Structure of Soil

The structure of a soil may be defined as the manner of arrangement and state of aggregation of soil grains. In a broader sense, consideration of mineralogical composition, electrical properties, orientation and shape of soil grains, nature and properties of soil water and the interaction of soil water and soil grains, also may be included in the study of soil structure, which is typical for transported or sediments soil. The engineering behaviour of soil is influenced by soil structure to varying degrees. Structural composition of sediment soil influences, many of their important engineering properties such as permeability, compressibility and shear strength. Hence, a study of the structure of soil is important. The following types of structure are commonly considered.

1) Single Grained Structure

Single grained structure is characteristic of coarse grained soils, with a particle size greater than 0.02 mm. Gravitational forces predominate the surface forces and hence grain to grain contact results. The deposition may occur in a loose state, with large voids or in a sense state, with less of voids. When such soils settle out of suspension in water, the particles settle independently of each other. The major force causing their deposition is gravitational and the surface forces are too small to produce any effect. There will be particle-to-particle contact in the deposit. The void ratio attained depends on the relative size of grains.

Fig. 1 Single-grained Structure

2) Honeycomb Structure

This structure can occur only in fine-grained soils, especially in silt and rock flour. Due to the relatively smaller size of grains, besides gravitational forces, inter-particle surface forces also play an important role in the process of settling down. When particles approach the lower region of suspension they will be attracted by particles already deposited as well as the neighbouring particles leading to formation of arches. Miniature arches are formed, which bridge over relatively large void spaces. This results in the formation of a honey-comb structure, each cell of a honey-comb being made up of numerous individual soil grains. The structure has a large void space and may carry high loads without a significant volume change. The structure can be broken down by external disturbances.

Fig. 2 Honey-comb Structure

3) Flocculent Structure

This structure is characteristic of fine-grained soils such as clays. In the case of flocculated structure, there will be edge-to-edge and edge-to-face contact between particles. The concentration of dissolved minerals in water leads to formation of flocculated structure with very high void ratio as in the case of marine deposits. Mutual repulsion of the particles may be eliminated by means of an appropriate chemical; this will result in grains coming closer together to form a ‘floc’. Formation of flocs is ‘flocculation’. But the flocs tend to settle in a honeycomb structure, in which in place of each grain, a floc occurs. Thus, grains grouping around void spaces larger than the grain-size are flocs and flocs grouping around void spaces larger than even the flocs result in the formation of a ‘flocculent’ structure.

Fig. 3 Flocculent Structure

Very fine particles or particles of colloidal size (< 0.001 mm) may be in a flocculated or dispersed state. This type of structure is common in fresh water deposits. In the case of dispersed or oriented structure, the particles will have face to face contact. This type for formation is due to net electrical forces between adjacent soil particles at the time of deposition being repulsive in nature. The flaky particles are oriented edge-to-edge or edge-to-face with respect to one another in the case of a flocculated structure. Flaky particles of clay minerals tend to from a card house structure, when flocculated. When inter-particle repulsive forces are brought back into play either by remoulding or by the transportation process, a more parallel arrangement or reorientation of the particles occurs. This means more face-to-face contacts occur for the flaky particles when these are in a dispersed state. In practice, mixed structures occur, especially in typical marine soils.

Fig. 4 Card House Structure

Fig. 5 Dispersed Structure

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Survey Stations

Survey stations are important points fixed on ground indicating the starting point and the end point of the survey line. These are also the basic control points of the survey. There can be two types of survey stations.

1) Main Stations

Main stations are control points at the ends of the chain lines commanding the boundaries of survey and the lines joining the main stations are called the main survey line or the chain lines (A, B, C, D and E in Fig.1).

2) Subsidiary or Tie Stations

These are stations selected on the main survey lines for running auxiliary lines drawn to locate, measure and plot interior details such as fences, hedges, building, etc. (a and b in Fig.1).

