CORRECTION PROCEDURE FOR THE DETERMINATION OF SOIL SPECIFIC SURFACE

: Specific surface has a very important role in geotacnic especially with that home dell with gypseous soils or other types of salty soils. Because its calculation need for high accuracy, a procedure is presented to calculate a correction factor for Specific surface determination. In a previous work, grain size distribution curves of many soil samples are collected. A value for the specific surface of each soil is determined summing the surface area of subintervals in the distribution curve. In this work, the values of specific surface are obtained from these gradation curves and compared to those calculated using the values of the equivalent diameter for each soil. Fitting has been made and gets the best equation representing these points. From this equation, new values for specific surface are obtained by interning the specific surface calculated from the equivalent diameter and again the point is draw with the origin point (specific surface obtained from these gradation curves). Fitting is made again and the new equation is obtained. Finally, the equation of the calculated corrected specific surface is written. The results showed a very good agreement when using the corrected procedure.


INTRODUCTION
The usual method to calculate the specific surface of a soil is the summation of the surface area of several sub divisions of the soil grains according to corresponding intervals on the gradation curve.There are various techniques to measure the specific surface of solids.Gas adsorption (i.e., the condensation of molecules on the mineral surface) determines surface area from the relationship between applied pressure and volume of gas forced into the specimen (water vapor is included in this group).Another technique is the absorption of molecules from solution onto a solid surface, in particular, dyes such as methylene blue.Additionally, specific surface values can be inferred from known thermodynamic properties (e.g., heat of immersion of a powder in a liquid), the rate of dissolution of soluble materials, microscopy, and the diffusiveness of X-ray diffraction patterns.Details of these measurement techniques can be found in Adamson (1990).The potential use of specific surface in various geotechnical engineering applications and in the characterization of mineral resources.
A few examples are as follows: (i) assessing the extent of internal and interconnected micro porosity; (ii) characterizing the average slenderness of fine particles; (iii) computing the charge density on particle surfaces ,knowing the specific surface and the cation exchange capacity ; (iv) identifying the extent of fines coating coarse particles; n petroleum production, fines coating coarser particles may detach when the pore fluid is changed ("water shock"), migrate, and clog pore throats, thereby causing a dramatic decrease in permeability ("formation damage "); and (v) quality control and process monitoring, including natural and industrial situations such as the evolution of residual soils ,cement hydration, pyro-etamorphosis of minerals (e.g., ochre, bentonite),and the effectiveness of mineral separation processes, ( Santamaria et al, 2002).

