Determination of elastic moduli and bearing capacity of sediments using geophysical and cone penetration test techniques in Yenagoa, Southern Nigeria

ABSTRACT In order to quantify the P- and S-wave velocities, dynamic elastic moduli and bearing capacity of shallow alluvial sediments, seismic refraction and cone penetration test (CPTu) soundings were carried out in two sites in Yenagoa. The seismic refraction data was analysed using the intercept–time technique to obtain the seismic velocities which were subsequently used to estimate the dynamic elastic moduli. The relevant CPTu data were emplaced into an established empirical equation to determine the shear wave velocity (V s), with which the compressional wave velocity (V p) was estimated. Combing the compressional and shear wave velocities, the dynamic elastic moduli of the shallow sediments were determined within the depth range of 0.5–8.0 m. On comparison, it was observed that the average values of V p and V s from the two methods are fairly in agreement. Significant difference in the average values was only observed in the dynamic elastic moduli. Correlation of the Vs-wave and the dynamic moduli from the CPTu data show linear relationship between S-wave velocity and the dynamic elastic moduli with correlation coefficients (R 2) greater than 0.9 in all cases. These elastic moduli values can be used for the design of foundation of structures, site response and settlement analysis.


Introduction
In the design of foundations for sensitive engineering structures, values of the dynamic elastic moduli of the subsurface are crucial requirements. Dynamic moduli refer to the elastic stiffness of a geomaterial often derived from seismic velocities in combination with density (Fjaer 2019). The dynamic elastic properties prior to rock failure are Young's modulus, shear modulus, bulk modulus and Poisson's ratio. These parameters provide valuable information about the subsurface rock and thus play an important role in solving geomechanical problems. For instance, knowledge of the values of the dynamic elastic properties is useful for the design of foundations of structures on which vibrating machines are placed to avoid resonance during operation (Mcdowell 1990), and in locating and extracting mineral resources (Emujakporue and Ekine 2009). Dynamic moduli values are also essential for dynamic response analysis and soil-structure interaction problems and can play an important role in the study of liquefaction potential under seismic loading (Youd et al. 2001). Aside, in determining soil competent parameters such as concentration Index (Ci), material index (Mi), stress ratio (Si), etc., the dynamic elastic moduli are key input parameters, and thus are useful for the characterisation of soils in terms of geotechnical and mechanical properties (Robertson et al. 1995). Furthermore, in reservoir studies, rock mass elastic moduli play important role in wellbore stability, fraction prediction (Chang et al. 2006;Abdulraheem et al. 2009) and are key requirements for reservoir-scale modelling (Berard and Cornet 2003).
The dynamic elastic properties have been studied by many authors in different geological settings. For instance, Othman (2005) determined the elastic constants and attenuation coefficients using an ultrasonic technique for cores from an oil well in northeast Qatar. Studies of dynamic moduli were also carried out and reported by Emujakporue and Ekine (2009); Ajayi et al. (2014); Alaminiokuma and Omigie (2018); George et al. (2010) in parts of the Niger Delta. Singh et al. (2015) estimated the dynamic elastic moduli values of alluvium sediments for the design of foundations for a structure intended to be used as a nuclear power plant in India using seismic velocities derived from cross-hole seismic survey. The results show that the compressional P-wave velocity varies from 442 to 1287 m/s while the shear wave velocity shows a variation of 228-627 m/s. The Young's modulus varies from 0.29 to 1.62 GPa, the bulk modulus varies from 0.19 to 1.58 GPa, the shear modulus from 0.12 to 0.62 GPa and the Poisson's ratio varies from 0.24 to 0.33.
Inspite of the usefulness of the elastic parameters of the near-surface soil, determination of these parameters has not received adequate attention and thus have remained largely inadequately described in the Niger Delta. Generally, elastic properties of rocks are determined using static (high strain) and dynamic (low strain) methods. Static methods are conducted in the laboratory with specific test equipment that can contain core specimens. In this method, specimens are usually compressed within the equipment until failure is observed. In this approach, stress-strain curves generated are recorded using a computer and the dynamic properties determined from the curves. On the other hand, dynamic methods use compressional and shear wave velocities as input parameters substituted into Hookean equations. Generally, geophysical measurements particularly by seismic pulse techniques are being increasingly used to determine the elastic properties. This is due largely because the tests are carried out in situ at an appropriate strain rate. Geophysical methods used to obtain in situ seismic velocities include crosshole seismics, multi-channel analysis of surface waves (MASW) and surface refraction surveying techniques. However, due to their environmental, time and cost ineffectiveness, surface non-invasive seismic methods have become more favoured. It is pertinent to mention that in the design of engineering projects, characterisation of the soil elastic moduli is not enough. The soil-bearing capacity and the settlement or subgrade reaction are additional key factors (Shafiqu et al. 2018). Keceli (1990Keceli ( , 2000 indicated that allowable capacity can be determined using seismic technique.
In this study, attempt is made to evaluate the seismic velocities, dynamic elastic moduli and bearing capacity of shallow alluvial sediments in two sites. For purposes of comparison, seismic refraction and cone penetration methods are used.