Fig. 1 Layout of Chain Survey

The survey stations are suitably selected with care so that at least main survey stations are mutually visible and survey lines run through as flat ground as possible and are as close to the boundaries as possible. The main survey lines should form well-conditioned triangles. These should be as few as possible and suitably selected so as to avoid obstacles in chaining and ranging.

Survey Lines

The lines joining survey stations are the survey lines. The survey lines between main stations are thus called main survey lines or chain lines. The different survey lines are listed below.

1) Base Line

The longest of the main survey line is normally called base line running primarily through the middle of the area to be surveyed. The framework of triangles shall have one or two base lines since the entire survey is built around base line. It shall be measured with higher care and accuracy. 

2) Chain Line (Main Survey) Line 

The lines that join main stations are termed as chain line or main survey line.

3) Tie or Subsidiary Line

The survey line joining the subsidiary or tie stations on main line is termed tie line. It helps to check the accuracy of surveying and to locate the interior details. The position of each tie line should be close to some features such as paths, buildings, etc.

4) Check Line or Proof Line

A check-line also termed as a proof-line is a line joining the apex of a triangle to some fixed points on any two sides of a triangle. A check-line is measured to check the accuracy of the framework. The length of a checking line, as measured on the ground should agree with its length on the plan. It is preferable to have at least one check line in each triangle of the framework.

Offsets

The details on ground such as fences, buildings and towers, etc. are to be located with reference to main chain lines by means of lateral measurements. These lateral measurements with reference to the chain line are referred to as offsets. Offsets are classified based on its length and inclination to the survey line.

1) Classification Based on Length of Offset

a) Short Offset

Offset whose length is less than 15m is called short offset.

a) Long Offset

Offset whose length is greater than 15m is called long offset.

2) Classification of Offset Based on the Inclination to the Survey Line

a) Perpendicular Offset

Perpendicular offsets are the lateral distances taken at right angles (normal) to the chain line.

b) Oblique Offset

If the inclination of offset line to chain line is anything other than 90^o, the offsets are termed as oblique offsets.

Fig. 2 Offsets 

Factors Affecting Survey Station Selection 

• Stations should be visible from at least two or more stations. 
• As far as possible, main lines should run on level ground. 
• All triangle will be well conditioned triangle. 
• Each triangle should have at least one check line. 
• Survey lines should be as few as possible. 
• Obstacles to ranging and chaining should be avoided. 
• Sides of the larger triangles should pass as close to the boundary lines as possible. 
• Trespassing and frequent crossing of the roads should be avoided.

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Clay Mineralogy

A ‘mineral’ is an inorganic chemical compound formed in nature. As a solid, it may occur in an amorphous state or in a crystalline state. A ‘crystal’ is a homogenous body bounded by smooth plane surfaces. Soil particles are largely composed of mineral crystals. Molecules of minerals are composed of atoms of chemical elements. The atoms in a crystal are arranged in a definite orderly manner to form a three dimensional net-work, called a “lattice.” Earth is about 12,500 km in diameter and most geotechnical engineering work is confined to the top few hundred meters of the crust, which is comprised essentially of oxygen (49.2%), silicon (25.7%) and aluminum (7.5%) present in the form of oxides, with some Fe³⁺, Ca²⁺, Na⁺, K⁺, Mg²⁺, etc. The atomic structure of a clay mineral is made of one of the two structural units: tetrahedrons containing a silicon atom at the center surrounded by four oxygen atoms at the corners and octahedrons containing aluminum or magnesium ions at the center surrounded by six hydroxyl or oxygen ions at the corners.

Formation of Clay Minerals

A soil particle may be a mineral or a rock fragment. A mineral is a chemical compound formed in nature during a geological process, whereas a rock fragment has a combination of one or more minerals. Based on the nature of atoms, minerals are classified as silicates, aluminates, oxides, carbonates and phosphates.

