Mechanical Parameters and Bearing Capacity of Soils Predicted from Geophysical Data of Shear Wave Velocity

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1 Mechanical Parameters and Bearing Capacity of Soils Predicted from Geophysical Data of Shear Wave Velocity Qassun S. Mohammed Shafiqu a, Erol Güler b and Ayşe Edinçliler c a Assistant Professor, Dr., Civil Engineering Department, Al-Nahrain University, College of Engineering, Baghdad, Iraq. Professor, Dr, Civil Engineering Department, Bogazici, University, College of Engineering, Istanbul, Turkey. Professor, Dr, Earthquake Department, Bogazici, University, College of Engineering, Istanbul, Turkey. a ORCID: Abstract The analysis of foundation vibrations and earthquake problems in geotechnical engineering demands characterization of dynamic soil properties by geophysical techniques. Also the dynamic structural analysis of the superstructures needs knowledge of the dynamic response of the soil-structure, which, in turn depends on dynamics properties of soil. The estimation of seismic velocities, modulus of elasticity and structural properties of soils is not enough in the design of engineering projects. Therefore, an ultimate bearing capacity has been predicted using the seismic shear wave velocity. It is indicated that the allowable bearing pressure and the coefficient of subgrade reaction together with many other elasticity parameters may be obtained rapidly and reliably once the seismic wave velocities are determined in situ by convenient geophysical survey. In this study, S-wave and P-wave velocities data were obtained from seismic borehole survey in the foundation layers of Iraq. Use was made of the existing mathematical relations between various parameters and seismic wave velocities for the study of foundation layers in the study areas. Based on the results, the elastic constants, allowable bearing capacity, and other parameters were determined and evaluated. It was indicated that for cohesive and cohesionless soils, up to a shear wave velocity of 3 m/s and 4 m/s respectively, the shear wave velocity predicts the bearing capacity relatively well. Keywords: Bearing capacity, soil parameters, shear wave velocity, seismic technique, shear modulus. INTRODUCTION A footing is the supporting base of a building which forms the interface across which the loads are transmitted to the sublayers. If the structural loads are transmitted to the nearsurface soil, then it is referred to as shallow foundation. Earthquakes may cause a reduction in bearing capacity and increase in settlement and tilt of shallow foundations due to seismic loading. The foundation must be safe both for the static as well for the dynamic loads imposed by the earthquakes. Soilfoundation-structure system should work together in a coherent manner. In particular, if the site is exposed to high seismic loadings it is highly desirable that the soil-foundation part of the system should play an appropriate role in delivering the required overall performance. In the design of shallow foundation one of the main factors related to soil is bearing capacity and the other is settlement or in other words the subgrade reaction. The seismic S-wave velocity is an effective parameter for estimating the bearing capacity of soils [1]. Elastic parameters such as Young s modulus, Bulk modulus, shear modulus, Poisson s ratio, Oedometric modulus and others are related to shear wave velocity leading to the determination of allowable bearing capacity for shallow foundations [2]. For the calculation of allowable bearing capacity, the geophysical methods, utilising seismic wave velocity measuring techniques with absolutely no disturbance of natural site conditions, may yield relatively more realistic results than those of the geotechnical methods, which are based primarily on bore hole data and laboratory testing of so-called undisturbed soil samples [3]. Many researchers have extensively studied to obtain a relation between the various parameters of soil mechanics and the seismic wave velocities. Hardin and Black [4], and Hardin and Drnevich [5] established indispensable relations between the shear wave velocity, void ratio, and shear rigidity of soils based on extensive experimental data. Also, Ohkuba and Terasaki [6] supplied different expressions relating the seismic wave velocities to density, permeability, water content, unconfined compressive strength and modulus of elasticity. Also the use of geophysical methods in foundation engineering has been extensively investigated [7, 8, 9, 1, 11 and 12]. Keçeli [1 and 13] indicated that the determination of the allowable bearing capacity could be obtained by means of the seismic technique. Tezcan et al. [2]; Kaptan et al. [14] has defined an allowable bearing capacity and a settlement as depending on the layer thickness. But, it is well known that the soil bearing capacity, settlement and modulus of elasticity cannot be dependent on the layer thickness. Nevertheless, they obtained also an allowable bearing capacity by changing the notation of the relations in the article of Keçeli [13]. GEOLOGY AND SEISMISITY OF THE STUDY AREA Iraq lies at the north east comer of the Arabian Peninsula. It is a land of contrasting geography with an arid desert in the west and the rugged mountains of the Taurus and Zagros in the north east, separated by the central fertile depression of Mesopotamia: long known as the cradle of civilization. This 175

