Subgrade Reaction Modulus (Ks) of Clayey Soils

Journal of Engineering Geology, Vol.8, No.1, Spring 2014

2021

Subgrade Reaction Modulus (K s) of Clayey Soils Based on Field Tests *

Naeini S. A., Ziaie Moayed R., Allahyari F.;

Department of Civil Engineering, Imam Khomeini International University, Received: 22 Nov 2012

Revised 10 March 2013

Abstract One of the most important engineering challenges in the design of structure, is the reaction of soil in contact with structure. In engineering design of structures, the subsoil can be simulated by a much simpler system called subgrade reaction model. In order to evaluate the in situ modulus of the clayey deposits of the Qazvin alluvium, the results of a large number of in situ tests carried out by many researchers were analyzed. Vertical plate load tests, standard penetration tests and test pit exploration e xploration were conducted o n over 170 different locations. The results of the plate load and standard penetration tests are analyzed and discussed. The correlation cor relation between subgrade reaction modulus (K s), modulus of elasticity (E s) and corrected standard penetration test blow counts (N) are presented for clayey deposits of the Qazvin alluvium. Results show that there is a significant correlation between subgrade reaction modulus (K s) and SPT blow counts.

Keywords: Subgrade reaction modulus, Modulus of elasticity, SPT, PLT, Clayey

soils, Qazvin alluvium. *

Corresponding author

[email protected] Naeini_h@ikiu. ac.ir

2022


Introduction One of the most important engineering challenges in the design of structures underlying soils is the reaction of soil in contact with structure. Mechanical behavior of soil is very complex. Because soil is naturally non-linear, anisotropic and heterogeneous and its deformation is depended on the stresses that are applied to soil. Hence, in engineering works, for design of the structure, instead of modeling the subsoil in all its complexity, it can be replaced by a much simpler system called a subgrade reaction model. 1. Coefficient of Subgrade Reaction, K s

Winkler [1] proposed a model that assumes the soil stiffness that is considered as ratio between the contact pressures (Δσ) and the associated vertical displacement (Δδ) is linear, and it can be given by the coefficient of subgrade reaction, Ks. It has units of force per unit volume (MN/m3). K s= Δσ / Δδ Δδ

(1)

This theory simulates the soil behavior as a group of independent springs, governed by governed by the linear-elastic model (Figure 1). The coefficient of subgrade reaction that is spring stiffness is the initial slope of the curve until the limit pressure. At first, this concept was introduced for using in the analysis of rigid plates, but during the following decades the theory was developed extended to include the computation of stresses in flexible foundations (Terzaghi [2]). In the area of soil-foundation interaction, many of researchers have utilized this model (Biot [3]; Terzaghi [2]; Vesic [4]; Horvath [5]; Daloglu and Vallabhan [6]).

Subgrade Reaction Modulus (K s) of Clayey Soils Based on Field Tests

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Figure 1. Winkler theory simulations of the soil behavior as a group of springs

Values of Ks may be obtained from a) Field and laboratory tests, b) Empirical equation and c) Tabulated values. Field test is included plate load test, and laboratory tests are consolidation and triaxial test (Dutta and Roy [7]), and CBR test (Nascimento and Simoes [8]). Other researchers such as Elachachi et al. [9] and Bowles [10] proposed some empirical relations. Also Bowles [10] proposed some tabulated values for coefficient of subgrade reaction. The plate load test (PLT) has been a traditional in situ test to estimate the modulus of subgrade reaction (Terzaghi [2]). PLT is a direct test to determine both Ks and Es. It is a direct measurement of the compressibility and bearing capacity of the soil. The δ versus σ plot is generally nonlinear, and one must obtain Ks as the slope of either a tangent or secant line. Either a tangent (solid line) or secant (dashed) line slope of Figure 2 can be used for Ks. Usually, initial values (through the origin) are used; however, one can choose any tangent point or an averaged value using the two points cut by a secant line along the curve. The secant slope defined by the origin (δ = 0) and at δ = 25.4 mm (or 1in.). δ = 25.4 mm is recommended as an initial selection for Equation 1 (Bowles [10]).

