Geophysical Investigations for Design Parameters Related to Geotechnical Engineering

Abstract

Geophysical investigations for design parameters related to geotechnical engineering consider the application of geophysical methods such as electrical methods, seismic methods, magnetic prospecting method, electromagnetic prospecting methods, and these methods are needed to delineate the subsurface geological features before the erection of building structures, and design parameters used for geotechnical engineering can be investigated using geophysical methods. Moreover, geological structures such as fractures, faults, contacts, dykes, etc. can easily be delineated using geophysical methods, these geological structures are responsible for ground subsidence, building foundation problems, and building failures, which can affect the development of geotechnical engineering, and case studies will be referenced for easy understanding.

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, 2, 3, 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 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.

• Compressional or P-(primary) wave: They cause a back-and-forth (compressional) motion which is parallel to the direction in which the wave is travelling.

• Shear or S waves: They cause a to-and-fro (shear) motion which is perpendicular to the direction in which the wave is travelling. Particle motions involve oscillation about a fixed-point at right angles to the direction of wave propagation. If all the particle oscillations are in the same plane, the shear wave is said to be plane-polarised. Unlike compressional waves, shear waves cannot travel through liquids or gases.

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 (V_p and V_s) respectively are related to the elastic moduli and density of material. The relationships are shown below:

2.2 P-wave velocity

$$\mathit{Vp}=\sqrt{\frac{K+\left(\frac{4}{3}\right)\mu }{\rho }}$$E1

This involves change of shape and volume

2.3 S-wave velocity

$$\mathit{Vs}={\left(\frac{\mu }{\rho }\right)}^{\frac{1}{2}}$$E2

$$\mathit{Vs}=\sqrt{\frac{\epsilon }{\rho }\frac{1}{2\left(1+\sigma \right)}}$$E3

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)

   $$\mu =\frac{\gamma {V_s}^2}{g}$$E4

   Where g is the acceleration due to gravity (9.8 m/s²), where g is given as $\raisebox{1ex}{$\mathit{\gamma }$}\!\left/ \!\raisebox{-1ex}{$\mathit{\rho }$}\right.$ , γ is the unit weight of the soil and ρ is the mass density. The unit mass density relates with P-wave velocity V_p as shown in Eq. (5)

   $$\gamma ={\gamma }_0+0.002V_P$$E5

   ${\mathit{\gamma }}_{\mathbf{0}}$ is defined as the reference unit weight value in KN/m³ [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)

   $$E=2\mu \left(1+\sigma \right)$$E6

   μ is shear modulus and σ is the Poisson’s ratio.

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

   $$E_c=\frac{\left(1-\sigma \right)E}{\left(1+\sigma \right)\left(1-2\sigma \right)}$$E7

   E is modulus of elasticity

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

   $$K=\frac{2\mu \left(1+\sigma \right)}{3\left(1-2\sigma \right)}$$E8

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

   $$\sigma =\frac{\alpha -2}{2\left(\alpha -1\right)}$$E9

   Where

   $$\alpha =\frac{E_c}{\mu }={\left(\frac{V_p}{V_S}\right)}^2$$E10

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

   $$K_S=4\gamma V_S$$E11

7. Ultimate Failure (Ultimate Bearing Capacity (q_f))

   $$q_f=\frac{K_S}{40}$$E12

   which is for shallow foundation.

8. Allowable Bearing Pressure (q_a)

   $$q_a=\frac{q_f}{n}$$E13

   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.

5. Structural mapping of the Bedrock

The structural setting of the bedrock (possible fault location, fracture, joints, buried river channels etc.) can be investigated with the seismic and electrical resistivity method. Fractures in bedrock occur most often in competent rocks unable to adjust to the stresses placed upon them. Fractures in bedrock are characterized by moisture making them more electrically conductive than a non-fractured bedrock. Fractured region may be topographically more depressed than the surrounding unfractured bedrock.

6. Location of construction materials

Electrical resistivity profiling method is mainly used in the search for sand and gravel deposits needed for construction projects. The data can be inverted to depict the resistivity variation, both laterally and vertically, against depth. The low-resistivity area (less than 20 ohm-m) corresponds to clay layers and high-resistivity zones (greater than 100 ohm-m) correspond to sand and gravel lenses.