Location and geological setting of the study area
Yenagoa is the capital city of Bayelsa State. It is located within the Niger Delta Basin in the southern part of Nigeria. The study area is within Yenagoa and environs, an area of about 50 kKm 2 . The coordinates of Yenagoa are longitudes 006° 10´ 3.07ʹʹ and 00 6° 25´ 10.53ʹʹ east of the prime meridian and latitudes 04° 51´ 39.73ʹʹ and 05° .2´ 25.53ʹʹ north of the equator. Geographically, Yenagoa is situated within the coastal area of the Niger Delta sedimentary basin ( Figure 1). The ground surface is relatively flat and the sloping is gentle seawards (Okiongbo and Mebine 2015). Its mean elevation is about 8 m above mean sea level (Akpokodje and Etu-Efeotor 1987). The area has a tropical rain forest climate characterised by rainy season and dry season. April to October constitute the rainy season with a very brief dry period in August, while November to March is the period for the dry season. The average annual rainfall is about 4,500 mm (Akpokodje 1986), and much of the rain falls during the rainy season. Temperature variation is between 25 and 32°C. The people are mainly into subsistence fishing and farming. Akpokodje (1986) reported that Yenagoa is within the freshwater and meander belt geomorphic unit of the Niger Delta basin. The Niger Delta is an alluvial plain consisting of various types of Quaternary sediments. These sediments overly the Benin Formation. The Quaternary deposits are made up of floodplain deposits such as clay, silt, slity-clayey sand (Abam 1999). The geostratigraphy of the sediments consists of a fining-up sequence of sand overlain by silt and clay which indicate a fluvial environment of deposition (Short and Stauble 1967;Amajor 1991). Most small and medium civil engineering structures are constructed on the Quaternary deposits which vary greatly both in type and depth. The nature and properties of the sediments are dependent on the types of depositional environment under which they were formed. The Benin, Agbada and Akata formations are the key subsurface formations reported in the Niger Delta Basin. The Benin Formation is fluvial in origin and is overlain by Quaternary sediments.
The Benin Formation is the regional aquifer and is reported to be very porous and highly permeable. The sediments of the Benin Formation are lenticular in places and unconsolidated and are composed of coarse-medium-fine grained sands with localised intercalations of clay/shale. The sediments are poorly cemented and moderately sorted (Mbonu et al. 1991).

Theoretical foundation
The foundation in a building responds to both static and dynamic loading. Dynamic loading includes both natural and man-made vibrations such as machine vibrations, seismic loading, liquefaction and cyclic transient loading (Teme 1990). The dynamic elastic soil parameters related to dynamic loading are shear wave velocity, Poisson's ratio, Young's modulus, shear modulus and bulk modulus. These are used to measure the degree of stiffness of the subsurface (Clayton 2011). These parameters are usually computed using Hookean elastic equations using compressional and shear wave velocities as input parameters usually determined from low strain dynamic tests such as seismic refraction.