2 morphology facilitated early human migration and dispersion of knowledge between the East and West. Sumerian cities as old as 6 years are a witness not only to a thriving early civilisation but also to the early industrial use of raw-materials. With respect to geological terms Iraq lies at the transition between the Arabian Shelf in the west and the intensely deformed Taurus and Zagros Suture Zones in the north and north east. The evolution of the Arabian Shelf has been effected by the mobility of the Precambrian basement and by tectonism along the Neo-Tethyan margin. The tectonic framework of Iraq has been affected by intracratonictranspressional and transextensional movements controlled by the interactions of stress along the plate margin with the Precambrian basement fabric and structural grain. After 19, earthquakes in Iraq were better known in amounts ranging from (M=2.7 to 7.2) within the geographical boundaries of Iraq's earthquake map, with the majority of shocks deep in the Earth's crust. The earthquakes in Iraq have a general and distinct increase from the west to the east and from the south to the north. The eastern side of the study area is a relatively wide zone of compressional deformation along the Zagros Taurus active mountain belt, which is entrapped between two plates, the Arabian in the southwest and the Iranian plate in the northeast [15], although the territory of Iraq not directly located on a dense cluster of recent earthquake epicenters; But geodynamic formations for high seismic risks show medium. This will be coupled with the increasing vulnerability of the major highly populated cities. Over the past two decades, the state of seismological research, seismic monitoring and earthquake risk education has seen better times [16]. Tectonically the study area is in a relatively active seismic zone at the northeastern boundaries of the Arabian Plate. The corresponding Zagros - Tauros Belts manifest the subduction of the Arabian plate into the Iranian and Anatolian Plates.The seismic history reveals annual seismic activity of various strength. The north and northeastern zones shows the largest seismic activity with strong diminution in the south and southwestern parts of the country. The geodynamic configurations of Iraq show a medium to high seismic risk, although the territory of Iraq not directly located on a dense cluster of recent earthquake epicenters. This will be coupled with the increasing vulnerability of the major highly populated cities. The state of seismological research, seismic monitoring, and seismic hazard awareness have seen better times during the last two decades. THEORY The response of soils to dynamic loading is controlled mostly by the mechanical properties of the soil. Many types of geotechnical engineering problems are associated with dynamic loading, such as: machine vibrations, seismic loading, liquefaction and cyclic transient loading, etc. The dynamic soil parameters related with dynamic loading are shear wave velocity (Vs), damping ratio (D), shear modulus (G), and Poisson s ratio (ν), which are also used in many non-dynamic type problems. The problem of predicting the bearing capacity of soils from wave propagation properties is that the soil undergoes only very low strain during the wave propogation. However when soils are subjected to earthquake loads or static loads upto failure, they undergo large strains. The P and S-wave velocities are usually denoted by V p and V s respectively. Once the seismic wave velocities are measured, shear modulus (G), Bulk modulus (K), Young s modulus or modulus of elasticity (E), Poisson s ratio (ν), Oedometric modulus (E c) and other elastic parameters may be obtained from the Equations (1) to (8) below. These expressions make the determination of the allowable bearing capacity possible. 1) Shear modulus (G) relates with shear wave velocity as expressed in Equation (1): G = ρ V s 2 (1) Where ρ is the mass density equal to ρ = γ/g, γ is the unit weight of the soil and gis the acceleration due to gravity which isgiven as 9.8g m.s 2. The unit mass density relates with P-wave velocity V pas shown in Equation (2) γ = γ +.2 V p (2) Tezcan et al., [2] defines γ o as the reference unit weight value in kn/m 3.γ o= 16 for loose, sandy and clayey soil. According to [17], some elastic parameters were defined in Equations (3) to (9): 2) Young s modulus/modulus of elasticity (E d) E = ρ V p 2 (3) 3) Oedometric modulus (Ec) given by Equation (4) E c = E (1-v)/(1+v)(1-2v) (4) 4) Bulk modulus (K) is expressed in Equation (5) as K =2(1+v)G / 3(1-2v) (5) 5) Poisson s ratio (ν) is given as in Equation (6) as ν=(α -2) / 2(α-1) (6) where α= E c / G= (V p / V s) 2 (7) 6) Subgrade Coefficient ks, ultimate bearing capacity q ult and allowable bearing capacity q all are given by Equations (8) to (1) according to [18] and [19] as, k s = 4 γ V s = 4 q ult (8) 7) Ultimate Bearing Capacity (q ult) q ult=k s/4= 4 γ V s/4=.1 γ V s (9) for shallow foundation [18] 8) Allowable Bearing Capacity (q all) q all=q ult / n =.1 γv s / n (1) Where n is the factor of safety (n = 4. for soils) 176

3 Low compressibility and compliance and high bearing capacity are required in construction or foundation sites which can be determined from the reciprocal values of bulk modulus (K) and Young s modulus (E) respectively. Shear modulus and shear wave velocity of the soil layer is reduced with increasing shear strain [2]. MATERIALS AND METHODS OF DATA ANALYSIS Resources of Geophysical and Geotechnical Data For many projects in Iraq the engineering parameters of the different strata from many geophysical and geotechnical investigation reports are collected [21], and a data base is prepared for static, shear and compression wave velocities parameters of different soils for most zones in Iraq. The available geotechnical and geophysical reports were collected from different forty nine projects like gas power station, cement plant, multi-story buildings, thermal Power plant, water sewerage system, oil refinery and other projects from different locations of Iraq and the data has been grouped into nine regions, based on the governorates, namely (North, Eastern North, Western North, Middle, East, West, Western South, Eastern South and South) as shown in Table (1) and Figures (1 and 2), where the zones borders are according to the governorate boundaries. These parameters are evaluated from field and laboratory tests results of the available geotechnical and geophysical investigation reports collected from different resource such National Center of Construction Laboratories and Research (NCCLR), engineering consulting bureaus of Baghdad and Al-Nahrain universities together with some private companies and laboratories such as Andrea Engineering Test labs, AL-Ahmed Engineering Test lab and others. When the seismic wave velocities, V s and V p, are obtained, several parameters of elasticity, like shear modulus G, oedometric modulus of elasticity E c, modulus of elasticity E (Young s modulus), bulk modulus K, and Poisson s ratio ν may be obtained from the Equations (1) to (7). Also the subgrade modulus k s, ultimate and allowable bearing capacities are onbtained depending on the Equations (8), (9) and (1) respectively and as will be presented in Table (2). Figure 1. Map study of seismic zones in Iraq [21 Figure 2. Map study of projects locations in Iraq [21] 177