7. Soil corrosivity

Corrosivity is defined as soil’s ability to corrode a material that may be buried in it. As soils at building site would normally host metallic pipes etc., it becomes mandatory that a well-organized site testing exercise be carried out to evaluate soil aggressivity (corrosivity) taking into consideration the type of materials to be buried in it. The degree of corrosivity of the soil can be predicted using the electrical resistivity values. The electrical resistivity values of the top soil at the site can be used to assess the corrosivity of the soil of that site. Soils with resistivity values of less or equal to 10 ohm-m are strongly corrosive. Soils with resistivity values ranging between 10 and 60 ohm-m are moderately corrosive while those with resistivity between 60 and 180 ohm-m are slightly corrosive. Soils with resistivity values greater than 180 ohm-m are practically non corrosive.

8. Site subsoil competence

The strength of any geological material is influenced by several factors such as the mineralogy of its particles, the character of the particle contrast and agents of weathering. However, in a given locality, apparent resistivity values can be used for the evaluation of earth materials and their competence. Materials underlying a site can be judged to be generally competent or incompetent. High apparent resistivity zones are said to be competent in comparison with regions of relatively low resistivity values. Certain ranges of apparent resistivity values can be correlated with lithologic competence.

9. Mapping of seepage zones

Earth and rock-fill dams are large civil engineering structures designed to impound surface water. The design of dams makes provisions for control seepage and spillage. In spite of advances made in the field of geotechnical engineering, it is not possible to have 100% leak-proof structure. Anomalous seepages may sometimes occur through permeable soils, rock aquifers controlled by their structural bedrock topography and fault/joints structures. Geophysical method play an important role in mapping seepage paths and monitoring the changes of the seepage with time, enabling to plan technically and economically worthwhile remedial measures

10. Magnetic prospecting method

The origin of the earth’s magnetism is commonly believed to be the liquid part of the earth’s core, which cools at the outside as a result of which material becomes denser and sinks towards the inside of the outer core and new warm liquid matter rises to the outside; thus, convection currents are generated by liquid metallic matter which move through a weak cosmic magnetic field which subsequently generates induction currents. It is this induction current that generate the earth’s crust magnetic field. Most rocks of the earth’s crust contain crystals with magnetic minerals; thus most rocks have a certain amount of magnetism, which usually has two components induced by the magnetic field present while taking measurement, and remanent which is formed during geologic history [8]. The aim of magnetic survey is to investigate subsurface geology on the basis of anomalies in the Earth’s magnetic field resulting from the magnetic properties of the rocks [9]. Although most rock-forming minerals are effectively nonmagnetic, certain rock types contain sufficient magnetic minerals to produce significant magnetic anomalies. An observed anomalous magnetization might be associated with buried magnetic objects that are potentially of commercial interest. Anomalies recorded in the measured field are interpreted in terms of variations in magnetic susceptibility and/or remanent magnetism, the physical rock properties affecting the measurements. Magnetic susceptibility is the physical property on which the response of magnetic method is based, and it is the property whose distribution we are trying to investigate.

11. Very low frequency electromagnetic method

Very Low Frequency (VLF-EM) is an effective reconnaissance geophysical tool for mapping geologic features. It may be used wherever an electrical conductivity contrast exists between geological units, this includes Fault mapping, Groundwater investigation, Overburden (summation of all the materials on the bedrock) mapping, contaminant mapping. Electrical conductive features include fault zones which tend to be more conductive than the surrounding bedrock or host rock. Other conductive geologic units include moist, clayey or fine grained soils which tends to be more conductive than dry, sandy or coarse grained soils. Hence, these geologic objectives are reasonable “targets” and can be mapped using electromagnetic methods. In reconnaissance mode, VLF profiles can be run quickly and inexpensively to determine anomalous areas which requires further investigation.

