a mass of 50g was used. The sample was saturated by water immersion in a bath with periodic agitation to remove trapped air. Its saturated‐submerged mass Msub was determined to accuracy of 0.1g.

The sample container with its lid was cleaned and dried, and it Mass A was determined. The sample was removed from the immersion bath and surface‐dried with a moist cloth, care being taken to remove only surface water and to ensure that no rock fragments were lost. The sample was transferred to the sample container, the lid replaced, and the Mass B of saturated‐surface dry sample plus container was determined.

The lid removed and the sample dried to constant mass at a temperature of 105OC, the lid replaced and the sample allowed to cool for 30 minute in a dessciator. The Mass C of oven‐dry sample plus container was measured.

Materials and Methods Sample Descriptions and Preparation

Then, saturated‐surface dry mass;

Five sandstone samples were collected from Banda in western part of Kogi State, Nigeria at various locations to ensure the representativeness of the rock. The samples were labelled Sand1, Sand2, Sand3, Sand4, and Sand5. GPS was used to record the coordinate of the locations where samples were taken. The samples for the density, porosity and point load tests were prepared in an irregular form and the preparation was carried out in accordance with the standard suggested

by ISRM (1981) and conforms to ASTM (1994).

M sat  B  A Grain weight M s  C  A Pore Volume

V  (V2  V1 )cm 3 . Then, the density was calculated

from Equation 1.

where M is mass in g and volume in cm3.

40

(3)

Hardness test involves the use of Schmidt Impact Hammer of type L for the hardness determination of in situ rock. The rebound value of the Schmidt Hammer is used as an index value for the intact strength of rock material, but it is also used to give an indication of the compressive strength of rock material (ISRM, 1981). The relationship established by Deere and Miller (1966) was used to estimate uniaxial compressive strength in this work because of its universal acceptability. Its application involves interpolating the value of density and average Schmidt hammer values of each sample (sandstone) on the chart to obtain the equivalent uniaxial compressive strength.

The change in volume was calculated as

w

Hardness Test

A Bouyancy and saturation technique was employed in the determination of density of sandstone, five samples weighed and recorded. Water was poured inside the cylinder and the volume were noted as V1 (cm3) and the sample was dropped in the water in the cylinder and the volume were recorded as V2 (cm3).

M sat  M s (2)

Porosity,   100Vv % V

Determination of Density of Sandstone

  M V ( g / cm 3 )

Vv 

(1)

V is the change in

The standard method for the Schmidt Hammer test as described by ISRM (1981) and ASTM (1994) was

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To  1.5 I s ( 50 )

followed. The measured test values were ordered in descending order. The lower 50% of the values were discarded and the upper 50% values were averaged to obtain the Schmidt Rebound Hardness (ISRM, 1981).

The result of the density of sandstones determined from the laboratory is shown in Table 1.

This test is intended to determine point load strength of an irregular sandstone rock samples.

TABLE 1 THE DENSITY OF SANDSTONES

Procedure

Rock Description

Weight (g)

Initial vol (cm3)

Final vol. (cm3)

Change in Volume (cm3)

Density (g/cm3)

Sand1

18.30

160

170

10

1.83

Sand2

18.30

170

180

10

1.83

Sand3

18.96

130

138

8

2.08

Sand4

22.30

160

170

10

2.23

Sand5

24.20

160

170

10

2.42

(i) The irregular sample was prepared. (ii) The sample width was measured with veneer calliper. (iii) The specimen was placed between the platen point in a way to allow at least 0.5 the diameter and the distance between the platens was measured.

Average

TABLE 2 POROSITY OF SANDSTONES

(v) The maximum load achieved was recorded. (vi) The pressures released valve was opened and manually forced the lower platen down to allow the next specimen to be tested. The same procedures were followed on other samples.

Calculation The calculation was carried out by using uncorrected point load test method.

(4)

diameter.

V cm

V cm

Sand1

20

2.8

14.0

Sand2

20

2.6

13.0

Sand3

20

2.6

13.0

Sand4

20

2.5

12.5

Sand5

20

2.5

12.5

Average

13.0

0.45

(5)

(6)

TABLE 3 THE UNIAXIAL COMPRESSIVE STRENGTH ESTIMATED FROM SCHMIDT HARDNESS VALUE STRENGTH OF SANDSTONES SCHMIDT Rock HARDNESS UCS Rock Description VALUES (MPa) Classification* SANDSTONE

F is the correction factor.