4 NO. Zone Governorate Site symbol 1 Table 1: Iraq seismic zones and sites symbols according to [21] Map symbol NO. Zone Governorate Site symbol Dohuk N Middle Babylon M Dohuk N Diyala E1 27 North East 3 Irbil N Diyala E Irbil N West Anbar W2 3 5 Sulaymaniyah EN1 5 3 Karbala WS Sulaymaniyah EN Karbala WS Kirkuk EN Karbala WS3 33 Eastern Western 8 Kirkuk EN North south Karbala WS Kirkuk EN Najaf WS Kirkuk EN Najaf WS Kirkuk EN Missan ES Mosul WN Eastern Missan ES Western Mosul WN South Missan ES North Mosul WN Missan ES Salah Al-den WN Al Dewaniya S Salah Al-den WN Al Dewaniya S Baghdad M Al Nasiriya S Baghdad M Al Nasiriya S Baghdad M Al Nasiriya S5 45 South 2 Baghdad M Al Basrah S Middle Baghdad M Al Basrah S Baghdad M Al Basrah S Baghdad M Al Basrah S Baghdad M Al Basrah S Babylon M9 25 Map symbol Investigated Soil Parameters The data for soil parameters investigated were taken from geotechnical and geophysical investigation reports for most Iraqi soil. Soil parameters such as; γ wet,γ dry, c and ϕ which are given in the geotechnical reports had evaluated by the field or laboratory tests, also the depth of the water table and description of the soil types according to borehole logs were presented in these reports. While the seismic wave velocities V s, V p values are listed in the geophysical reports that been evaluated from the cross hole and down hole tests. The geotechnical bore hole should be the same for the geophysical bore hole or might be different bore hole but they should be near to each other or collected either from the same borehole or two adjacent ones which have the same soil layers profile. The soil strength parameters (c or ϕ ) were evaluated by the correlations from N value (SPT) according to the type of soil when their values are not mentioned or evaluated in some of the soil investigation reports. Soil Parameters Evaluation As mentioned earlier the soil parameters γ wet,γ dry, c, ϕ determined from field and laboratory tests results are presented in the geotechnical investigation reports, and the dynamic parameters V s and V p are prepared from geophysical investigations reports. Once seismic wave velocities, V p and V s, together with the density are measured, many parameters of elasticity, such as shear modulus G, oedometric modulus of 178

5 elasticity E c, modulus of elasticity E (Young s modulus), bulk modulus K, and Poisson s ratio ν may be obtained from the Equations (1) to (7). Also the subgrade modulus k s, ultimate and allowable bearing capacities are obtained depending on the Equations (8), (9) and (1) respectively. able (2) presents the geotechnical and geophysical parameters collected and evaluated together with the values of k s, q ult and q all estimated. Table 2: Soil properties and bearing capacity in different locations and zones of Iraq. No. Site Depth Soil Type WT γwet γdry c ϕ Vp Vs E 1 3 G 1 3 ν K 1 6 Ks 1 8 qult qall qult qall qall m m kn/m 3 kn/m 3 kn/m 2 ( o ) m/s m/s kn/m 2 kn/m 2 kn/m 2 N/m 2.s kn/m 2 kn/m 2 kn/m 2 n=4 n=3 1 N 1-3 Brown silty clay with little fragment 3-1 Dense grey gravel with sand to gravel with silt and sand (GP,GP-GM) NO W.T N Reddish brown rock > fragment of limestone with silty sand 3 N Brown silt/clay with No few sand & trace of W.T gravel,(cl-ml) 4. N4-6 Brown silt/clay with few sand,(cl) 6-1 Brown silt/clay with little sand& few gravel,(cl-ml) EN 1-4 Unknown Unknown EN 2-5 Unknown Unknown EN 3-4 Stiff brown lean to fat clay (CL, CH) 8 EN Medium brown silty Sand (SM) 6-12 Dense grey gravel with sand to gravel with silt and sand(gp,,gp-gm) -2 Brown silt with (ML) 2-6 Stiff brown lean clay (CL) 6-15 Stiff brown to grey lean clay (CL) 9 EN Stiff brown sandy silt (ML) Very stiff to hard brown lean to fat CLAY (CL,CH) 15-2 Very dense silty gravel with sand (GM) 1 seismic method [17] 2 conventional method [18] >