Out of these, silicate minerals are the most important as they influence the properties of clay soils. Different arrangements of atoms in the silicate minerals give rise to different silicate structures. Basic structural units soil minerals are formed from two basic structural units: tetrahedral and octahedral. Considering the valencies of the atoms forming the units, it is clear that the units are not electrically neutral and as such do not exist as single units. The basic units combine to form sheets in which the oxygen or hydroxyl ions are shared among adjacent units. Three types of sheets are thus formed, namely silica sheet, gibbsite sheet and brucite sheet.

Isomorphous substitution is the replacement of the central atom of the tetrahedral or octahedral unit by another atom during the formation of the sheets. The sheets then combine to form various two-layer or three-layer sheet minerals. As the basic units of clay minerals are sheet-like structures, the particle formed from stacking of the basic units is also plate-like. As a result, the surface area per unit mass becomes very large.

Atomic and Molecular Bonds

Forces which bind atoms and molecules to build up the structure of substances are primarily of electrical nature. They may be broadly classified into “primary bonds” and “secondary bonds’’. Primary bonds combine the atoms into molecules. Secondary bonds link atoms in one molecular to atoms in another. They are much weaker than the primary bonds. Primary bonds are the ionic bond and the covalent bond. Secondary bonds are the hydrogen bond and the Van der Waals bond.

1) Ionic Bond

The ionic bond is the simplest and strongest of the bonds which hold atoms together. This bond is formed between oppositely charged ions by the exchange of electrons. Atoms held together by ionic bonds form “ionic compounds”’, e.g. common salt (sodium chloride) and a majority of clay mineral crystals fall into this group. Ionic bonding causes a separation between centres of positive and negative charge in a molecule, which tends the molecule to orient in an electric field forming a “dipole”. Dipole is the arrangement of two equal electro-static charges of opposite sign. A dipolar molecule is one which is neutral but in which the centres of positive and negative charges are separated such that the molecule behaves like a short bar magnet with positive and negative poles.

2) Covalent Bond

The covalent bond is formed when one or more bonding electrons are shared by two atoms so that they serve to complete the outer shell for each atom.

Fig. 1 Covalent Bonding

3) Hydrogen bond

A hydrogen bond is the attractive interaction of a hydrogen atom with an electronegative atom, such as nitrogen, oxygen or fluorine, that comes from another molecule. Thus when water molecules are close together, their positive and negative regions are attracted to the oppositely-charged regions of nearby molecules. The force of attraction, shown in Fig. 2 as dotted line, is called a hydrogen bond. Each water molecule is hydrogen bonded to four others. Hydrogen bond can link the oxygen from a water molecule to the oxygen on the clay particles surface. Hydrogen bonding between two oxygen atoms is responsible for some of the weaker bonds between crystal layers for holding water at the clay surface and for bonding organic molecules to the clay surface.

Fig. 2 Hydrogen Bonding

4) Van der Waals Bond

It is the sum of the attractive or repulsive forces between molecules (or between parts of the same molecule) other than those due to covalent bonds or ionic bond. The covalent bonds within the molecules are very strong and rupture only under extreme conditions. The bonds between the molecules that allow siding and rupture to occur are called Van der Waals forces.

When ionic and covalent bonds are present, there is some imbalance in the electrical charge of the molecule. The angle hydrogen atoms are bonded to oxygen atom in water produces a positive polarity at the hydrogen-rich end of the molecule and a negative polarity at the other end. As a result of this charge imbalance the water molecules are attracted to each other. This is the force that holds the molecules together in a drop of water, shown in Fig. 3. Heat can be used to break the Van der Waal forces between the molecules and change the form of the material from solid to liquid gas.

Fig. 3 Van der Waals Bonding

Basic Structural Units of Clay Minerals

The clay minerals are a group of complex alumino-silicates, i.e., oxides of aluminium and silicon with smaller amounts of metal ions substituted within the crystal. The atomic structures of clay minerals are built up of two basic units such as Silica tetrahedral units and Aluminium (or magnesium) octahedral unit. These units are held together by ionic bonds.