I s ( 50 )  FI s

Porosity %

Rock Description

Tables 3, 4 and 5 show the results of uniaxial compressive strength of sandstone estimated from Schmidt hardness values, point load index of sandstone obtained from laboratory and tensile strength respectively.

where P is the failure load and De is the equivalent

D  F  e   50 

2.08

The result of porosity of sandstone determined from the laboratory is shown in TABLE 2.

(iv) The lower platen was raised into firm contact with the specimen using the pump.

De2

(7)

Results

Point Load Strength Index

Is  P

where I s ( 50 ) is the corrected point load strength index.

Tensile Strength The mathematical model suggested by Brook (1993) and ISRM (1989) was used to estimate the tensile strength (To) from the determined point load strength (Is(50)) as shown in Equation 7.

Sand1

20.0

24.0

high strength

Sand2

21.7

24.9

high strength

Sand3

21.0

24.9

high strength

Sand4

23.7

27.1

high strength

Sand5

22.1

30.3

high strength

AVERAGE

21.7

26.3

* Broch and Franklin (1972)

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TABLE 4 THE POINT LOAD S INDEX OF SANDSTONE

Rock Description

Diameter ,De (mm)

Equivalent Diameter,De2 (mm)

Area (mm2)

Failure load (kN)

Point load Strength Index IS (MPa)

Size Correction Factor

Standard strength Index IS(50) (MPa)

Sand1

8.55

73.10

57.42

0.15

2.05

0.45

0.92

Sand2

5.75

33.06

25.97

0.10

3.02

0.38

1.15

Sand3

8.87

78.68

61.80

0.12

1.53

0.46

0.70

Sand4 Sand5

5.85 5.85

34.22 34.22

26.88 26.88

0.14 0.14

4.09 4.09

0.38 0.38

1.55 1.55

Medium strength high strength Medium strength high strength high strength

AVG.

2.96

1.17

High strength

Rock Classification*

*Broch and Franklin (1972)

TABLE 5 TENSILE STRENGTH OF SANDSTONE Rock Description Sand1 Sand2 Sand3 Sand4 Sand5 *Broch and Franklin (1972)

Tensile Strength (MPa) 1.38 1.73 1.05 2.33 2.33

Discussion

Tables 6, 7 and 8 show the results of models developed using SPSS software.

Table 1 shows the result of density of sandstone determined from laboratory test with the values ranging from 1.83 g/cm3 to 2.42 g/cm3. The result of porosity of Sandstones determined from the laboratory is shown in Table 2 the values range from 14% to 12.5%. Table 3 shows the result of uniaxial compressive strength of sandstone, the value ranges from 24.0 MPa to 30.4 MPa. The uniaxial compressive strength of sandstones falls within the range of high strength (Broch and Franklin, 1972). Table 4 shows the result of point load test of sandstones, the value ranges from 0.70 MPa and 1.55 MPa. Table 5 shows the result of tensile strength of sandstone, the value ranges from 1.05 MPa to 2.33 MPa. The point load index values and tensile strength also fall within the range of medium to high strength according to Broch and Franklin (1972) classification.

TABLE 6 MODEL COMPUTATION FOR SANDSTONES (DEPENDENT VARIABLE IS THE UNIAXIAL COMPRESSIVE STRENGTH) Model

B

constant Density Porosity Rebound Hardness

17.522 8.466 ‐0.524 ‐0.095

Std. Error 87.953 6.314 4.133 1.434

Beta

t

Sig

0.854 ‐0.126 ‐0.051

0.199 1.341 ‐0.127 ‐0.066

0.875 0.408 0.920 0.958

TABLE 7 MODEL COMPUTATION FOR SANDSTONE (DEPENDENT VARIABLE IS THE POINT LOAD INDEX) Model

B

Constant Density Porosity Rebound Hardness

‐10.451 0.717 0.333 0.267

Std. Error 17.813 1.279 0.837 0.290

Beta

t

Sig

0.486 0.540 0.900

‐0.587 0.561 0.398 0.920

0.662 0.675 0.759 0.526

Statistical models were generated to relate the mechanical properties with the physical properties.

The results of models revealed that as the uniaxial compressive strength of sandstones increases density and porosity decreases while rebound hardness value decreases (Equation 4), as the point load index of sandstone increases with both density and porosity while decreases with rebound hardness value.

(Equation 5), as tensile strength decreases density of sandstones increases while porosity and rebound hardness value increases (Equation 6).