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Figure 2. Modulus of subgrade reaction (Bowles [10])

Semi-empirical methods such as that proposed by Vesic [4] may be used to determine the K s values. K s= Es/ [B (1- υ2)]

(2)

In the above equation, B is plate dimension and υ is Poissonʼs ratio. These methods, however, require soil parameters, such as modulus of elasticity (Es) and Poisson’s ratio (υ), which are also difficult to estimate. For this reason, researchers have proposed a simpler empirical equation for various soils, which relates Ks to standard penetration test values. In this respect Scott [11] has been proposed an empirical equation for calculation of Ks in sandy soils based on N values. K s (MN/m3) = 1.8N

(3)

In the above equation, N is standard penetration resista nce and Ks are the coefficient of subgrade reaction. Bowles [10] proposed a relation that is for approximating Ks from the allowable bearing capacit y (qa) proposed by the geotechnical consultant. K s= 40(SF) qa

(in SI units)

(4)

in which SF is safety factor. This equation is based on q a=qult/SF and


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the ultimate soil pressure is at a settlement of ΔH= 25.4mm (1in.). Ziaie Moayed and Janbaz [12] proposed Equation 5 which relates coefficient of subgrade reaction to SPT values for Tehran alluvium. Tehran alluvium is composed of cemented gravelly deposits. K s (MN/m3)=2.821N+79.6

(5)

Naveac [13] provided a relation between Ks values and unconfined compressive strength (qu). Figure 3 shows Ks values versus soil stiffness proposed by NAVFAC [13]. Upper line is for coarse grained soils and lower line is for fine grained soils. In this figure, Ks can be estimated from unconfined compressive strength or soil stiffness. Many of other researchers like Bowles [10] and Das [14] have suggested tabulated values for Ks that can be used as a guide and for comparison when using approximate equations. 2. Modulus of elasticity, E s

The modulus of elasticity (Es) of a soil is a soil parameter that is commonly used in the estimation of settlement. Es like Ks can be estimated from many field and laboratory tests results, empirical equation and tabulated values. Many researchers have proposed some empirical equation for calculation Es. Bowles [10] proposed some empirical correlation that may be used to estimate Es from soil parameter like undrained shear strength (su) and cone penetration test results. For example, the correlations between Es and s u for normally consolidated sensitive clay is: Es= (200 to 500)  su

(6)

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Figure 3. Modulus of subgrade reaction versus unconfined compressive strength (NAVFAC

[13]

)

These correlations require knowledge of other soil parameters that are also difficult to estimate. Other correlations, that are simpler, relate Es to standard penetration values. Bowles [10] suggested some equations for a wide range of soils, from coarse to fine grained soils: Es= 0.32N+4.8 for clayey sand (7) Es=0.3N+1.8 for silts, sandy silt, or clayey silt. (8) In both equations Es is in MPa. Webb [15] based on his investigations on sands and clayey sand soils proposed these equations: Es=0.5N+7.5 Es=0.33N+1.66

for sand for clayey sand

(9) (10)

Behpoor and Ghahramani[16] according to field and laboratory tests on CL and CL-ML soils suggested an empirical equation for determination of modulus of elasticity based on standard penetration resistance (Figures 4).


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Figure 4. Field modulus of elasticity versus SPT number (Behpoor and Ghahramani [16])

According to these results, they proposed the correlation between the SPT number and modulus of elasticity: Es (MPa) = 0.17 N

(11)

Ziaie Moayed and Janbaz [12] proposed the following equation which relates the modulus of elasticity, Es, to SPT values for Tehran alluvium which is composed of cemented gravelly deposits. Es (MN/m2)=0.77N + 21.74

(12)

In this study, for providing a correlation between coefficient of Ks , modulus of elasticity (Es) and standard penetration test (SPT) values for southern part of Qazvin alluvium, which consists of clayey soils with low plasticity, several field and laboratory tests were conducted on more than 170 locations by the research group and the results were evaluated. The southern alluvium of Qazvin is a significant part of the metropolitan area of this city. Accordingly, geotechnical studies and

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identifying the profile of the land in these projects are important. This part of the Qazvin alluvium primarily has fine grained aggregate. Conducted studies indicate that the physical and mechanical characteristics of the southern alluvium of the Qazvin city are considerably uniform. For this reason, the results of the study in some parts of this alluvium are extensible to other areas. Because of the widespread use of the standard penetration test in geotechnical projects across Qazvin city, providing these relationships would be very useful to calculate Ks and Es based on SPT results.