12. Case studies: application of electrical and very low frequency electromagnetic method to pre-construction investigations

12.1 Site descriptions, geomorphology and physiography

The study area as shown in Figure 1 is located within Igarra, Southwestern Nigeria expressed in Universal Traverse Mercator (UTM) Zone 3, and the study area is located within Northings 807054 mN and 807265 mN and Eastings 179000 mE and 179210 mE. The landforms are of two main groups, the high hills which are found in the north-eastern part of Igarra, while the other is low lying around north-western and south-western part of Igarra. The Igarra area is made up of untarred roads, footpaths, rivers, the tributaries converges at the point to form rivers which flows along the strike direction of the outcrops in the area.

Figure 1.

Data acquisition map of the study area.

12.2 Brief geology of the study area

Three major rocks overlie the basement complex in the Igarra area. The successions of the rocks are namely;

• Granodiorite which are rich in biotite and hornblende, diorite which are unmetamorphosised pegmatite which has large quartz clasts.

• Rocks formed under low temperature and pressure(low grade metasediments) such as schists, calc-silicate gneiss, marble, metaconglomerate and quartzites.

• Metamorphic rocks such as gneiss rich in biotite-hornblende with bands of minerals, the metasediments are younger than the basement complex [10] and the older granites represents the youngest group of rocks of the Precambrian age in this area.

The sequence of rocks in the Igarra area is made up of four main groups which includes Calc-silicate gneiss and marble, Metaconglomerate, Mica-schist and Quartz-biotite schist

12.3 Method of study

The geophysical investigation involved electrical resistivity method (Dipole-Dipole Technique) and Very Low Frequency-Electromagnetic Method, the steps includes geologic mapping (reconnaissance survey of the study area) and establishing of traverses, production of geophysical location maps from the base/topographical map, data acquisition for all the geophysical methods followed by processing and interpretation. Inverted 2D Model of VLF data was generated using K-H Filter (Karous-Hjelt Filtering software). The Dipole-Dipole array was used for the data acquisition. The inter-electrode spacing (a) of 5 m was adopted while inter-dipole separation factor (n) was varied from 1–5. The apparent resistivity values were calculated using πn(n + 1)(n + 2)a as the geometric factor. 2-D inversion modelling of the Dipole-Dipole data was carried out using DIPRO^TM Software developed by the Korea Institute of Geoscience and Mineral Resources

12.4 2-D resistivity structure along South-North direction

The dipole-dipole pseudosections and the 2D resistivity structure along the S-N direction are shown in Figure 2. The 2D resistivity structure revealed four geoelectric/geologic subsurface layers marked A, B, C and D separated by geologic boundaries; namely topsoil marked by A (generally blue colour except at few points with green colour), B (green and blue colour), weathered/fractured basement marked by C (generally green except at few points with yellow colour).The topsoil is generally thin and subsume into the weathered layer in many places due to its thickness and it is characterised mainly by clay but few sandy clay. The weathered layer is characterised by clay and sandy clay, its thickness increases from the centre of the traverse towards the southern and the northern flanks respectively. The northern flank of the weathered layer exhibit very low resistivity values which may be due to high level of saturation and diagnostic effect of wet clay.

Figure 2.

2-D modelling of dipole-dipole along S-N direction.

The weathered/fractured basement is characterised by two linear features which are between stations 4 and 5(distance at 40 m and 50 m) and stations 14 and 16 (distance at 140 m and 160 m). The upper part of the weathered/fractured basement exhibits lower resistivity than its lower section, signifying that the upper part (green colour) is more weathered than the lower part of the pseudosection.

The depth to bedrock is thinner between stations 7 and 10 (distance at 70 m and 100 m), but increases towards the southern flank (between stations 2 and 7) and increases towards the northern flank(stations 10 and 19), this shows that the bedrock extends beyond the depth of study (30 m) between the stations 2 and 6 and stations 12 and 19. The overburden at the northern flank is characterised by higher portion of clay due to its lower resistivity values when compared with the southern flank.

12.5 2-D resistivity structure along West-East direction

The 2D resistivity structure (Figure 3) reveals four geologic/geoelectric subsurface layers separated by geologic boundaries; namely topsoil marked by A (generally blue except few points with yellow and green colour), weathered layer marked B (generally blue except few points with yellow and green colour), weathered/fractured basement marked C (green and yellow colour) and fresh basement marked D (generally red except few points with yellow colour). The topsoil is generally thin but subsume into the weathered layer in many places due to its thickness, the topsoil is characterised mainly by clay with few portions of laterite and sandy clay. The weathered layer is characterised mainly by clay (lowest resistivity represented by blue colour) between stations 5 and 8 (distance at 50 m and 80 m), but the resistivity values increases from the above stations towards the western and the eastern flank signifying the reduction of clay to sand ratio.