Seismic velocities
Using seismic refraction data, the P-wave velocity is usually obtained as the reciprocal of the slope of the various segments of the regression line of the traveltime versus distance graphs. The relationship between shear wave velocity (V s ) and primary wave velocity (V p ) according to Adewoyin et al. (2017) is expressed as Vp ¼ 1:7 Vs (1)

Poisson's ratio (σ)
The Poisson's ratio represents the lateral extension to longitudinal contraction. It is a measure of the geometrical change in the shape of an elastic body. Its value is 0.5 for fluids, and it approaches 0 for very hard indurated anisotropic rocks. Poisson's ratio can be determined using the following equation.
Thus, Poisson ratio (σ) may be expressed as where V p and V s are compressional and shear wave velocities and α is the velocity squared ratio. Weak materials have higher Poisson's ratio and vice versa.

Shear modulus (μ)
The shear modulus (μ) is the ratio between shear stress and shear strain. Shear stress cannot be applied to ideal liquids and gases. For these substances μ = 0. Only solids possess the physical properties described by the shear modulus. The shear modulus may be written in terms of the shear wave velocity (V s ) as where ρ is the density and g is the gravity acceleration.

Young's modulus (E)
Young's modulus (E) is a material property that describes elastic stiffness and thus considered as one of the key properties required in engineering design. Young's modulus (E) is the ratio of stress applied to the strain produced on the loading plane along the loading direction. Young's modulus can be related to shear modulus (μ) and Poisson's ratio (σ) using the expression:

Bulk modulus (K)
When a compressive or tensile stress is uniformly applied on a body, the relative change observed in the volume of the body is called bulk modulus. It gives an idea of the resistance of the substance to compression when load is applied to the substance.
where μ is the shear modulus and σ is the Poisson's ratio.

Lames constant (λ)
The Lamé parameters are also called the Lamé coefficients, Lamé constants or Lamé moduli, and is denoted by symbol λ. The Lames constant can be determined using the equation But the unit mass density (γ) is given as Thus, Unit mass density is expressed in kNm À 3 (Tezcan et al. 2009) γ o is the reference unit weight value in KN/m 3. The value of γ o is 16 for loose, sandy and clayey soils (Terzaghi and Peck 1967). Subgrade coefficient k s ð Þ is expressed in Nm À 2 s À 1 (Bowles 1982)

Ultimate and allowable bearing capacity
The ultimate bearing capacity (Qult) can be expressed as The allowable bearing capacity (qall) can be expressed as For soils the safety factor n is (n = 4.0).

Seismic velocities, dynamic elastic moduli and bearing capacity from cone penetration test (CPTu) sounding
The dynamic elastic moduli and bearing capacity can also be determined using data from conventional geotechnical methods such as cone penetration test (CPTu) sounding. Using this method, the dynamic elastic moduli and bearing capacity including the compressional (P) wave velocity and shear (S) wave velocity can be evaluated using the following established empirical equations.

Shear wave velocity
Using CPTu data, the shear wave velocity can be determined using the equation of McGann et al.
whereq t = corrected cone tip resistance in kPa I c = soil behaviour index Z = depth (m) The soil behaviour index is determined using the equation of Robertson and Wride (1998) q c1N = normalised cone penetration resistance corrected for overburden stress F = normalised friction ratio in percent q c = cone penetration resistance in MPa f s = CPTu sleeve friction σ v = total overburden stress in MPa P a = is a reference pressure in the same units as σ 1 vo (i.e. P a = 100 kPa if σ 1 vo isinkPa) P a2 = is a reference pressure in the same units as q c , i.e. P a2 = 0.1 MPa if q c is in MPa. Using the values of the shear wave velocity, the P-wave velocity can be determined using Equation 1.

Shear modulus
Using the corrected cone tip resistance (q t ) and effective stress values obtained from the CPTu sounding, the small-strain shear modulus is calculated using the equation of Robertson (2009) where q t is the corrected cone tip resistance (MPa) and σ 1 v is the effective stress (MPa).

Young's modulus
The Young's modulus can be estimated using the equation where σ 1 is the Poisson's ratio equal to 0.2. This is used when the conditions are drained, i.e. sandy soil. σ u is the Poisson's ratio equal to 0.5. This is used when the conditions are undrained, i.e. clayey soil, and G is the shear modulus. Other parameters such as bulk modulus (K), Lames' constant (λ), subgrade coefficient (k s ), ultimate and allowable bearing capacity can be calculated using eEquations 6, 7, 10, 11 and 12.