6 Table (2): Continue No. Site Depth Soil Type WT γwet γdry c ϕ Vp Vs E 1 3 G 1 3 ν K 1 6 Ks 1 8 qult qall qult qall qall m m kn/m 3 kn/m 3 kn/m 2 ( o ) m/s m/s kn/m 2 kn/m 2 kn/m 2 N/m 2.s kn/m 2 kn/m 2 kn/m 2 n=4 n=3 1 EN 6-1 Stiff to very stiff brown lean or fat clay (CL,CH) 11 EN 7-1 Very stiff to hard brown lean clay (CL) 12 WN 1-15 Very Stiff to hard moderately gypseous, brown lean to fat clay (CL,CH) WN Dark brown sand silt > with rock fragments Brown sand gravel WN Medium dense to very dense grey silty gravel with sand (GM,GP) WN 4-2 Grey gravel with silt sometimes with sand(gm) 2-5 Medium stiff to hard brown lean clay sometimes with sand and gravel to silt(cl,ml) 5-1 Dense to very dense grey gravel with silt and sand to gravel 16 WN 5-4 Highly gypseoussilty sand to sandy silt with little gravel 4-2 Silty sand with gravel to sand with gravel 17 M 1-1 Stiff to very stiff brown to green slightly gypseousmarly lean to fat clay and silt clay (CL,CH,CL- ML) 1-16 Loose to medium grey to green silty sand (SM) No W.t M 2-8 Medium to stiff to very stiff brown lean clay (CL) 8-15 Loose to dense grey silty sand to clayey silty sand M 3-1 Soft to stiff brown lean or fat clay or silt sometimes lean clay with sand to sandy silt (CL,CH,ML) Medium to very dense grey silt sand or clayey sand (SM,SC) 2 M 4-1 Stiff to very stiff brown lean clay

7 1-15 Stiff to very stiff grey to brown to black lean clay sometimes with sand (CL) 15-2 Medium grey silty sand (SM) M Loose to medium grey silty sand (SM) 22 M 6-1 Brown clayey silt to sandy silt with filling materials, organic to salts (ML) 1-15 Brown to grey silty clay to clayey silt (ML,CL,CH) 15-2 Grey sand to silty or clayey sand to gravilly sand (SM,GP) 23 M7-6 Medium stiff to stiff brown fat clay (CH) 6-12 Very stiff brown lean clay (CL) Medium dense to dense silty sand to silty sand with gravel M8 Stiff to very stiff brown lean to fat 1.58 CLAY(CH) Medium to very dense grey silty sand (SM) 25 M 9-5 Very soft to stiff brown lean to fat clay sometimes with sand (CL,CH) Losse to dense grey silty SAND(SM) M Grayish sandy silty clay soil, medium consistency Grayish silty sand soil, medium dense E 1-1 Very stiff to hard brown to grisg brown marl lean clay (CL) 28 E 2-15 Stiff brown clay (CL) W 2-5 Stiff to very stiff brown lean clay(cl) 5-1 Loose to dense grey to dark grey silty sand and clayey silty sand sometimes with gravel (SM,SC-SM) WS 1-5 Stiff brown to green

8 lean clay 5-9 Loose to medium brown to grey silty sand (SW-SM) 9-15 Very dense grey silty sand WS 2-18 Loose to very dense off white yellow, light brown to grey sometimes moderately gypseoussilty sand or sand with silt or sand (SM,SP- SM,SP) NO W.T WS Stiff brown silty to moderately gypseous fat clay (CH) 34 WS Dense white to yellow slightly to moderately gypseous sand with silt to silty sand with gravel (SP,SM) Dense to very dense white to yellow sand with silt (SP,SM) Very dense white to yellow sand with silt to silty sand (SP,SM) WS 5-1 Very loose grading to very dense slightly to moderately gypseous sand (sm) or sand with silt (SP-SM) WS6-1.2 Medium- dense light brown slightly gypseoussilty sand (SM) Medium- dense to very dense light brown sand (SP) 7-1 Very dense light brown silty sand (SM) 37 ES 1-6 Stiff to very stiff brown to green sandy lean to fat CLAY (CL,CH) 6-14 Loose grey silty sand (SM) 14-2 Stiff to very stiff brown to green fat clay (CH) 38 ES 2-5 Medium stiff to stiff brown lean to fat clay (CL,CH) 5-8 Stiff brown lean to fat clay (CL,CH) 8-17 Stiff brown lean clay (CL)