1) Silica Unit

The silica unit consists of a silicon ion surrounded by four oxygen ions arranged in the form of a tetrahedron. The basic units combine in such a manner as to form a sheet. In the silica sheet, the bases of the tetrahedrals are all in the same plane and the tips all point in the same direction. Each of the three oxygen at the base is shared by two silicon of adjacent units.

2) Aluminium (or Magnesium) Octahedral Unit

The octahedral unit has an aluminium ion or a magnesium ion endorsed by six hydroxyl radicals or oxygen arranged in the form of an octahedron. In some cases, other cations (e.g. Fe) are present in place of Al and Mg. Combination of octahedral units forms an Octahedral sheet, which is called a ‘gibbsite” sheet if the central action of the unit is aluminum or a “brucite” sheet if the central cation is magnesium.

Types of Clay Minerals

From an engineering point of view, three clay minerals of interest are kaolinite, montmorillonite and illite.

1) Kaolinite

This is the most common of the Kaolin group. Each structural unit of Kaolinite is a combination of two layers with a silica layer joined to one of a gibbsite layer. Successive layers of structural units are held together to form kaolite particles which occur as platelets joined by strong H-bond. Kaolinite is used for making paper, paint and in pharmaceutical industry.

Fig. 4 Kaolinite

2) Montmorillonite

The montmorillonite mineral is a stacking of basic sheet like structural units, with each unit made up of gibbsite sheet sandwiched between two silica sheets joined by weak Van der Waal’s bond. It is easily separated by water. Because of the fact that bonding by Van der Waals forces between silica sheet of adjacent structural units is weak and there is a net negative charge deficiency in octahedral sheet, water and exchangeable cations can enter and separate the layers. Thus soil containing montmoriillonite mineral exhibits high swelling and shrinkage characteristics.

Fig. 5 Montmorillonite

3) Illite

The basic structural unit of illite is the same as that of montmorillonite except for the fact that there is some substitution of aluminium for silicon in the silica sheet and the resultant charge deficiency is balanced by potassium ions, which bond the layers in the stack. There is about 20% replacement of aluminium with silicon in the gibbsite sheet due to isomorphous substitution. The bond with the non-exchangeable K⁺ ions are weaker than the hydrogen bond in the Kaolite but is stronger than the water bond of montmorillonite. The illite crystal does not swell so much in the presence of water as does in montmorillonite particles.

Fig. 5 Illite

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Corrections to Linear Measurements

The following corrections are to be applied to the linear measurements with a chain or a tape where such accuracy is required.

1) Correction for Standard Length of Tape

Before using a tape, its actual length is ascertained by comparing it with a standard tape of known length. The designated nominal length of a tape is its designated length e.g. 30m or 100m. The absolute length of a tape is its actual length under specified conditions. Incorrect length of a tape can be one of the most important errors. It is systematic. An error due to incorrect length of a tape occurs each time the tape is used. If the true length, known by standardization, is not exactly equal to its nominal value of 100.00 m recorded for every full length, the correction can be determined and applied from the formula given below.

Where,

        l - Actual tape length at the field

        l’ - Nominal tape length

        L - Measured length of the line

Sometimes, the changes in length are quite small and of little importance in many types of surveys. The actual length of a working tape must be compared with a standard tape periodically. When its actual length is known, the tape is said to be standardized. A correction must be added or subtracted to a measured distance whenever its standardized length differs from its nominal or graduated length. In measuring unknown distances with a tape that is too long, a correction must be added. Conversely, if the tape is too short, the correction will be minus, resulting in decrease.

2) Correction for Temperature

This correction is necessary because the length of the tape or chain may be increased or decreased due to rise or fall of temperature during measurement. Steel tapes are standardized for 68⁰F or 20⁰C. A temperature higher than or lower than this value causes a change in length that must be considered. The coefficient of thermal expansion and contraction of steel used in ordinary tapes is approximately 1.16 x 10^-5 per length per ⁰C. For any tapes the correction for temperature can be computed and applied using the formula.