Site selection
Two sites (Opolo and Tombia) within Yenagoa and environs were used for this study (Figure 2). The selection of these two sites was based on the results of previous geophysical investigations carried out in the study area (Okiongbo and Gede 2017;Okiongbo and Soronnadi-Ononiwu 2018). The stratigraphic sequence of Opolo consists of top soil, clay and sand while the Tombia site consists of top soil, silty sand and sand. The stratigraphic sequence of Opolo is prevalent in the study area and covers over 80% of the subsurface stratigraphy.

Seismic refraction survey
Seismic refraction survey was carried out as a low strain dynamic test to determine the seismic velocities in the sites. The seismic refraction survey was carried out along straight profiles using 12-Channel ABEM Terraloc MK8 seismograph with a sledgehammer and a plate (energy source). In each site, three profiles were surveyed. The geophones were connected in an in line split spread configuration (Figure 3), using a geophone spacing of 5 m, with shots points located at 30 m from the first and last geophones of each spread. The geophones were firmly pinned to the ground and their take-outs placed on small wooden stands about 25 cm above the ground, in order to prevent wind, moisture, etc., from influencing the recording. The trigger cable reel connects the sledgehammer to the equipment and each time it is triggered, by hitting the hammer on a base plate, the seismogram records a seismic event. Data was acquired from the two ends of the traverse of each profile. Hitting the ground vertically generated the seismic P-waves, and 3-4 stacks were made per every P-wave shot. The seismic line was about 60 m and was covered by 12 geophones (Figure 3). The recording time was 500 ms, and the sampling rate was 500 μs. The data were stored in SEG-2 format. Samples of the recorded P-wave seismogram are shown in Figures 4(a) and 5(a), respectively. In processing the data, the first step included accurate picking of the first arrival time (first breaks) from the shot records. The arrival times were plotted against offset distance. The P-wave velocity was obtained as the reciprocal of the slope of the various segments of the regression line of the travel-time versus distance graphs. The Easy Refract seismic software which is based on the generalised reciprocal method (GRM) was used to generate the velocity-depth models. The various elastic moduli such as Poisson's ratio, bulk modulus, shear modulus (rigidity) and Young's modulus including the bearing capacities were determined using the compressional P-wave and shear wave velocities (Abdulraheem et al. 2009) obtained using eEquations 1-12.

CPTu sounding
In order to determine in situ dynamic elastic moduli of the sub-soil at the study sites , cone penetration tests were also carried out using a Dutch cone penetrometer with a capacity of 10 tons. The procedure followed for the cone penetration tests is in agreement with ASTM D3441 (2016). A total of nine CPTu test was carried out at each site. The field test locations are shown in Figure 2.
The equipment has a cylindrical probe with an area of about 10 cm 2 and a tip apex angle of 60° and a side friction sleeve with a surface area of 150 cm 2 .The test involved advancing the 60° steel cone into the ground so as to obtain the degree of compaction or stiffness of the soil. The field operation consisted of balancing the winch frame on the ground by means of two anchors. With these anchors, the CPTu system has sufficient power to push the cone into the ground at the rate of 2 cm/s by exerting pressure on the outer sounding tube. As this goes on, parameters such as resistance to penetration, sleeve friction, etc., are recorded. Pore pressure was measured through a filter element placed between cone tip and sleeve. The sounding depths range between 4 and 8 m. The tests were terminated at depths where the machine anchors began to pull out of the ground.
Parameters recorded by the CPTu sounding test include cone resistance, sleeve friction and pore pressure readings. These parameters are usually plotted against depth and displayed (Figures 6 and 7). Emplacing the CPTu data into empirical equations, the seismic velocities and dynamic elastic moduli including the bearing capacity of the geomaterials in the study sites were determined.