Figure 3.

2-D modelling of dipole-dipole along West-East direction.

A linear feature is noticed between stations 5 and 7 (distance at 50 m and 70 m) which has significant depth extent. The low resistivity zone is between stations 5 and 7 (50 m–70 m) which could be diagnostic of a suspected fault zone with a width of approximately 19 m. The suspected fault zone is flanked on both sides by regions of higher resistivity. The extremely low resistivity value (blue colour) that was noticed at the lower part of the fault zone signifies the effect of high saturation and diagnostic effect of wet clay. The resistive parts are seen at the lower part of the section which is the fresh basement.

12.6 VLF profile along South-North and West-East direction

On the traverse one which is trending South-North, the VLF-EM profile (Figure 4) identified peak positive filtered real values at distances 2 m, 40 m, 83 m, 110 m, 138 m, 168 m and 200 m. The amplitude of the peak positive filtered real values are very low, the inverted model shows that most of the peaks manifest as non-anomalous conductive zones, except for the peak positive filtered real noticed at 200 m. The VLF-EM profile and the inverted model are shown on the profile.

Figure 4.

VLF profile and inverted 2D model obtained along traverse one (S-N).

On the traverse trending North-South, the VLF-EM profile (Figure 5) identified peak positive filtered real values at distances 18 m, 43 m and 58 m. The amplitude of the peak positive filtered real values are very low, the inverted model shows that most of the peaks manifest as non-anomalous conductive zones, except for the peak positive filtered real noticed at 18 m.

Figure 5.

VLF profile and inverted 2D model obtained along traverse three (South-North).

On the baseline which is trending West-East direction, the VLF-EM profile and the inverted model are shown in Figure 6, the VLF-EM profile identified peak positive filtered real values at distances 18 m, 32 m, 46 m, 60 m, 82 m, 112 m and 138 m, the observation agree with conductive zones delineated by the inverted model at distance 20–60 m, 80–100 m and 122–138 m. The conductive zone between distance 122–138 m and 20–60 m are typical of a linear feature (fracture) because of its depth and it is dipping to the west.

Figure 6.

VLF profile and inverted 2D model obtained along baseline (West-East).

On the traverse which is trending West-East, the VLF-EM profile and the inverted model are shown in Figure 7. The VLF-EM profile identified peak positive filtered real values at distance 78 m, 102 m, 118 m and 138 m, the observations agree with the conductive zones delineated at distances 3–20 m, 110–140 m, the conductive zones between 110 m and 140 m is typical of a linear feature (fracture) and it is dipping to the east.

Figure 7.

VLF profile and inverted 2D model obtained along traverse two (West-East).

13. Conclusion

In this chapter geophysical investigations for design parameters related to geotechnical engineering was explored.

The strength of the geophysical methods lies in the ability of the method to image the subsurface in a faster and cost effective approach when compared with geotechnical investigations. Geophysical methods provides adequate guidance to civil engineers before embarking in boring and drilling operations, this will avoid excessive damage of subsurface materials which result in environmental risks such as flooding activities.

Seismic refraction, electrical methods, electromagnetic method and magnetic method have been proven to be useful for evaluating design parameters/geologic subsurface deductions needed before the construction of engineering structures such as buildings, rail ways, dams, bridges etc. Case studies involving the application of electrical method and Very Low Frequency Electromagnetic method at Study area within Igarra, South-western Nigeria was explained to reveal the importance of geophysical methods in geotechnical engineering. Geologic features such as faults and fractures were delineated from the Electrical Resistivity Image of the subsurface, VLF profile and the Inverted 2D Model, the compositions (sandy clay, clay, clayey sand and laterite) of the subsurface/geoelectric layers were also classified based on their competence.

In conclusion, the importance of geophysical investigations for evaluation of the design parameters related to geotechnical engineering cannot be neglected in the pre-construction phase.