Engineering Geology of Qazvin Alluvium The Qazvin Plain with its adjacent watersheds has an area of 9,300 km 2. It is located between 49 °25' to 50 °35' east longitude and 35 °25' to 36°25' north latitude. Approximate area of Qazvin Plain is about 450,000 ha. Qazvin province is situated in the interface of northern margin of central Iran and western Aborz zones. In other words, northern heights of this province belong to southern parts of Alborz range and largest territory of this province that is Qazvin plain and southern heights belong to central Iran zone. The boundary between these two zones corresponds to north Qazvin thrust zone. The exact boundary of these zones cannot be correctly defined; therefore, it is preferred to assign the whole province to Alborz-Central Iran zones. Northern mountain ranges are composed of east-west trending fold-thrust belt which are


2029

trusted to the south. The intensity of deformation is highest in the mountain-plain boundary. Piedmont heights are gradually vanishing toward the plain which is in turn covered by young alluvial deposits crusted by salt and clay pans and sand dunes. The southern part of this province has a mountainous feature with Paleozoic, Mesozoic and Cenozoic feature forming rocks. Tectonostratigraphic units of northern (Alborz) part and southern parts (Central Iran) have no conspicuous differences. In both parts, rock sequences start with Late Precambrian platform deposits of Soltanieh formation and continue with some sedimentary gaps to Middle Triassic. Upper Triassic middle Jurassic is a single tectonostratigraphic unit limited a period between two organic phases of the early Kimmerian (Upper Triassic) and Middle Kimmerian (Middle Jurassic). It is composed of shale, sandstone (Shemshak formation) coal bearing sediments which are accumulated in early kimmerian foreland basins. Middle Jurassic Upper Cretaceous rock sequences are marly carbonatic continental shelf deposit exposed in the form of small outcrops in Avaj area. Cenozoic rock sequences start with Karaj Formation intruded partly by Pyrneean Orogenic intrusive bodies. Most of the Cenozoic rocks of this province are synorogenic Cenozoic sequences which are accumulated in intermountainous basins with limited outcrops at the foot hill of mountain ranges.

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Experimental Program The experimental programs consisted of field and laboratory tests. The field studies included test pit exploration, plate load test and standard penetration test (SPT). The grain size distribution and Atterberg limits are part of laboratory tests. The pit exploration include in-place weight and moisture content tests and are conducted according to ASTM D 2167-94 [17] and ASTM D 2216-98[18], respectively. The standard penetration test (SPT) is

performed according to ASTM D 1586-08a [19], in a machine borehole, near the location of each plate load test, at the same site. The SPT values for each borehole are obtained at the same depth as the plate load test is done. The number of blow count (N), is measured for 300mm penetration into the soil. Various factors affect the corrected number of SPT blow counts. The SPT results should be corrected. For this purpose, the National Center for Earthquake Engineering Research ( NCEER ) procedure (Youd [20]) were used in this study. The grain size distribution and Atterberg limits which are part of laboratory test are conducted according to ASTM D 422-63 [21] and D 4318-00 [22], respectively. The plate load test that is carried out for each borehole is based on ASTM D 1194 [23]. In this test, the plate is placed at the center of the

borehole, and then load is applied to the plate in steps equal to about 20-25% of the estimated ultimate load by means of a jack. During each loading step the settlement of the plate is observed on dial gauges. At each step of loading, the load is allowed to elapse at least 1


2031

hour. The test will continue until failure, or until the plate has settled by at least 25mm.

Physical Properties of Soils The southern part of Qazvin alluvium generally consists of clayey soils with low plasticity. The materials can be classified according to the Unified Soil Classification System (USCS) as CL and CH. The in situ unit weight of the deposits varies between 16 and 20 kN/m3. The moisture content is about 5.7 to 24.6%. The grain size distribution at different sites varies approximately 51 to 99% fine content.

In Situ Test Results 1. Plate load test results

The major difficulty in applying the Winkler model is quantifying the modulus of subgrade reaction. As it was mentioned in the last section, the plate load test is the best way for calculation Ks values. Therefore, the vertical displacement and the corresponding contact pressure for each test are measured and are plotted in Figure 5. It is evident that the Ks values depend on whether it is the tangent or secant modulus, and on the location of the coordinate of σ and δ. It is obvious that the σ-δ curve can be divided into several regions so that Ks values are dependent on the values of the slope in several regions; however, with this approach, large quantities for Ks may be obtained and refinement of these values will be very difficult. Therefore, the

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secant modulus to the maximum settlement point, for each graph, is determined as Ks. The results are presented in Table 1. The modulus of subgrade reaction, Ks, obtained from the plate tests results varied between 10 and 50 MN/m 3, with an average of 30 MN/m3. These values appear consistent with the values suggested by Das [15] for stiff and very stiff clay, that is, 12-25 MN/m3 and 25-50 MN/m3, respectively.