Results and discussion
Sample records of the seismic P-wave from the study sites, plots of travel time against source receiver distance and depth-velocity model showing vertical distributions of velocity with depth in each site are shown in Figures 4  and 5, respectively. The results show two-layered ground models. Table 1 (a,b)) shows the thicknesses and velocities obtained from analysis of the seismic refraction data using the intercept-time method (Barton and Barker 2003). Also shown in Table 1 are the elastic moduli, Lames constant and the bearing capacity. The results show that in the Opolo site, the first layer thickness and P-wave velocity vary from 10-12 m and 127-157 m/s with an average of 134 m/s, while the S-wave velocity vary from 64 to 92 m/s with an average of 77 m/s. The P-wave and S-wave velocity of the second layer vary between 224 and 374 m/s with an average of 304 m/s and 132-220 m/s with an average of 179 m/s. We attribute the limitation in the depth of coverage to the energy source that was used or length of profile deployed. Drill test hole in the Opolo site shows that the depth interval of 0-12 m corresponds to Plio-Pleistocene and recent superficial deposits composed mainly of clay while the second layer is made up of sand. The contact between layers 1 and 2 is characterised by a relatively high acoustic impedance contrast considering the fairly high P-wave velocity contrast between the first and second layers. In the Tombia site, the thickness and P-wave velocity of the first layer vary between 5-13 m and 123-152 m/s with an average of 141 m/s, respectively. The S-wave velocity of the first layer varies between 72-89 m/s with an average of 83 m/s. In the second layer, the P-wave and S-wave velocity vary between 176-204 m/s with an average of 188 m/s and 103-120 m/s with an average of 110 m/s. The variation in velocity even in the same layer is attributed to variations in lithology, grain size, porosity and saturation (Salem 2000). The low velocities especially in the first layer are presumably due to the presence of fine deposits such as clays and silts. In general, the velocity of the second layer is higher than the velocity of the first layer consistent with the fact that velocity increases with depth as porosity decreases (Salem 1993).
The P-wave velocity results of the shallow alluvial sediments in this study are fairly in agreement with those reported in the study of Alaminiokuma and Omigie (2018) in the first layer in the Eastern Niger Delta (Bonny Island) within the depth range of 0-10 m, although the S-wave velocities are slightly higher than the values obtained in this study. The results of the seismic velocities (V p and V s ) from the western Niger Delta (Escravos Area) reported by Ajayi et al. (2014)   the Tombia site in the first and second layers. The values of the Poisson's ratio in this study are consistent with those reported by Salem (2000) and Singh et al. (2015).
The Lames constant (λ) values range from 9.8 × 10 6 -20.5 × 10 6 with an average of 14.4 × 10 6 in the first layer but range between 11.4 × 10 6 − 81.3 × 10 6 with an average of 44.4 × 10 6 in the second layer in the Opolo site. In the Tombia site, the Lame's constant (λ) values range from 12.6 × 10 6 − 19.2 × 10 6 with an average of 16.6 × 10 6 in the first layer but varies from 25.9 × 10 6 -34.0 × 10 6 with an average of 29.3 × 10 6 in the second layer. The ultimate bearing capacity in the Opolo site range between 104 and 150 Nm −2 with an average of 125.3 Nm −2 in the first layer but varies between 217 and 369 Nm −2 with an average of 298.3 Nm −2 in the second layer. In the Tombia site, the ultimate bearing capacity values range from 117 to 142 Nm −2 with an average of 134.7 Nm −2 in the first layer but varies from 168 to 197 Nm −2 with an average of 180.7 Nm −2 in the second layer. The allowable bearing capacity in the Opolo site range between 25.9 and 37.5 Nm −2 with an average of 31.3 Nm −2 in the first layer but range from 54.3 to 92.1 Nm −2 with an average of 74.5 Nm −2 in the second layer. In the Tombia site, the allowable bearing capacity values range between 29.2 and 36.3 Nm −2 with an average of 33.6 Nm −2 in the first layer but range between 42.1 and 49.0 Nm −2 with an average of 45.1 Nm −2 in the second layer.
In order to compare the seismic velocity, elastic moduli and bearing capacity values determined using geophysical with those obtained from conventional geotechnical methods at the same point, CPTu soundings were also carried out in the study sites (Figures 6  and 7). The values of the compressional and shear wave velocities and elastic moduli from a depth of 0.5-8.0 m obtained using the CPTu data are shown in Tables 3 and 4 Table 4). The lithological information shows that this depth range consists of sand.
On comparing the average values of the seismic velocities of the formations derived from the two methods, we observed that the CPTu-derived average values of the velocities in the Opolo site in the clayey formation are slightly greater than the average values of the velocities derived using the seismic refraction technique. We also observed the same pattern in the Tombia site. Based on the ASSHTO Guidelines for the seismic design of Highway Bridges, soils are classified into six groups namely, A, B, C, D, E and F with reference to shear wave velocity. Group A represents hard rock with measured shear wave velocity greater than 600 m/s, while E and F classes represent weak to very weak soil with measured shear wave velocity values less than 180 m/s (Hammam and Eliwa 2013). The results of the shear wave velocities shown in Tables 3 and 4 (Table  3). In the Tombia site (Table 4), the Poisson's ratio ranges between 0.233 and 0.235 with an average of 0.235 within the depth range of 0.5-6.0 m corresponding to the silty sand but varies from 0.233 to 0.235 with an average of 0.234 within the sandy formation. Figure 8b shows that Poisson's ratio increases as with depth increases in the Opolo site but decreases as depth increases in the Tombia site (Figure 9b). Generally, the range of Poisson's ratio values derived using the CPTu method is consistent with those derived using the seismic refraction method.
The shear modulus exhibits a range between 18 and 72 Nm −2 with an average of 42 Nm −2 in the Opolo site but varies between 12 and 45 Nm −2 with an average of 35 Nm −2 between 0.5 and 8.0 m depth (silty sand) in the Tombia site and varies between 49 and 70 Nm −2 with an average of 61 Nm −2 between 6.0 and 8.0 m depth. Shear modulus increases with depth in both sites (Figures 8 and 9 (c)). Values of the Young's modulus in the Opolo site range between 53 and 217 Nm −2 with an average of 125 Nm −2 , but vary between 37 and 148 Nm −2 between the depth range of 0.5-6.0 m and 168-210 Nm −2 between 6.0 and 8.0 m depth in the Tombia site. In both sites, the Young's modulus increases with depth ( Figures 8  and 9 (c)). The bulk modulus values range between 41 and 137 Nm −2 with an average of 79 Nm −2 in the Opolo site, but vary between 23 and 120 Nm −2 with an average of 66 Nm −2 in the Tombia site within the depth range of 0.5-6.0 m and 106-131 Nm −2 with an average of 124 Nm −2 between 6.0 and 8.0 m depth. In both sites, the Young's modulus increases with depth (Bowles 1982).
The Lame's constant varies between 19 and 79 with an average of 45 in the Opolo site. In the Tombia site, the Lame's constant varies between 13 and 68 with an  average of 38 in the depth range of 0.5-6.0 m and 60-75 with an average of 71 between 6.0 and 8.0 m depth. In the Opolo site, the ultimate and allowable bearing capacity values vary between 168 and 296 Nm −2 with an average of 220 Nm −2 and 39-74 Nm −2 with an average of 55 Nm −2 . In the Tombia site, between the depth range of 0.5-6.0 m, the ultimate and allowable bearing capacity values range between 127 and 251 Nm −2 with an average of 190 Nm −2 and 32-63 Nm −2 with an average of 47 Nm −2 . Between the depth range of 6.0-8.0 m, the ultimate and allowable bearing capacity values range between 249 and 728 Nm −2 with an average of 386 Nm −2 and 62-182 Nm −2 with an average of 97 Nm −2 .
Generally, the elastic moduli values derived using the seismic refraction method (small strain 10 −4 % test) are greater than the elastic moduli values derived using the CPTu (large strain measurement) method. This is consistent with the observation of Seed et al. (1986) and Do et al. (2018), who opined that differences exist between Young's modulus values derived from small strain (10 −4 %) down hole test and values from large strain measurement such as the CPTu. Similar observations are also reported by Fjaer (2009), Martínez-Martínez et al. (2012 and Brotons et al. (2016) for studies carried out in heterogeneous geomaterials. Kolesnikov (2009) observed that the difference is due to differences in non-linear elastic response at different strain amplitudes, the effect of pore fluids, etc (Kolesnikov 2009).