DEFINITION OF THE EQUIVALENT DIAMETER AND THE SPECIFIC SURFACE
The usual method to calculate the specific surface of a soil is the summation of the surface area of several sub divisions of the soil grains according to corresponding intervals on the gradation curve.If a grain size distribution curve such as the one shown in Fig. 1 is divided into n intervals, the specific surface of the soil, assuming spherical particles, is calculated according to the following.The average surface area of particles in an interval i of this gradation curve is Where iav D is the average diameter in this interval, while the average volume of a particle in this interval is Hence, the total surface area of particles of this interval will be: - where W is the total weight of soil particles in grams, f i and f i-1 are the cumulative percentages by weight of the particles finer in diameter than those at the beginning and the end of the interval i respectively, substituted in decimals, G is the average specific gravity of soil particles and w  is the density of water = 1gm/cm 3 .To unify the units, diameters are substituted in centimeters and the surface areas are obtained in cm 2 .The specific surface of the soil, in cm 2 per 100gm of soil, may then be computed as: - In 2005 Al-Mufty and Al-Hadidi, presented a procedure to predict the effective diameter.The equivalent diameter is defined as the diameter that may substitute the whole soil grains for calculating the specific surface.The specific surface in cm 3 per 100gm of a soil may be calculated from the equivalent diameter as: - where S pe and V pe are the surface area in cm 2 and the volume in cm 3 respectively, of a particle having a diameter equal to the equivalent diameter, D e in cm.
Equating the specific surface from Eq. ( 5) and Eq. ( 4), the following is obtained: - From which the equivalent diameter may be obtained for a specific grain size distribution curve.It is obvious that the equivalent diameter represents the harmonic mean of the particle diameters available, cf.Kezdi (1974).The aforementioned steps which were presented by Al-Mufty and Al-Hadidi, (2005) were devoted to determine an average diameter for a specific interval of a small width within the grain size distribution curve.Next, it is required to assess the value of the percentage finer corresponding to the diameter closest to the effective equivalent diameter, the latter being adopted to calculate the average specific surface of the soil as a whole.It is plausible to assume that the required value of the percentage finer is dependent on the number of logarithmic cycles and on the properties of the cumulative distribution of the grains.The cumulative distribution which assumed following the well-known cumulative normal probability distribution.This enables the calculation of the cumulative function corresponding to a certain diameter and vise versa.The most significant range of the probability distribution assumed as from -3 to +3,  and  being the mean and the standard deviation of the distribution, giving a confidence level of 99.73%.This is called the "3 rule" advised by Duncan (2000) for reliability problems in geotechnical engineering.Thus, the N cycles will correspond to 6 of the by weight distribution of the logarithms of diameters of particles.Then, it is possible to determine the standard deviation of the distribution.
The standard random variable of the standard normal probability distribution will be Substituting Eq.( 9) in Eq.( 5) and Eq. ( 7) and equating the latter equations as in Eq. ( 6), the following is obtained: - The mean  is the logarithm of D 50 which may be easily determined.Nevertheless, its value is cancelled out from both sides if the equation is multiplied by (10  ).The variables z e and z i represent the standard normal variables that correspond to the effective diameter in question and the diameter at the end of the interval i in the gradation curve.If a standard cumulative normal distribution curve is divided into n intervals within the range z=-3 to z=+3, z e may be easily found as; - For a specified number of intervals, n, and a known value of the number of cycles N, the values of the standard deviation  and the interval width b are determined.For each interval i, the value of z i is determined from the inverse of the cumulative standard normal distribution function as the random variable corresponding to f i ,the cumulative frequency.
After z e is found, the corresponding cumulative frequency f e may be found from the cumulative standard normal distribution function as being the percentage finer that corresponds to the required effective diameter D e .The specific surface of the soil may be determined through Eq. 5 using a single diameter obtained from the gradation curve.To put a single equation for simple assessment of f e , several trials to solve Eq. 11 are performed using different number of intervals and logarithmic cycles.The results of these trials are given in Table 1.Of course, the range of N for natural soils is from about one cycle for uniform soils to about five or six cycles for widely sorted soils (very well graded).The results have shown that 200 intervals would be enough to assess properly accurate values for f e .A regression analysis has been performed and a best-fit curve is found to be the following: - with f e in percent.The coefficient of correlation is found to be 0.999994, which is very high indeed.
The equation is limited to the range N [0.5,6] where the trend of the relation with f e is completely different for N values lower than 0.5, while for N>6, the fitting equation should be changed (particle diameters in natural soils yield no values out of this range practically).
It is obvious now that for a certain soil, the equivalent diameter can be easily determined from the grain size distribution curve of that soil.It will be the diameter corresponding to the effective percentage finer determined from the table or from the graph given in Fig. 3 or using Eq.( 12) directly.As the equivalent diameter is determined, the specific surface of the soil can be calculated using Eq. ( 5).
The target equivalent diameter may be calculated by using equation derived in 2005 by Al-Mufty and Al-Hadidi .

CORRECTION PROCEDURE
By using Eq. ( 7), the specific surface of soil particles is obtained.Meanwhile, the number of logarithmic cycles, N, for each soil is determined and the percent finer corresponding to the equivalent diameter is found using Eq. ( 12).Accordingly, the equivalent diameter is determined and the corresponding specific surface is calculated using Eq. ( 5).The results from the latter equation are compared with those obtained from Eq. ( 7) and plotted in Fig. 5.

Fig. 5.
Comparison between values of specific surface obtained from Eq. ( 7) and Eq. ( 5) for the analyzed soils Fitting has been made for specific surface obtained from eq.( 7) and that obtained from eq.( 5) and from this fitting it is found that the best equation representing this relationship is: Y= (0.4587)*X (1.0755) (13) by using this equation new Spe is found as follows: S pe(new) =(1/0.4587)*Spe (1/1.0755)(14) And this S pe(new) is re drawn with original S PT obtained from equation no.(7), as shown in Fig. 6 Fig. 6.Comparison between values of specific surface obtained from Eq. ( 7) and Eq. ( 14) for the analyzed soils Fitting has been made for specific surface obtained from eq.( 7) and that obtained from eq.( 14) and from this fitting it is found that the best equation representing this relationship is: Y = (1.0563)*X(15) By using this equation another new Spe is found as follows: S pe(final) =(1/1.0563)*S pe(new) (16)  7), as shown in Fig. 7 Fig. 7. Comparison between values of specific surface obtained from Eq. ( 7) and Eq. ( 16) for the analyzed soils Fitting has been made for specific surface obtained from eq.( 7) and that obtained from eq.( 16) and from this fitting it is found that the best equation representing this relationship is: Y=X (17) The comparison has proved better agreement and the coefficient of correlation between the results of the two equations is found to be 0.982921.The values obtained for the ratio of the specific surface calculated using the equivalent diameter to the specific surface calculated through summing the interval surface area of particles (S pe(new) /S PT ) varied from 1.594972 to 0.453831 with an average of 1.025342, which is more close to 1.0.The standard deviation of the ratio distribution is found to be 0.225367 .