9 `39 ES 3-9 Medium stiff to stiff brown lean to fat clay (CL,CH) 9-18 Stiff brown lean CLAY (CL) 4 ES Medium stiff to stiff brown lean to fat clay (CL,CH) Loose grey silty sand Stiff brown lean clay (CL) S 1-5 Stiff to very stiff brown to green sandy lean to fat clay (CL,CH) Loose grey silty sand (SM) Stiff to very stiff brown to green fat clay (CH) S Brown lean clay(cl) loose grey silty sand layer (SM) 2-1 Medium stiff to very stiff brown to green lean to fat clay (CL,CH) S 3-8 Medium stiff to hard brown or grey or dark grey lean to fat clay sometimes with sand to sandy lean clay or silt or sandy silt(cl,ch,ml) 8-15 Dense to very dense grey or dark grey or brown silty sand otsilty clayey sand or sand with silt (SM,SC-SM,SP-SM) 44 S 4-12 Soft to medium black, brown, green light, green lean to fat clay (CL,CH) Loose grey silty sand (SM) Very stiff brown, green lean clay(cl) S 5-4 Very stiff brown lean clay (CL) 4-1 Stiff to hard brown lean to fat clay (CL,CH) S 6-3 Medium light brown gypseous soil 3-1 Medium to very dense light brown to grey slightly to highly gypseoussilty sand or sand with silt or sand (SM,SP) S Grey gypseous

10 sand (SM) Grey gypseous silty sand (SM) 48 S 8-6 Very soft to stiff brown lean clay (CL) 6-15 Very loose grey clayey silty sand (SC-SM) 49 S 9-6 Medium to stiff brown lean to fat clay (CL,CH) 6-12 Stiff brown lean clay (CL) 5 S 1-1 Very soft to stiff brown lean or fat clay(cl,ch) Grey silty sand (SM) Very soft to stiff lean clay (CL) RESULTS AND DISCUSSION Evaluation of the Allowable Bearing Capacity In this research, geotechnical parameters, i.e. Young modulus, bulk modulus, shear modulus, subgrade modulus were obtained from the result of the secondary wave velocities for each layer of the areas of study using Equations (1) to (8). These relationships also led to the determination of the ultimate bearing capacity and the allowable bearing capacity according to the Equations (9) and (1) respectively. The results obtained are presented in Table (2). Also, following the classical procedure of [18], the ultimate and allowable bearing capacities were determined, by assuming the factor of safety equal to n=3 and 4 and as given in Table (2) for the purpose of comparison. The numerical values of the ultimate and allowable bearing capacities determined in accordance with the conventional Terzaghi theory and seismic technique (Tezcan et al., 26) for cohesive soils are plotted in Figures (3 and 4 respectively). And the results of ultimate and allowable bearing capacities estimated from both methods for cohesionless soils are plotted in Figures (5 and 6 respectively). Two separate linear regression lines were also shown in the Figures (3 and 5), for the purpose of indicating the average values of ultimate bearing pressure determined by seismic and conventional methods. For cohesive and cohesionless soils it can be indicated that up to a shear wave velocity of 3 m/s and 4 m/s respectively, the shear wave velocity predicts the bearing capacity relatively well. Above 3 m/s and 4 m/s the scatter is large and it looks like there are quite many points that are falling below the bearing capacity estimated by the shear wave velocity. The linear regression line indicates for Vs values smaller than 3 m/s and 4 m/s a narrow band, which should be regarded as quite acceptable. The seismic method proposed herein yields allowable bearing cabacities (on the order of 1 to 2%) greater than those of the conventional method for V s values smaller than 4 m/s. In fact, the conventional method fails to produce reliable and consistent results for relatively strong soils, because it is difficult to determine the appropriate soil parameters c and ϕ for use in the conventional method [22]. Therefore, from the results the use of seismic method can give an order of magnitude for such strong soils with V s > 3 m/s for cohesive soils and >4 m/s for cohesionless soils. The allowable bearing capacity has been obtained at different sites in various regions of Iraq as shown in Table (2) and Figures (4 and 6) for cohesive and cohesionless soils respectively. Factor of safety used for allowable bearing capacity estimated from shear wave velocity is 4 (Tezcan, 26), and allowable bearing capacity is estimated from Terzaghi equation using factor of safety, n=3 and 4, it can be indicated that values from shear wave velocity are close to that from conventional method till Vs=3 m/s for cohesive soils and 4 m/s for cohesionless soils and above these velocities the scatter is large. It can be concluded from these graphs that allowable bearing capacity estimated from shear wave velocity may be obtained for n less than 4 for soils that have Vs less and equal than 4 m/s. Table (3) shows the range of values for seismic wave velocities and allowable bearing capacity for different types of soil with various description. In order to demonstrate that the technique used covers all soils types, the values of seismic velocities and allowable bearing capacity given in Table (3) are compared with the values for foundation materials given in building codes with entire seismic velocities covering all soils and rocks types and with the values calculated by using seismic velocities of soils and rocks [23] which has been obtained at thousands of construction sites in various regions of Turkey since 199. The comparison shows that the allowable bearing capacity values obtained from hard through loose soils were in agreement with the building codes and Keçeli [23] values. Thus, allowable bearing capacity values obtained by the technique proposed here are evaluated for accuracy.table (3) also demonstrated awide range for soil types description. Allowable bearing capacity for cohesive and cohesionless soils is plotted in each case against the shear wave velocity for each of the layers as given in Figures (4 and 6 respectively) which shows linear empirical relationships between the allowable 184

