**1. Introduction**

Geophysical investigations for design parameters related to geotechnical engineering provides a cost effective and faster way of civil engineering related investigations, the reliable results usually obtained from integrated investigations are indispensable in the pre-construction procedures, examples of such studies include [1–4]. In cases of large area of coverage for construction of engineering structures, it becomes necessary to adopt the use of geophysical methods as a means of reconnaissance procedure before embarking on geotechnical investigation, in order to increase safety net ratio, borehole drilling can be done without having environmental implication such as drilling a confined fracture which can lead to flooding, drilling of contaminant plumes prone subsoil which can cause groundwater contamination, omission of important subsoil information along distances between boreholes. In order to perform a sound geotechnical project design, the subsurface profile information must be obtained. subsurface exploration also known as geotechnical investigations usually involves drilling holes in the ground, retrieving soils or rock samples through the boreholes at predictable depths, extent of subsoil exploration depends on the spread size of the project (road, bridges, builds etc.). Geophysical investigations which are fast and cost effective avoid the destructive effects of drilling and can generate profile for the subsurface features. Bearing capacity is the capacity of the soil beneath foundation to support a super structure load. The maximum load-bearing capacity of the soil, that is the maximum stress then soil can carry without failure, For instance, in the basement complex of the south-western Nigeria, subsoil is categorized into sand, sandy-clay, clayey sand, clay, lateritic-clay, clay to sand ratio determines the bearing capacity of the soil beneath a foundation, the subsoil can be delineated by using geophysical investigations. when the ultimate bearing capacity of the soil beneath a foundation is exceeded by stress caused by the superstructure, the soil may compress and slide (shear) and a sliding(shear) surface may develop in the soil, this is called bearing capacity failure, this also manifests as cracks on the walls of a building [2]. Low subsurface bearing capacity results in a case where the foundation settles excessively, if the groundwater table is near the ground surface, it may affect the ultimate bearing capacity, but if the groundwater table is close to the ground surface, it may not affect the ultimate bearing capacity, groundwater table can be located through geophysical investigations.

When saturated soil is subjected to an external load, the pore water pressure increases immediately on the application of external load, with time, the increase of pore water pressure gradually decreases and effective stress gradually increases, as pore water drains from the soil, the pore volume and total volume of the soil gradually decrease, it is important to locate the geologic features such as faults, fractures, dykes using geophysical methods due to the fact that the drained water migrates from the soil through the geologic features which serve a conduits for movement of groundwater, but the soil exhibits weakness at these zones, therefore resulting into structural failure. The soil volume decrease in the vertical direction due to primary consolidation, thereby resulting into primary consolidation settlement, geophysical methods can ascertain the sand and clay compartments of subsoil that can result into differential settlement.

The essence of an exploration phase of geotechnical engineering is to identify the significant features of a typical geologic environment that may have significant impact on the proposed construction of an engineering structure. This includes the definition of the lateral distribution and thickness of the soil and rock strata within the zone of influence of the proposed construction; definition of groundwater conditions considering seasonal changes; identification of geologic hazards such as unstable slopes, faults, ground subsidence; identification of geologic materials for identification, classification and measurement of engineering properties

In this chapter, the applications of geophysical methods to derive the geotechnical parameters needed for building design are thoroughly explained. Section 2 discusses geotechnical parameters that can be derived from seismic refraction method. Section 3 discusses the application of the electrical method to the delineation of geotechnical parameters necessary for building construction, important factors such as subsurface layers and geologic features were explained. Section 4 illustrated the brief concept of magnetic method. Section 5 explains the application of Very Low Frequency Electromagnetic Method (VLF-EM). Section 6 explains relevant case studies.

### **2. Seismic exploration**

The origin of seismic methods dates back to the early 1900s when instrumentation was designed to detect wave signals propagating through the earth arising from

#### *Geophysical Investigations for Design Parameters Related to Geotechnical Engineering DOI: http://dx.doi.org/10.5772/intechopen.108712*

earthquakes. These waves propagated outwards from the focus (source) of the earthquakes and were detected and recorded by instruments on the surface of the earth. The study and analysis of the recorded signals resulted in the resolution of the source/focus and the magnitude of the earthquake. More importantly the nature of the internal structure of the earth's subsurface was well known from more detailed analysis of the form of the recorded waves and their travelled ray trajectories. These records showed waves that had propagated deep into the earth and had been reflected and/or refracted back to the surface from seismic/acoustic interfaces of the subsurface.

By the extension of these earthquake studies, the techniques of refraction and reflection seismology using artificial seismic sources were carried out about 1915 by Minthrop.

Seismic surveying has since been and still is the single most utilised geophysical surveying method in the search for oil and gas and also in hydrogeological, environmental and geotechnical problems. Seismic waves are generated and they propagate through the earth, get detected and recorded usually on the surface of the earth.

#### **2.1 Seismic waves**

Seismic waves are elastic waves that travel within the Earth; i.e. they spread out from a source by elastic deformation of the rocks through which they travel. This propagation depends on elastic properties that are described by the relationships between stress and strain. The linear relationship between stress and strain in the elastic range is specified for any material by its various elastic moduli), each of which expresses the ratio of a particular type of stress to the resultant strain. Seismic wave velocities are determined by the type of seismic wave and by elastic modulus and the density of the rocks they travel through. There are two groups of seismic waves: body waves and surface waves.

Body Waves: an elastic medium can be subjected to two types of deformation; namely the compressional/dilatational and Shear. Hence all the elastic waves are basically 'compressional/dilatational' or 'shear' waves. The essential difference between the two types is that one entails a volume change without rotation of the medium particles, whereas the entails rotation without any change of volume. These first two waves propagate along the surface or into the subsurface, returning to the surface by reflection or refraction.