TABLE 8 MODEL COMPUTATION FOR SANDSTONE (DEPENDENT VARIABLE IS THE TENSILE STRENGTH) Model

B

Constant Density Porosity Rebound Hardness

‐15.659 1.072 0.498 0.402

42

Std. Error 26.859 1.928 1.262 0.402

Beta

t

Sig

0.483 0.535 0.969

‐0.583 0.556 0.394 0.918

0.664 0.677 0.761 0.527

Rock Classification* High strength High strength High strength High strength High strength

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UCS I T

17.522

8.466ρ

10.451 15.659

0.524

0.717ρ

1.072ρ

0.333

0.498

0.0958RH

TABLE 9 VALUES OBTAINED BEFORE AND AFTER VALIDATION OF THE MODELS

(4)

0.267RH (5) 0.402RH

UCS(MPa) Before using the models 24.0 24.9 24.9 27.1 30.3

(6)

where UCS is the uniaxial compressive strength in MPa, I is the point load MPa, T , is the tensile strength in MPa ρ is the density in g/cm3, is the porosity in %,and RH is the rebound hardness value.

Model Validation The models were validated by using data obtained from the laboratory analyses and in situ tests. The results revealed that the developed mathematical models can be used to determine mechanical properties of sandstones or that of any rock having similar properties.

After using the models 23.76 24.12 26.31 27.58 29.34

IS(50) (MPa) Before using the models 0.92 1.15 0.70 1.55 1.55

After using the models 0.86 0.98 0.98 1.64 1.35

Ts (MPa) Before using the models 1.38 1.73 1.05 2.33 2.33

After using the models 1.32 1.50 1.49 2.48 2.04

Graphical Representation of the Statistical Models The determined mechanical properties were also correlated with the regression standardized predicted value as shown in Figures 2 to 4. The positive linear relationship exists between them. The coefficients of the correlations (R2) indicate strong relationships between them.

Table 9 shows the results obtained before using the models and after using the models.

UCS

17.522

8.466ρ

0.524

0.0958RH

FIGURE 2 RELATIONSHIP BETWEEN UNIAXIAL COMPRESSIVE STRENGTH AND REGRESSION STANDARDIZED VALUE

I

10.451

0.717ρ

0.333

0.267RH

FIGURE 3 RELATIONSHIP BETWEEN POINT LOAD STRENGTH INDEX AND REGRESSION STANDARDIZED VALUE

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T

15.659

1.072ρ

0.498

0.402RH

FIGURE 4 RELATIONSHIP BETWEEN TENSILE STRENGTH AND REGRESSION STANDARDIZED VALUE

Engineering Geology, 81 (2005), Elsivier International,

Conclusions

pp. 1‐14

This research work analyzed the determination of physical and mechanical properties of sandstones in Kogi state using developed models. The research was conducted through field work and laboratory tests.

The results of the analyses revealed that the average density of is 2.08 g/cm3 and the average porosity of is 13.0%. The average uniaxial compressive strength value of is 26.3MPa. While the average point load index value of is 1.17 MPa and the average tensile strength value of is 1.76MPa. The uniaxial strength of the rock falls in the range of high strength according to Bell (1992) classification. The point load and tensile strength also fall in the range of high strength according to Broch and Franklin (1972) classification.

The sandstone from Kogi State therefore, has good engineering properties.

Bell, F. G. (1992): Engineering in Rock Masses Butterworth – Heinemann, Jordan Hill, Oxford p.58 Broch, E. and Franklin, J. A. (1972): The Point Load Test, Int. J. Rock Mech. in. Sci. (9) p 63.

Brook, N. (1993): The Measurement and Estimation of Basic

Rock

Strength.

Rock

Testing

and

Site

Characterization‐Compressive. Rock Engineering, Ed: J.A.Hudson, 3, pp 41‐66.

Cristescu N. D. and Hunsche U. (1998): Time Effects in Rock Mechanics. Wiley, New York, 342pp.

Daemen J. J. K. (1983): Slip Zones for Discontinuities Parallel to Circular Tunnels of Shafts. lnt. J. Rock Mech. Min. Sci. Geomech. Abs. 20, 135‐148.

Deere, D. U. and Miller, R. P. (1966): Engineering

The statistical equations (4 to 6) generated in this research work are useful tools for the determination of uniaxial compressive strength, point load index and tensile strength of rocks having similar physical properties as the rocks tested in this research work.

Classification and Index Properties for Intact Rocks.

Tech Rep Air Force Weapons Lab, New Mexico, no AFNL‐TR, 65–116.

Dott, R. H. (1996): Journal of Sedimentary Petrology, V‐34, pp.623‐632.

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