Ct = 𝛼 (Tm – T0) L

Corrected Length = L + Ct

Where,

     Ct - Correction in length of a line due to nonstandard temperature

     𝛼− Coefficient of thermal expansion and correction of the tape

    Tm - Tape temperature at the time of measurement

    To - Tape temperature when it has standard length

     L - Measured length of the line

3) Correction for Pull / Tension

During measurement the applied pull may be either more or less than the pull at which the chain or tape was standardized. Due to the elastic property of materials the strain will vary according to the variation of applied pull and hence necessary correction should be applied. When a steel tape is pulled with a tension greater than its standard, the tape will stretch and be no longer than its standard length. Conversely, if less than standard pull is used, the tape will be shorter than its standard length. The modulus of elasticity of the tape regulates the amount that it stretches. Correction pull can be computed and applied using the following formula.

Corrected Length = L + Cp

Where,

        Cp - Total elongation in tape length due to the pull, in meter.

        P1- Pull applied to the tape, in Kg.

        P - Standard pull for the tape, in Kg.

        A - Cross sectional area of the tape.

        E - Modulus of elasticity of the steel.

        L - Measured length of the line in meter.

4) Correction for Sag

In case of suspended measurement across a span L the chain or tape sag to take the form of curve known as catenary. Sag shortens the horizontal distance between end graduations, because the tape length remains the same. Sag can be diminished but not eliminated unless the tape is supported throughout. The following formulas are used to compute the sag correction.

Where,

        Cs - Correction for sag in meter.

        Ls - Unsupported length of the tape in meter.

        w - Weight of the tape per meter of length.

        W - Total weight of the tape between the supports in Kg.

        P1 - Pull on the tape in Kg.

In measuring lines of unknown length, the sag correction is always negative. After a line has been measured in several segments and a sag correction has been calculated for each segment, the corrected length is given by

Corrected Length = L + ΣCs

Where,

        L - Recorded length of the line

        ΣCs - Sum of individual sag corrections.

5) Normal Tension

By equating equations Cs = Cp,

i.e. the elongation due to increase in tension is made equal to the shortening due to sag; thus, the effect of the sag can be eliminated. The pull that will produce this condition, called Normal Tension Pn is given by the formula.

Where,

        Pn - Normal tension

        P - Standard pull for the tape, Kg

       W - Total weight of the tape between the support, Kg

        A - Cross sectional area of tape

        E - Modulus of elasticity of steel

6) Correction for Alignment

Generally, a survey line is set out in a continuous straight line. Sometimes, it becomes necessary due to obstruction to follow a bent line which may be composed of two or more straight portions subtending an angle other than 180º as shown in Fig. 1.

Fig.1 Correction for Alignment

Let        AC = L1, CB= L2

            < BAC = 𝜃1, BAC = 𝜃2

                                               Length AB = L1 cos 𝜃1 + L2 cos 𝜃2

                   The required correction = (L1+ L2) - (L1 cos 𝜃1 + L2 cos 𝜃2)

7) Correction for Slope

The distance measured along the slope between two stations is always greater than the horizontal distance between them. The difference in slope distance and horizontal distance is known as slope correction which is always subtractive.

Fig. 2 Slope Correction

Let,

      L - Slope distance AB

     D - Horizontal distance AC

     H - Difference in reduced levels of A and B

Question 1

The length of a survey line measured with a 30m chain was found to be 631.5m. When the chain was compared with a standard chain, it was found to be 0.1m too long. Find the true length of the survey line.

Solution

                   

                           L’ = 30.1m. L = 30m

                Measured length of the survey line = 631.5m

               Thus, true length of the survey line = 30.130 x 631.5

                                                                                         = 633.603 m.

Question 2

A 20m chain was found to be 4 cm too long after chaining 1400m. It was 8 cm too long at the end of day’s work after chaining a total distance of 2420m. If the chain was correct before commencement of the work, find the true distance.