Figure 5. Typical stress-settlement curve obtained from plate loading test

2. Standard penetration test results

The standard penetration test is the most popular in situ test to determine soil resistance parameter. Various factors influence the SPT blow counts; therefore, the SPT results were corrected by procedure described by Youd [20]. The SPT blow counts are corrected, and are presented in Table 1. The corrected SPT blow counts (N) vary between 9 and 49 blows for 300 mm penetration and is in consistent with the tabulated values suggested by Das [14] for stiff, very stiff and hard clay (Table 2).


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Table 1. Correlation between clayey soils stiffness and SPT values (Das

[14]

)

Stiffness

SPT values

Very soft

0-2

Soft

2-5

Medium

5-10

Stiff

10-20

Very stiff

20-30

Hard

>30

Analysis of Test Data 1. Correlation between Es and N

One of the most important parameters for settlement analysis of shallow foundations is the modulus of elasticity, Es. There are many significant factors in determining Es, including anisotropy and stress history. Due to the difficulties in obtaining undisturbed samples and maintaining the stress history and the nature of the samples, laboratory -based values of Es are not reliable, so the standard penetration test has often been used to obtain Es. Statistical analysis of the Es and N values obtained for the Qazvin alluvium was performed. The obtained results are presented in Figure 6. As this shows, the modulus of elasticity of clayey alluvium of southern part of Qazvin city can be estimated a s: Es = 0.264N

(13)

Equation 13 shows that with increasing SPT numbers, modulus of elasticity increases. This is in accordance with other correlations

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proposed by other researchers, (Bowles [10]; Webb [15]; Behpoor and Ghahramani [16]; Ziaie Moayed and Janbaz [12]).

Figure 6. Correlation between E s and N for Qazvin alluvium 2. Comparison of proposed equation for Es with other relationships

Figure 7 shows the comparison of the obtained results of Es versus N values for Qazvin alluvium with other correlations presented in Table 3. As is evident from this figure that the general behavior of proposed correlation by previous researchers with obtained results for Qazvin alluvium is identical. Suggested correlation for Qazvin alluvium is between correlations proposed by Behpoor and Ghahramani [16] and Bowles [10]. According to USCS classification that is presented in Table 1, Qazvin alluvium mainly is CL. Obtained results for Qazvin alluvium is upper than the values obtained from correlation proposed by Behpoor and Ghahramani [16], and lower than correlation suggested by Bowles[10]. It is obvious that soils that are CL have lower strength than silts, sandy silts or clayey silt soils. This indicates that correlation obtained for Qazvin alluvium has a good agreement with other correlations proposed by other researchers.

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Table 2. Correlations between E s and N proposed by other researchers Reference Bowles[10] Webb Bowles[10] Behpoor And Ghahramani Ganbari

Soil type Clayey sand Clayey sand Silts, sandy silts, or clayey silt CL and CL-ML CL, CH, ML

Correlation(MPa) Es=0.32N + 4.8 E s=0.33N+1.66 Es=0.3N + 1.8 E s= 0.17N Es= 0.35(N+2D) + 3.2

Figure 7. Comparison between E s equation of Qazvin alluvium with other correlations

3. Correlation between Ks and N

Because of the widespread use of the standard penetration test in geotechnical projects across Iran, the presentation of a relation between SPT results and other geotechnical parameters such as Ks would be very useful. Figure 8 shows the correlation between the corrected SPT blow counts (N), and modulus of subgrade reaction (Ks). The best fit between the plate load test data and the corrected standard penetration test results for southern part of the Qazvin alluvium which is consisted of clayey soils with low plasticity is provided by: Ks = 0.96N

(14)

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Equation 14 shows that the modulus of subgrade reaction increases as the SPT blow count increases. By using this equation, the modulus of subgrade reaction may be evaluated from standard penetration test results in stiff and very stiff clayey soils. It should be noted that the obtained relationship is applicable only to determine Ks for a small plate with a diameter of B=30 cm. Therefore, to use in the actual size of the foundation these values should be modified (Terzaghi [2]).