The equations of motion for dilatation(P-wave) and shear (S-wave) disturbances can be derived in terms of dilatational and rotational strain the results obtained from these equations is that the velocities of P- and S-waves (Vp and Vs) respectively are related to the elastic moduli and density of material. The relationships are shown below:

#### **2.2 P-wave velocity**

$$\text{V}p = \sqrt{\frac{K + \left(\frac{4}{3}\right)\mu}{\rho}}\tag{1}$$

This involves change of shape and volume

#### **2.3 S-wave velocity**

$$\text{Vs} = \left(\frac{\mu}{\rho}\right)^{\frac{1}{2}} \tag{2}$$

$$\text{Vs} = \sqrt{\frac{\varepsilon}{\rho} \frac{1}{2(1+\sigma)}}\tag{3}$$

This involves Change in shape only

Where,

*K* = Bulk modulus

σ = Poisson ratio

ε= Young modulus

μ= Shear modulus/Lame's constant

ρ = Density of the medium

These symbols are described in the diagram shown below:

Once the seismic wave velocities are measured, shear modulus (*μ*), Bulk modulus (*K*), Young's modulus or modulus of elasticity (ε), Poisson's ratio (*σ*), Oedometric modulus (ε*c*) and other elastic parameters may be obtained from the Eqs. (4)–(11) below. These expressions make the determination of the geotechnical parameters needed for building design as derived below:

1.Shear Modulus: Shear modulus (*μ*) relates Shear wave velocity with acceleration due to gravity as expressed in Eq. (4)

$$
\mu = \frac{\gamma V\_s^2}{\mathbf{g}} \tag{4}
$$

Where *g* is the acceleration due to gravity (9.8 m/s<sup>2</sup> ), where *g* is given as *<sup>γ</sup>=<sup>ρ</sup>* , *γ* is the unit weight of the soil and *ρ* is the mass density. The unit mass density relates with P-wave velocity *Vp* as shown in Eq. (5)

$$
\chi = \chi\_0 + \mathbf{0.002} V\_P \tag{5}
$$

*γ***<sup>0</sup>** *is defined* as the reference unit weight value in KN/m<sup>3</sup> [3, 5, 6]. *γo* = 16 for loose, sandy and clayey soil. According to [5], some elastic parameters were defined in Eqs. (6)–(9):

2.Young's modulus/modulus of elasticity (*E*)

$$E = 2\mu(\mathbf{1} + \sigma) \tag{6}$$

*Geophysical Investigations for Design Parameters Related to Geotechnical Engineering DOI: http://dx.doi.org/10.5772/intechopen.108712*

*μ* is shear modulus and *σ* is the Poisson's ratio.

3.Oedometric modulus (*Ec*) given by Eq. (7)

$$E\_c = \frac{(1 - \sigma)E}{(1 + \sigma)(1 - 2\sigma)}\tag{7}$$

*E* is modulus of elasticity

4.Bulk modulus (*K*) is expressed by Eq. (8) as

$$K = \frac{2\mu(1+\sigma)}{3(1-2\sigma)}\tag{8}$$

5.Poisson's ratio (*σ*) is given as in Eq. (9) as

$$
\sigma = \frac{a-2}{2(a-1)}\tag{9}
$$

Where

$$a = \frac{E\_c}{\mu} = \left(\frac{V\_p}{V\_S}\right)^2\tag{10}$$

6. Subgrade Coefficient (*Ks*), ultimate bearing capacity *qf* and allowable bearing pressure are given by Eqs (11)–(13) according as,

$$K\_S = 4\gamma V\_S \tag{11}$$

7.Ultimate Failure (Ultimate Bearing Capacity (*qf*))

$$q\_f = \frac{K\_S}{4\mathbf{0}}\tag{12}$$

which is for shallow foundation.

8. Allowable Bearing Pressure (*qa*)

$$q\_a = \frac{q\_f}{n} \tag{13}$$

Where *n* is the factor of safety (*n* = 4.0 for soils)

The basic requirement for construction or foundation sites is low compressibility and compliance and high bearing capacity which can be estimated 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 [7]

## **3. Electrical method**

The purpose of electrical resistivity survey is to determine the subsurface resistivity distribution by making measurements on the ground surface. Electrical resistivity method involves the passage of direct current, (DC) into the ground through two current electrodes (C1 and C2) while the resulting potential difference is measured across another pair of electrodes called potentials electrodes (P1 and P2), which may or may not be located within the current electrode pair, depending on the electrode array.

The apparent resistivity of the ground is calculated from the measured resistance (R). The survey techniques includes the Vertical Electrical Sounding (VES) and horizontal profiling (HP). Variations of the apparent resistivity with depth are measured in the VES technique, while lateral variations in ground resistivity are measured in the HP technique.

These variations in the resistivity of rocks are influenced by factors such as porosity, degree of fluid saturation, temperature, rock texture, rock types, geological processes and permeability. Geologic features such as fractures, fault zones, contacts can be easily delineated using the electrical, subsurface layers configuration can also be easily ranked based on their competence, soil corosivity can also be ranked and classified for burying of metallic structures during building constructions.

Outlined below are important areas of applications of electrical resistivity method in site characterization.

### **4. Depth to Bedrock determination**

The determination of the overburden thickness and hence depth to the bedrock at a construction site or along the highway road is one of the major applications of electrical resistivity in site investigation. The depth to the competent bedrock is given by the total overburden thickness resting on the bedrock. Depth to bedrock is obtained from the summation of the thicknesses of the layers that constitutes the lithologic sequence in an area.