Correlation between CPTu-derived elastic moduli and S-wave velocity
The least-squares regression technique was used to analyse the CPTu-derived elastic moduli results and S-wave velocity. The results show a linear relationship between shear modulus, Young's modulus, bulk modulus and bearing capacity with S-wave velocity (Figures 10 and 11). Also shown in Figures 10 and  11 are the regression equation and the correlation coefficient (R 2 ) determined for each regression. The best fit lines were straight lines for all cases. In general, the elastic moduli increase with increase in P-wave velocity. The correlations are highly significant with correlation coefficients (R 2 ) greater than 0.90. The good correlation indicates a linear relationship exists between the elastic moduli and S-wave velocity of the alluvial sediments. Altindag (2012) reported similar results by correlating P-wave velocity and elastic moduli in sedimentary rocks. The strong correlation of shear wave velocity with the various dynamic elastic moduli demonstrates the utility of shear wave velocity in geotechnical studies. The shear wave velocity is a key parameter in the design of geotechnical structures that may undergo dynamic loading (Kuo et al. 2011;Hammam and Eliwa 2013). In site response analysis, evaluation of liquefaction, etc., shear wave velocity is indispensable and thus plays a very important role in the design of foundation of structures. The shear wave velocity represents the material and structural condition of a soil. It is required in the evaluation of layer structure, degree of compaction or consolidation of soft soil or linearments within a site (Bang and Kim 2009).