Figure 8. Correlation between K s and N60 for Qazvin alluvium 4. Comparison of proposed correlation for Ks with other relationships

In this section there is a comparison between proposed equation for Qazvin alluvium and relationships suggested by other researchers. Figure 9 shows comparison between obtained results for Qazvin alluvium and relationship proposed by NAVFAC [13] (Figure 3) and Equation 4 suggested by Bowles [10]. Both correlations are according to Ks versus bearing capacity (qa or qu). Therefore, initially, it is necessary to obtain q according to N values. For this purpose, Table 4 that is proposed by Bowles [10] for cohesive soils i s used.

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Figure 3 shows modulus of subgrade reaction versus unconfined compressive strength (qu). Therefore, with tabulated values proposed by Bowles [10] it can be converted into Figure 9 that is for modulus of subgrade reaction versus SPT values (N70). The same procedure were conducted for Equation 4 that is for approximating Ks from the allowable bearing capacity (qa). Obtained results of Qazvin alluvium is based on N 60, which indicates that actual hammer energy to sampler is 60% of the input energy, but Table 4 is N 70, thus initially it is necessary to convert N 60 values obtained for Qazvin alluvium into N 70 with using Equation 15. N70= (6/7)× N60

(15)

It is evident from Figure 9, the obtained results of Qazvin alluvium in the lower N values are in accordance with NAVFAC[13], but in greater N values is less; however the general behavior are identical. In the case of Bowles [10] correlation, it is obvious that with selected safety factor (1.4 and 2.9) which is common in the engineering works, results of Qazvin alluvium have a good agreement with Bowles correlation. Table 3. N70-qu correlation for cohesive soils (Bowles [10]) Consistency

N 70

qu , MPa

Very soft

0-2

<0.025

Soft

3-5

0.025-0.05

Medium

6-9

0.05-0.1

Stiff

10-16

0.1-0.2

Very stiff

17-30

0.2-0.4

Hard

>30

>0.4

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Figure 9. Comparison between Qazvin alluvium K s data and NAVFAC [13]

and Bowles

[10]

Figure 10 shows a comparison between obtained results for Qazvin alluvium with correlation suggested by Scott [11], which is for calculation Ks in sandy soils based on N values. This figure shows that proposed correlation by Scott [11] for sandy soils is upper than obtained results of Qazvin alluvium. Qazvin alluvium mainly is CL and has lower strength than sandy soils. For this reason obtained results of Qazvin alluvium lie beneath the Scott correlation.

Figure 10. Comparison between K s equation of Qazvin alluvium with [11]

Scott

correlation

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Table 4. K s-N correlations from Es-N relationships using Vesic’s [4] Equation Reference Bowles[10] Webb Bowles[10] Behpoor & Ghahramani [16]

E s Correlation (MPa) Es=0.32N + 4.8 E s=0.33N+1.66 Es=0.3N + 1.8

Soil type Clayey sand Clayey sand Silts, sandy silts, or clayey silt CL and CL-ML

K s Correlation (MN/m3) K s=1.17N+17.6 K s=1.2N+6.07

K s=1.1N+6.6

Es= 0.17×N

K s=0.622

Comparison between Ks-N correlation of Qazvin alluvium with other correlations between Ks-N or Es-N proposed by other researchers is presented in Figure 11. Some of the proposed correlations are between Es and N; therefore, initially it is necessary to achieve Ks in terms of Es. According to Es values, Ks values can be obtained from Equation 2 which is proposed by Vesic [4]. In Vesic’s [4] Equation, the side dimension, B of the plates is 0.3m, and the Poisson’s ratio, υ, of soil is taken as 0.3. Table 5 shows Ks-N correlations

obtained

from

Es-N

relationships

suggested

by

researchers by using Equation 2. Southern parts of Qazvin alluvium mainly consist of clayey soils with low plasticity (CL). As is apparent from Figure 11, coefficient of subgrade reaction (Ks) in Qazvin alluvium is between results obtained by Behpoor and Ghahramani [16] and Bowles [10]. This indicates the accuracy of the obtained results for Qazvin alluvium. Relationships that are located above Qazvin alluvium are Bowles [10], Webb [16] and Scott [11]. Bowles [10] and Webb [15] correlations are for clayey sand and Scott [11] correlation is for sandy soils. Qazvin alluvium

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which is mainly CL and in some parts CH in comparison with sandy soils has lower strength. Because of this lower strength Qazvin alluvium must has lower Ks, and locates beneath Bowles [10], Webb [15] and Scott [11] correlations, which is obvious from Figure 11.