SEPARATING THE SAMPLES
In order to find the best correction equation, the samples are separated to gap, well graded and uniformly graded samples.Well Graded Samples: Fitting has been made for specific surface obtained from eq.( 7) and that obtained from eq.( 5) for well graded samples as shown in from this fitting it's found that the best equation could represented this relationship is: And this S pe(final) re draw with original S PT that obtained from equation no. ( 7), as shown in Fig. 9 Fig. 9. Comparison between values of specific surface obtained from Eq. ( 7) and Eq. ( 18) for the well graded analyzed samples.
The comparison has proved better agreement and the coefficient of correlation between the results of the two equations is found to be 0.985730.The values obtained for the ratio of the specific surface calculated using the equivalent diameter to the specific surface calculated through summing the interval surface area of particles (S pe(new) /S PT ) varied from 1.67 to 0.5031 with an average of 0.9438, which is more close to 1.0.The standard deviation of the ratio distribution is found to be 0.2008.

Gap Graded Samples:
Fitting has been made for specific surface obtained from eq.( 7) and that obtained from eq.( 5) for gap graded samples as shown in from this fitting it's found that the best equation could represented this relationship is: And this S pe(final) re draw with original S PT that obtained from equation no.(7), as shown in Fig. 11 Fig. 11 Comparison between values of specific surface obtained from Eq. ( 7) and Eq. ( 19) for the gap graded analyzed samples.
The comparison has proved better agreement and the coefficient of correlation between the results of the two equations is found to be 0.985421.The values obtained for the ratio of the specific surface calculated using the equivalent diameter to the specific surface calculated through summing the interval surface area of particles (Spe(new)/SPT) varied from 1.420 to 0.3256 with an average of 0.8975, which is more close to 1.0.The standard deviation of the ratio distribution is found to be 0.2166 .

Uniform Graded Samples
Fitting has been made for specific surface obtained from eq.( 7) and that obtained from eq.( 5) for uniform graded samples as shown in  The comparison has proved better agreement and the coefficient of correlation between the results of the two equations is found to be 0.98545.The values obtained for the ratio of the specific surface calculated using the equivalent diameter to the specific surface calculated through summing the interval surface area of particles (Spe(new)/SPT) varied from 1.4161to 0.3256 with an average of 0.9712, which is more close to 1.0.The standard deviation of the ratio distribution is found to be 0.2170 .

CONCLUSIONS
Al-Mufty and Al-Hadidi proposed procedure for calculating the equivalent diameter by which the equivalent specific surface could be calculated.In this paper the equivalent specific surface could be corrected by a proposed procedure.Analysis of 154 soil gradation curves has shown a very good agreement between the surface area values cumulated from gradation curves and the corrected specific surface which was obtained from the proposed equation.

NOTATIONS D iav
The average diameter S piav The average surface area of a particle V piav the average volume of a particle S i the total surface area of particles of each interval W The weight of the whole soil in grams.

Fig. 1 .
Fig. 1.A typical gradation curve of a soil divided into n equal intervals, Al-Mufty and Al-Hadidi,(2005) -Mufty and Al-Hadidi presented the equivalent diameter which could be used to calculating the specific surface.

Fig. 4 .
Fig. 4. Comparison between (S pe /S PT ) values and coefficient of curvature (C C ) for uniformly graded samples Al-Mufty and Al-Hadidi (2005) found that the ratio (S pe /S PT ) decreases with the increase in the coefficient of curvature (C C ). Ratios closer to 1.0 are found for values of the coefficient of curvature in the range 1.0 to 3.0.Considering the soil type and gradation, it is found that the results are less accurate in clayey soils than in sandy soils.

Fig.( 12 )Fig. 12
Fig. 12Comparison between values of specific surface obtained from Eq. (7) and Eq.(5) for the uniform graded from this fitting it's found that the best equation representing this relationship is:

Fig. 13
Fig. 13Comparison between values of specific surface obtained from Eq. (7) and Eq.(5) for the uniform graded analyzed samples.

Table 1 .
The percentage finer f e corresponding to the equivalent diameter The values for the effective percentage of finer particles for the case of 200 intervals are plotted against the number of logarithmic cycles of the gradation curve in Fig.3.

Al-Hadidy Correction Procedure for the Determination of Soil Specific Surface 3575
And this S pe(final) is re drawn with original S PT obtained from equation no. (