11 bearing capacity and the shear wave velocity. This is demonstrated in Equations (11 and 12): For Cohesive Soils q all (kn/m 2 ) =(.53V s -.73) 1 2 (11) For Cohesionless Soils q all(kn/m 2 )=(.48V s + 4.E-6) 1 2 (12) The slopes in the equations are dimensionless constant which gives the coefficient of elastic deformability of shallow foundation geomaterial caused by the load applied on the considered shallow foundations. The slopes of qa and Vs plots reflecting the impulse/driving force producing the deformability of a layers per cubic meter of the foundation layers is about.5 kns m 3. From Equations (11 and 12), layers near surface are more relatively susceptible to deformation than sublayers based on the magnitudes of qall and shear modulus G which is plotted against Vs for cohesive and cohesionless soils as shown in Figures (7 and 8 respectively). As it increases, the degree of elastic deformation decreases. Although consolidation of subsurface increases with depth due to compaction, other tectonically induced secondary structures like divide, fault lineament and fold within the sedimentary facies could cause voids in the subsurface thereby leading to elastic deformation of subsurface. The layers also show polynomial relationships between q a and G as shown in Figures (7 and 8) for cohesive and cohesioless soils respectively. The unit weight of the soil layer also determines the shear modulus and S-wave velocity in Equation (1) constitutes the significant variation noticed in layers in the relation between allowable bearing capacity q a and shear modulus G which is given by Equations (13 and 14): For Cohesive Soils q all (kn/m 2 ) =(-4E-6G G ) 1 2 (13) For Cohesionless Soils q all (kn/m 2 ) = (-1E-6G G ) 1 2 (14) The highest value of q all for sublayers is seen on north zone and reduces through middle and south of Iraq. This trend shows that low allowable bearing capacity is associated with zones that are highly undrained with water while the high bearing capacity is associated with zones that are unsaturated with water. The appeared transition in magnitude of allowable bearing capacity toward high value with depth is due to cementation/compaction which increases with depth. The results show that the higher value of allowable bearing capacity in the study areas is obtained in North of Iraq (i.e., N 1) with a value of about 48 kn/m 2 and the lowest is at Middle and South regions (i.e., M 1 and S 1 respectively) with avalue of about 5 kn/m 2. According to the depths of investigation and soil descriptions shown in Table (2), three layers with approximate depths can be considered for investigation, layer one extends to about 6m from the ground surface, while layer two extends for a depth 6m to 1m and third one for depth between 1m to 15m. q all value has an average value of about 142 kn/m 2 for layer one, while the average bearing capacity for layer two is about 176 kn/m 2 and about 162 kn/m 2 for layer three. With respect to cohesive and non-cohesive soils, the results of the minimum, maximum and average values of shear modulus, G, and allowable bearing capacity, q all appears for the layers to a depth of about 15m from ground surface in the study areas are as shown in Table (4). Table 3: Allowable bearing capacity for different soil descriptions. Soil type Vp -range (m/s) Vs -range Rock Fragment of Limestone with Silty Sand to Gravel with Sand or Gravel with Silt and Sand Silty Sand (Loose) Silty Sand (Medium) Silty Sand (Dense) Gypseous Sand to Silty Sand Clay (Very Soft to Soft) Clay (Medium) Clay (Stiff) Clay (Very Stiff to Hard) (m/s) qall 1 2 (kn/ m 2 )

12 Table 4: Shear modulus and allowable bearing capacity for different depths in cohesive and cohesionless soils. Soil type Cohesive soil Depth Approx. (m) G 1 3 value (kn/m 2 ) qall 1 2 -value (kn/m 2 ) Min. Avg. Max. Min. Avg. Max Cohesionless soil seismic method [17] conventional method [18] q ult ( 1 2 kpa) V s (m/sec) Figure 3: Ultimate bearing capacity against shear wave velocity for cohesive soils. 186

13 q all ( 1 2 kpa) seismic method-n=4 [17] conventional method-n=4 [18] conventional method-n=3 [18] V s (m/sec) Figure 4: Allowable bearing capacity against shear wave velocity for cohesive soils. 7 6 seismic method [17] conventional method [18] 5 qall( 1 2 kpa) V s (m/sec) Figure 5: Ultimate bearing capacity against shear wave velocity for cohesionless soils. 187

14 seismic.22 method-n=4 [17] 4 conventional.8 method-n=4 [18] 5 conventional.45 method-n=3 [18] q al l ( 1 2 kpa) V s (m/sec) Figure 6: Allowable bearing capacity against shear wave velocity for cohesionless soils q all ( 1 2 kn/m 2 ) G( 1 3 kpa) Figure 7: Allowable bearing capacity against shear modulus for cohesive soils. 188