Solution

The correct length of the chain at commencement = 20m

The length of the chain after chaining 1400m = 20.04 m

The mean length of the chain while measuring = (20+20.04)/2 

                                                                                                  = 20.02m

The true distance for the wrong chainage of 1400m = (20.02/20)x1400 

                                                                                                           = 1401.4 m

The remaining distance = 2420-1400 

                                                  = 1020m

The mean length of chain while measuring the remaining distance = (20.08+20.04)/2 

                                                                                                                                           = 20.06m

The true length of remaining 1020m = (20.06/20) x 1020 

                                                                            =1023.06m

Hence, the total true distance = 1401.4 + 1023. 06 

                                                              = 2424.46 m

Question 3

A line was measured with a steel tape which was exactly 30 meters at 20℃ at a pull of 100N, the measured length being 1650.00 meters. The temperature during measurement was 30°C and the pull applied was 150N. Find the length of the line, if the cross-sectional area of the tape was 0.025 sq.cm. The co-efficient of expansion of the material of the tape per 1 ºC = 3.5x10^-6  and the modulus of elasticity of the material of the tape = 2.1x10⁵ N/mm².

Solution

i) Correction of temperature per tape length

                            Ct = 𝛼 (Tm – T0) L

                                 = 0.0000035 (30 – 20) x 30

                                 = 0.00105m (+ve)

ii) Correction for pull per tape length

                           CP = ((P-P0) x L)/(A E)

                                 = ((150-100) x 30)/(2.5x2.1x105)

                                 = 0.00286m (+ve)

Combined correction = 0.00105+0.00286

                                             = 0.00391m

True length of the tape = 30+0.0039

                                                 =30.0039m

True length of the line = (30.0039x1650.00)/30

                                               =1650.21m

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Errors in Chain Surveying

Surveying is a process that involves observations and measurements with a wide range of electronic, optical and mechanical equipment some of which are very sophisticated. Despite the best equipment and methods used, it is still impossible to take observations that are completely free of small variations caused by errors which must be guided against or their effects corrected.

Mistakes and Errors

No measurement can be perfect or exact because of the physical limitations of the measuring instrument as well as limits in human perception. The difference between a measured distance or angle and its true value may be due to mistakes and/or errors. These are two distinct terms. It is necessary to eliminate all mistakes and to minimize all errors when conducting a survey of any type.

Blunders

A blunder is a significant mistake caused by human errors. It may also be called a gross error. Generally, it is due to the inattention or carelessness of the surveyor and it usually results in a large difference between the observed or recorded quantity and the actual or the true value. Mistakes may be caused by sighting on a wrong target with the theodolite when measuring an angle and by tapping to an incorrect station. They also may be caused by omitting a vital piece of information such as the fact that a certain measurement was made on a steep slope instead of horizontally. The possibilities for mistakes are almost endless. However, they are only caused by occasional lapses of attention.

Errors

An error is the difference between a measured quantity and its true value, caused by imperfection in the measuring instrument, by the method of measurement, by natural factors such as temperature or by random variation in human observation. It is not a mistake due to carelessness. Errors can never be completely eliminated, but they can be minimized by using certain instruments and field procedures and by applying computed correction factors. Following are a few common mistakes in chain surveying.

• Once an arrow is withdrawn from the ground during chaining it may not be replaced in proper position, if required due to some reason.
• A full chain length may be omitted or added. This happen when arrows are lost or wrongly counted.
• The number may be read from the wrong direction; for instance, a 6 may be read as a 9.
• Some number may be called wrongly. For example, 50.2 may be called as fifty-two without the decimal point being mentioned.