N

Figure 11. Comparison between K s equation of Qazvin alluvium with other correlations

Conclusions In this paper, the relationship between subgrade reaction modulus, modulus of elasticity and corrected standard penetration test blow count (N) is presented for southern part of Qazvin alluvium which mainly consistes of clayey soils with low plasticity. The following conclusions may be drawn from the obtained results. 

As expected, Ks and Es increase as the SPT values increases. The following equations are presented for correlation between Ks, Es and N values in the southern part of Qazvin alluvium. Ks = 0.96N


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Es = 0.264 N 

Suggested correlation for Qazvin alluvium for Es is between correlations proposed by Behpoor and Ghahramani [16] and Bowles [10].



The obtained result of Qazvin alluvium for Ks in the lower N values are in accordance with NAVFAC [13], but in greater N values is less. However, the general behaviors are identical.



The proposed correlation for Ks by Scott [11] for sandy soils is upper than obtained results of Qazvin alluvium. Qazvin alluvium mainly is CL and has lower strength than sandy soils. For this reason obtained results of Qazvin alluvium lie beneath the Scott correlation.



The obtained correlation for coefficient of subgrade reaction, Ks, in Qazvin alluvium is between results obtained by Behpoor and Ghahramani [16] and Bowles [10]. This indicates the accuracy of the obtained results for Qazvin alluvium



The proposed relationship is applicable only for calculation the Ks for small plates (with the side dimension, B=0.3m), and the values would have to be modified for size effects before they could be applicable to general foundation problems.



From the correlation between Ks and N for southern part of Qazvin alluvium (Ks= 0.96N), it can be said that the subgrade reaction modulus for this region which is consisted of clayey soils with low plasticity is almost equal to the number of blow counts.

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Acknowldegments The authors wish to appreciate the Soil Mechanic Laboratory and the Deputy of Research and Technology of Imam Khomeini International University for their great cooperation during the completion of this research.

References 1. Winkler E., "Die Lehre von Elastizitat und Festigkeit (on elasticity and fixity)", Dominicus,Prague (1867). 2. Terzaghi K. V., "Evaluation of coefficient of subgrade reaction", Geotechnique, 5 (4) (1955) 297-326. 3. Biot M. A., "Bending of infinite beams on an elastic foundation", Journal of Applied Mechanics, 59 (1937) A1-A7. 4. Vesic A. S., "Bending of beams resting on isotropic solids ", Journal

of the engineering Mechanics division, ASCE, 87(EM2) (1961) 35-53. 5. Horvath J. S., "Subgrade Models for Soil-Structure Interaction Analysis",

Journal

of

Foundation

Engineering

on

Current

Principles of Practice Proceeding, ASCE, 20 (1989) 599-612. 6. Daloglu A. T., Vallabhan C. V. G., "Values of k for Slab on Winkler Foundation, Journal of Geotechnical and Geoenvironmental Engineering", ASCE (2000) 463-471. 7. Dutta S. C., Roy R. A., "Critical Review on Idealization and Modeling for Interaction among Soil Foundation-Structure System", Computers and Structures, 80 (2002) 1579-1594. 8. Nascimento V., Simoe A., "Relation between CBR and Modulus of Strength, Proceeding 4th International Conference on Soil Mechanic and Foundation Engineering", London (1957) 166-168.


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9. Elachachi S. M., Breysse D., Houy L., "Longitudinal Variability of Soils and Structural Response of Sewer Networks", Computers and Geotechnics, 31(8) (2004) 625-641. 10. Bowles J. E., "Foundation Analysis and Design. 5th ed.", New York: McGraw-Hill (1996). 11. Scott R. F., "Foundation Analysis", Englewood Cliffs, NJ. Prentice Hall (1981). 12. Ziaie Moayed R., Janbaz M., "Subgrade reaction modulus of Tehran alluvium", ICE Geotechnical Engineering Journal, 164 (4) 283-288. 13. NAVFAC Design Manual 7.02 (1986). 14. Das B. M., "Principles of Foundation Engineering", 2nd ed. Boston, MA. : PWS-Kent (1990). 15. Webb D. L., "Settlement of structures on deep alluvial sandy sediments in Durban", South Africa. Proceedings, Conference on In Situ Behavior of Soil and Rock, Institution of Civil Engineers, London (1969) 181-188. 16. Behpoor L., Ghahramani A., "Correlation of SPT to strength and modulus of elasticity of cohesive soils", 12th International conference on Soil Mechanics and Foundation Engineering, ISSMFE, Rio do Janeiro, Brazil (1989), 175-178. 17. "ASTM (American Society for Testing and Materials), D 2167-94: Standard Test Method for Density and Unit Weight of Soil in Place by the Rubber Balloon Method",ASTM International, West Conshohocken, PA (1994a). 18. "ASTM (American Society for Testing and Materials), D 2216-98: Standard Test Method for Laboratory Determination of Water