15 q all ( 1 2 kn/m 2 ) G( 1 3 kpa) Figure 8: Allowable bearing capacity against shear modulus for cohesionless soils. Evaluation of the Soil Parameters This study aimed also at obtaining model equations from the correlations of the shear wave velocities and the different geotechnical parameters studied. This was to obtain direct relationships between the S-wave velocity and the geotechnical parameters. These equations can be used for a quick evaluation and inexpensive estimation of the various soil parameters. The graphs of the parameters were plotted against the shear wave velocities. Also, the relations and correlations have been investigated between seismic velocities and geotechnical parameters using the best fit curve. The relations give obvious variations in the geotechnical properties affecting the velocities differently in different parts of the velocity ranges. The graphs of modulus of elasticity, E, bulk modulus, K, and subgrade modulus, k s, against the S-wave velocity (Figures 9, 11 and 13 respectively) gave the empirical equations defined in Equations (15, 16 and 17) for cohesive soils. And the plots of modulus of elasticity, E, bulk modulus, K, and subgrade modulus, k s, against the S-wave velocity (Figures 1, 12 and 14 respectively) gave the empirical equations defined in Equations (18, 19 and 2) for cohesionless soils. The equations shows polynomial relationships between E with Vs and exponential relationship between K and V s and linear relationship between k s with V s. The minimum, maximum, and average values of modulus of elasticity, E, bulk modulus, K, and subgrade modulus, k s for the cohesive and cohesionless soils estimated to a depth of about 15m from ground surface in the study areas are given in Table (4). This result shows that the lower layers are more compressed than the first layer. This may be as a result of the geologic formation of these layers, their level of saturation and the level of cementation of the geomaterial. It was also indicated that the Young modulus of the subsurface increased in direct proportion with the seismic wave velocity and the two parameters generally increased with depth. This also shows that the second layer has more strength than the other layers. The results also shows that the first layer would deform more easily under shear stress than the lower layers. The bulk modulus results further confirmed that the second geologic layer to be more competent than the first layer. The subgrade modulus ranges also reveals that the second geologic layer is more competent than the first layer. For Cohesive Soils E (kn/m 2 ) = (.47V s V s-47.13) 1 3 (15) K (kn/m 2 ) = (.1566e.74Vs ) 1 6 (16) k s (N/m 2.s)= (.8V s -.119) 1 8 (17) For Cohesionless Soils E (kn/m 2 ) = (.47 V s V s ) 1 3 (18) K (kn/m 2 ) = (.2789e.5Vs ) 1 6 (19) k s (N/m 2.s) = (.8V s -.2) 1 8 (2) 189

16 Table 4: Soil parameters for different depths in cohesive and cohesionless soils in the study areas. Soil type Depth Approx. (m) E 1 3 -value (kn/m 2 ) K 1 6 -value (kn/m 2 ) ks 1 8 -value (N/m 2.s) Min. Avg. Max. Min. Avg. Max. Min. Avg. Max. Cohesive soil Cohesionless soil E( 1 3 kpa) V s (m/sec) Figure 9: Young s modulus against shear wave velocity for cohesive soils. 19

17 E( 1 3 kpa) V s (m/sec) Figure 1: Young s modulus against shear wave velocity for cohesionless soils K( 1 6 kpa) V s (m/sec) Figure 11: Bulk modulus against shear wave velocity for cohesive soils. 191

18 K( 1 6 kpa) V s (m/sec) Figure 12: Bulk modulus against shear wave velocity for cohesionless soils k s ( 1 8 N/m 2.sec) V s (m/sec) Figure 13: Subgrade modulus against shear wave velocity for cohesive soils. 192

19 k s ( 1 8 N/m 2.sec) V s (m/sec) Figure 14: Subgrade modulus against shear wave velocity for cohesionless soils. CONCLUSION The conclusions that can be drawn from this study can be summarized as follows: 1. Ranges for values of seismic wave velocities and allowable bearing capacity for different types of soil with various description are presented, extending the knowledge for the limit of theses values. Also the allowable bearing capacity values obtained from hard through loose soils were in agreement with the building codes and references values. 2. Correlations between seismic velocity V s and allowable bearing capacity has been obtained. This relationship show direct proportionalities between V s with q all. The results show that the range of bearing capacity for the study area was btween 5 and 48 kn/m 2, being heighst at north regions and reduces through middle and south regions of Iraq. 3. Shear wave velocity can be considered as most powerfull soil parameter representing a family of geotechnical soil parameters, such as compressive strength, shear rigidity, angle of internal friction, cohesion etc. 4. Extensive bore hole and laboratory testing of soil samples would no longer be needed if the compression and shear-wave velocities are measured, as accurately as possible, right under the foundation level. Then, the allowable bearing capacity and the coefficient of subgrade reaction can be obtained. Also shear wave velocities can be used to determine the geotechnical parameters of a site that can be used to easily characterize its subsurface condition. 5. The cross and down hole tests results revealed three geologic layers with the second layer being more competent. q all value has an average value of about 142 kn/m 2 for layer one, while the average bearing capacity for layer two is about 176 kn/m 2 and about 162 kn/m 2 for layer three. 6. The empirical equations obtained can be used to evaluate and predict the geotechnical parameters of the study area studied. 7. The results obtained are applicable to any area with a similar geological formation as the current study area, but a similar procedure may be applicable in other areas as well. 8. Empirical expressions estimated for the allowable bearing capacity using shear wave velocities measured at low shear strains, is appropriate to produce reliable results for a wide range of soil conditions. Also allowable bearing capacity estimated from shear wave velocity may be obtained for factor of safety less than 4 for soils that have Vs less and equal to 4 m/s. 9. Allowable bearing capacity increases with increase in shear modulus enhanced by high shear wave velocity. For cohesive and cohesionless soils it was indicated that up to a shear wave velocity of 3 m/s and 4 m/s respectively, the shear wave velocity predicts the bearing capacity relatively well. 1. Using the empirical formulations generated from the sites data, surface layer has been found to show lower bearing capacity than layers two and three based on the the coefficients of elastic deformability of shallow foundation realized from the plots of q all against G. The layers also show relationships of seconed order 193