Conclusions
In this paper, we present results of seismic velocities, dynamic elastic moduli and bearing capacity obtained from the analysis of seismic refraction data and CPTu soundings. The study sites consist of quaternary alluvial sediments. Field measurements include low-strain seismic refraction and high strain CPTu soundings. The seismic refraction data was analysed using the Intercept-time technique to obtain the seismic velocities which were subsequently used to estimate the dynamic elastic moduli. The CPTu data such as corrected cone tip resistance and soil behaviour index were emplaced into established empirical equation to determine the shear wave velocity, with which the P-wave velocity was estimated. Combing the V p and V s , the dynamic elastic moduli of the shallow sediments were determined within the depth range of 0.5-8.0 m.
The results show that the average values of the compressional and shear wave velocity in the Opolo site obtained from the seismic refraction method in the first layer are 131 and 77 m/s, Poisson's ratio is Figure 11. Correlation of elastic moduli and S-wave velocity in the Tombia site 0.236, the shear modulus, Young's modulus and bulk modulus are 16.1 × 10 6 Nm −2 , 39.7 × 10 6 Nm −2 , and 25.1 × 10 6 Nm −2 , respectively. The Lames constant, ultimate and allowable bearing capacity are 14.1 × 10 6 , 125 Nm −2 and 31.3 Nm −2 , respectively. In the Tombia site, the average values of the compressional and shear wave velocities in the first layer are 141 and 83 m/s, respectively. The Poisson's ratio is 0.234. The shear modulus, Young's modulus and bulk modulus are 18.3 × 10 6 Nm −2 , 45.2 × 10 6 Nm −2 and 28.8 × 10 6 Nm −2 , respectively. The Lames constant, ultimate and allowable bearing capacity are 16.6 × 10 6 , 135 Nm −2 and 34 Nm −2 , respectively. From the CPTu data in the Opolo site, the average values of the compressional and shear wave velocity values are 227 and 133 m/s. The Poisson's ratio is 0.234. The shear modulus, Young's modulus and bulk modulus are 42, 125 and 79 Nm −2 , respectively. The Lames constant, ultimate and allowable bearing capacity are 45, 220 Nm −2 and 55 Nm −2 , respectively. In the Tombia site, the average values of the compressional and shear wave velocity values are 244 and 144 m/s. The Poisson's ratio is 0.235. The shear modulus, Young's modulus and bulk modulus are 42, 128 and 81 Nm −2 , respectively. The Lames constant, ultimate and allowable bearing capacity are 46, 229 Nm −2 and 60 Nm −2 , respectively. When the results from the two methods were compared, it was observed that the average values of V p and V s from the two methods are fairly in agreement in that the relative difference between the average values were small. Significant difference in the average values was only observed in the dynamic elastic moduli. Analysis of the S-wave and the dynamic moduli from the CPTu data shows that a linear relationship exists between S-wave velocity and the dynamic elastic moduli with correlation coefficients (R 2 ) greater than 0.9 in all cases. The determined dynamic moduli, i.e. shear wave velocity, shear modulus, Young's modulus and bulk modulus, can be used for the design of structures based on the Eurocode (CEN 2004), site response (Reiter 1990) and settlement analysis. The shear wave velocity is also widely used in the assessment of liquefaction (Kramer 1996).