2044


(Moisture) Content of Soil and Rock by Mass", ASTM International, West Conshohocken, PA (1999). 19. "ASTM (American Society for Testing and Materials), D 158608a: Standard Test Method for Standard Penetration Test (SPT) and Split-Barrel Sampling of Soils", ASTM International, West Conshohocken, PA (2000). 20. Youd T. L., "Liquefaction resistance of soils: summary report from the 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils", Journal of Geotechnical and Geoenvironmental Engineering 127 (10) (2001) 817-833. 21. "ASTM (American Society for Testing and Materials), D 422-63: Standard Test Method for Particle-Size Analysis of Soils", ASTM International, West Conshohocken, PA (1998). 22. "ASTM (American Society for Testing and Materials), D 4318-00: Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity

Index

of

Soils",

ASTM

International,

West

Conshohocken, PA (2000). 23. "ASTM (American Society for Testing and Materials), D 1194-94: Standard Test Method for Bearing Capacity of Soil for Static Load and Spread Footings", ASTM International, West Conshohocken, PA (1994b).

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Appendix I: In situ soil characteristics of Qazvin alluvium Sit

Depths(m

USCS

(N ) 1 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

3 4 6 2 8 14 4 4 2 6 4 10 4 4 4 6 2 6 4 14 12 2 12 12 12 14 4 8

CH CL CL CL CL CH CL CL CL CL CL CL CL CL CL CL CL CL CL CL CH CH CL CL CL CL CL CL CL

44 27 24 31 34 45 32 49 15 36 31 31 24 24 25 24 43 24 49 48 43 33 48 43 44 45 49 20 21

2

K s

E s( MN/m 3

48 26 23 27 38 43 33 43 16 36 35 29 21 22 24 26 46 23 47 44 46 36 47 45 42 43 45 22 23

13.11 7.10 6.28 7.38 10.38 11.74 9.01 11.74 4.37 9.83 9.56 7.92 5.74 6.01 6.56 7.10 12.56 6.28 12.84 12.02 12.56 9.83 12.84 12.29 11.47 11.74 12.29 6.01 6.28

Sit

Depths(m

USCS

(N ) 1 6

30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

14 4 8 10 12 8 14 2 6

CL CH CL CH CL CL CH CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL

32 45 40 35 47 18 47 28 33 38 23 24 48 32 15 16 49 38 44 44 37 47 41 28 24 25 20 32 18

10 4 6 8 14 12 14 14 6 6 10 4 6 10 6 2 8 10 12

2

K s

E s( MN/m 3

25 41 39 33 42 20 43 33 40 39 23 25 48 36 14 15 50 36 32 33 25 40 29 28 23 23 27 32 16

6.83 11.20 10.65 9.01 11.47 5.46 11.74 9.01 10.92 10.65 6.28 6.83 13.11 9.83 3.83 4.10 13.65 9.83 8.74 9.01 6.83 10.92 7.92 7.65 6.28 6.28 7.38 8.74 4.37

Appendix I: In situ soil characteristics of Qazvin alluvium (continue) Sit e

Depths(m

USCS classificatio

(N ) 1 6 0

K s 3 (MN/m )