20 between q a and G. 11. Correlations between seismic velocity V s and geotechnical properties have been derived. These relations show polynomial relationships between E with Vs and exponential relationship between K and V s and linear relationship between k s with V s. REFERENCES [1] Grant S.and West G. F., 1965, Interpretation Theory in Ap- plied Geophysics, McGraw-Hill, New York, p [2] Tezcan, S. S., Ozdemir, Z. and Keceli, A. 29, Seismic Tech- nique to Determine the Allowable Bearing Pressure for Shallow Foundations in Soils Sand Socks, Acta Geophy- sica, Vol. 57, No. 2, pp [3] Schulze, W.E., 1943, Grundbau, Deutsche Forschungsgesellschaft für Bodenmechanik, 7th ed., B.G. Taubner Publishers, Leipzig, Germany. Also available: Technical University of Istanbul, Issue 48, No DK624-15, Uçler Printing House, Istanbul, Turkiye. [4] Hardin, B. O., and Black, W.L., 1968, Vibration modulus of normally consolidated clays, Journal of the Soil Mechanics and Foundation Division, ASCE, Vol.94, No. SM2, pp [5] Hardin B. O. and Drnevich V. P., 1972, Shear Modulus and Damping in Soils, Journal of Soil Mechanics and Foun-dation Division ASCE, Vol. 98, pp [6] Ohkubo, T., and Terasaki, A., 1976, Physical property and seismic wave velocity of Rocks, OYO Corporation, Japan. [7] Imai T. and Yoshimura, 1976, The Relation of Mechanical Properties of Soils to P- and S-Waves Velocities for Soil in Japan, Urana Research Institute, OYO Corporation, Tokyo. [8] Willkens, R., Simmons G. and Caruso, L., 1984, The Ration Vp / Vs as a discriminant of composition for siliceous limestones, Geophysics, 49(11) [9] Phillips, D. E., Han, D. H. and Zoback, M. D., 1989, Empirical relationships among seismic velocity, effective pressure, porosity, and clay content in sandstone, Geophysics, 54:(1), pp [1] Keçeli, A. D., 199, Determination of bearing capacity of soils by means of seismic methods ( in Turkish), Geophysical Journal, Ankara, Turkiye, 4, pp [11] Sully, J. P. and Campanella, R.G., 1995, Evaluation of in situ anisotropy from crosshole and downhole shear wave velocities measurements, Geotechnique, 45(2):pp [12] Pyrak-Nolte, L. J., Roy, S. and Mullenbach, B., l., 1996, Interface waves propagated along a fracture, Journal of Applied Geophysics, (35), pp [13] Keçeli, A. D., 2, The Determination of the Presumptive Bearing Capacity by means of the Seismic Method, Geophysical Journal, Ankara, Turkey (in Turkish), 14: 1-2. [14] Kaptan, K., Ozdemir Z. and Tezcan S., 211, Review A refined formula for the allowable soil pressure using shear wave velocities The Journal of Soil Science and Environmental Management, Vol. 2,7, pp [15] Jasim, N. A., 213, Seismicity Evaluation Of Central And Southern Iraq, M.Sc. Thesis. Department of Geology, College of Science, University of Baghdad. Baghdad, Iraq. [16] Alsinawi, S.and Alqasrani, Z,Q., 23, "Earthquake hazard consideration for Iraq," Presented at proceeding of the international Conference of Earthquake Engineering and Seismology, May 12-14, Tehran, Iran. [17] Tezcan, S. S., Ozdemir, Z. and Keceli, A., 26, Allowable Bear- ing Capacity of Shallow Foundations Based on Shear Wave Velocity, Journal of Geotechnical and Geoenvi- ronmental Engineering, Vol. 24, pp [18] Terzaghi, K., and Peck, R.B., 1967, Soil Mechanics in Engineering Practice, 2nd ed., John Wiley&Sons, London. [19] Bowles, J.E., 1982, Foundation Analysis and Design, 3rd ed., McGraw-Hill Book Company, New York. [2] Massarsch, K. R., 24, Deformation properties of fine-grained soils from seismic tests, Keynote lecture, International Conference on Site Characterization, ISC 2, Sept. 24, Porto, [21] Mohammed Shafiqu, Q. S., and Abdulrasool M. A., 217 Database of Dynamic Soil Properties for Most Iraq Soils, American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS), Vol. 37, No. 1, pp [22] Kaptan, K., 212, A refined formula for the allowable soil pressure using shear wave velocities, Journal of Civil Engineering and Construction Technology Vol. 3(3), pp org/jcect [23] Keçeli, A. D., 212, Soil Parameters which can be Determined with Seismic Velocities, Jeofizik, 16,