59

2

CH

33

37

60

4

CL

30

61

6

CL

20

62

8

CL

63

10

CL

64

12

65 66

2

Site No

Depths(m

10.11

88

38

10.38

20

5.46

16

19

30

39

CL

34

8

CL

4

CH

67

6

68

2

69 70

2

USCS classificatio

(N ) 1 6 0

K s 3 (MN/m

12

CL

25

25

6.83

89

14

CL

40

43

11.74

90

2

CL

33

33

9.01

5.19

91

8

CL

42

45

12.29

10.65

92

14

CL

40

39

10.65

33

9.01

93

11

CL

38

36

9.83

20

19

5.19

94

9

CL

42

41

11.20

12

10

2.73

95

10

CL

34

28

7.65

CL

9

12

3.28

96

12

CH

40

29

7.92

CL

23

22

6.01

97

10

CL

37

31

8.47

4

CH

29

29

7.92

98

12

CL

40

30

8.19

6

CL

24

23

6.28

99

10

CL

41

47

12.84

71

2

CL

36

39

10.65

10

12

CH

42

50

13.65

72

10

CL

28

28

7.65

10

10

CL

47

47

12.84

73

8

CL

22

21

5.74

10

8

CL

27

24

6.56

74

2

CL

27

26

7.10

10

10

CL

23

22

6.01

75

4

CL

30

28

7.65

10

12

CH

34

36

9.83

76

12

CL

30

36

9.83

10

8

CL

31

29

7.92

E s( MN/m )

E s( MN/m )

2046


Sit e

Depths(m )

USCS classificatio

(N ) 1 6 0

K s 3 (MN/m )

77

2

CL

18

22

78

10

CL

15

20

79

12

CL

36

80

10

CL

20

81

8

CL

82

4

CL

83

10

84 85

2

2

Site No

Depths(m )

USCS classificatio

(N ) 1 6 0

K s 3 (MN/m

6.01

10

6

CL

25

23

6.28

5.46

10

2

CH

38

27

7.38

37

10.11

10

2

CL

49

43

11.74

25

6.83

10

4

CL

48

42

11.47

19

23

6.28

11

6

CL

38

43

11.74

20

22

6.01

11

2

CL

46

39

10.65

CL

42

33

9.01

11

4

CL

37

40

10.92

12

CL

21

26

7.10

11

8

CL

48

41

11.20

12

CL

32

31

8.47

11

8

CL

22

27

7.38

86

2

CL

32

34

9.29

11

10

CL

22

26

7.10

87

10

CL

43

47

12.84

11

2

CL

43

35

9.56

E s( MN/m )

E s( MN/m )

Appendix I: In situ soil characteristics of Qazvin alluvium(continue) Site No.

Depths(m )

USCS classificatio

(N ) 1 6 0

K s 3 (MN/m )

11

4

CL

38

42

11

6

CL

45

11

8

CH

41

12

4

CH

12

6

12

10

12 12

2

2

Site No

Depths(m )

USCS classificatio

(N ) 1 6 0

K s 3 (MN/m

11.47

14

5

CL

31

30

8.19

42

11.47

14

3

CL

26

29

7.92

39

10.65

14

4

CL

17

21

5.74

39

43

11.74

14

8

CL

16

19

5.19

CL

23

26

7.10

15

3

CL

28

27

7.38

CL

47

42

11.47

15

4

CL

17

20

5.46

10

CL

47

48

13.11

15

5

CL

16

20

5.46

14

CL

25

23

6.28

15

3

CL

30

29

7.92

12

15

CL

47

41

11.20

15

4

CH

31

29

7.92

12

6

CH

39

36

9.83

15

5

33

31

8.47

12

8

CL

41

31

8.47

15

5

CL

48

50

13.65

12

12

CL

40

33

9.01

15

4

CL

14

17

4.65

12

12

CL

42

32

8.74

15

3

CL

39

36

9.83

13

14

CH

22

23

6.28

15

3

CL

18

17

4.65

13

10

CH

41

31

8.47

16

4

CL

40

40

10.92

13

10

CL

27

24

6.56

16

4

CL

41

40

10.92

13

8

CL

24

29

7.92

16

5

CL

40

43

11.74

13

10

CL

39

39

10.65

16

3

CL

15

16

4.37

13

12

CL

41

43

11.74

16

4

CL

16

16

4.37

13

8

CL

18

22

6.01

16

5

CL

14

14

3.83

13

10

CL

26

24

6.56

16

4

CL

14

15

4.10

13

4

CL

20

22

6.01

16

5

CL

30

29

7.92

13

3

CL

16

16

4.37

16

3

CL

30

27

7.38

14

3

CL

21

23

6.28

16

3

CL

27

26

7.10

14

4

CL

11

15

4.10

17

4

CL

28

26

7.10

14

3

CL

17

17

4.65

17

5

CL

13

14

3.83

14

4

CL

30

28

7.65

14

10

CL

29

27

7.38

14

4

CL

32

26

7.10

E s( MN/m )

CL

E s( MN/m )

Subgrade Reaction Modulus (Ks) of Clayey Soils

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