Types of errors

1) Gross Errors

These are referred to mistakes or blunders by either the surveyor or his assistants due to carelessness or incompetence. On construction sites, mistakes are frequently made by in – experienced Engineers or surveyors who are unfamiliar with the equipment and method they are using. These types of errors include miscounting the number of tapes length, wrong booking, sighting wrong target, measuring anticlockwise reading, turning instruments incorrectly, displacement of arrows or station marks etc. Gross errors can occur at any stage of survey when observing, booking, computing or plotting and they would have a damaging effect on the results if left uncorrected. Gross errors can be eliminated only by careful methods of observing booking and constantly checking both operations.

2) Systematic or Cumulative Errors

Errors, which may occur in the same direction and which finally tend to accumulate are said to be cumulative. They seriously affect the accuracy of the work and are proportional to the length of the line (L). The errors may be positive or negative. The errors, that occur always in the same direction are called cumulative errors.

• Bad ranging
• Bad straightening
• Erroneous length of chain
• Temperature variation
• Variation in applied pull
• Non-horizontality
• Sag in the chain.

These are repetitive errors and cumulative in effect and are caused by badly adjusted instrument and the physical condition at the time of measurement must be considered in this respect. Expansion of steel, frequently changes in electromagnetic distance (EDM) measuring instrument, etc. are just some of these errors. Systematic errors have the same magnitude and sign in a series of measurements that are repeated under the same condition, thus contributing negatively or positively to the reading hence, makes the readings shorter or longer. This type of error can be eliminated from a measurement using corrections (e.g. effect of tension and temperature on steel tape). Another method of removing systematic errors is to calibrate the observing equipment and quantify the error allowing corrections to be made to further observations. Observational procedures by re-measuring the quantity with an entirely different method using different instrument can also be used to eliminate the effect of systematic errors.

Under the same conditions of measurement, systematic errors are constant in magnitude and direction or sign (either plus or minus). They usually have no tendency to cancel if corrections are not made. For example, suppose that a 30-m steel tape is the correct length at 200c and that it is used in a survey when the outdoor air temperature is, say 350c. Since steel expands with increase in temperatures, the tape will actually be longer than it was at 200c. Theodolites and even EDM are also subjected to systematic errors. The horizontal axis of rotation of the theodolite, for instance, may not be exactly perpendicular to the vertical axis.

a) Positive Cumulative Error

The error, which make the measured length more than the actual is known as positive cumulative error.

Sources

i) The length of chain / tape is shorter than its standard length due to

• Bending of links
• Removal of too many rings due to adjustment of its length.
• Knots in connecting links
• The field temperature is lower than that at which the tape was calibrated
• Shrinkage of tape when moist
• Clogging of rings with mud

ii) The slope correction is ignored while measuring along slopping ground

iii) The sag correction, if not applied when chain / tape is suspended at its ends

iv) Incorrect alignment

b) Negative Cumulative Error

The error, which make the measured length less than the actual is known as negative cumulative error.

Sources

a) The length of chain / tape is longer than its standard length due to

• Flattening of connecting rings
• Opening of the ring joints
• The field temperature is higher than that at which the tape was calibrated

3) Random or Accidental Error or Compensating Error

Errors, which may occur in both directions (that is both positive and negative) and which finally tend to compensate are known as compensating errors. Although every precaution may be taken certain unavoidable errors always exist in any measurement caused usually by human limitation in reading/handling of instruments. Random errors cannot be removed from observation but methods can be adopted to ensure that they are kept within acceptable limits. In order to analyse random errors or variable, statistical principles must be used and in surveying their effects may be reduced by increasing the number of observations and finding their mean. It is therefore important to assume those random variables are normally distributed. Some compensating errors includes the following.

• Incorrect marking of the end of a chain.
• Graduations in tape may not be exactly same throughout.

An accidental or random error is the difference between a true quantity and a measurement of that quantity that is free from blunders or systematic errors. Accidental errors always occur in every measurement. They are the relatively small, unavoidable errors in observation that are generally beyond the control of the surveyor. These random errors, as the name implies, are not constant in magnitude or direction. One example of a source of accidental errors is the slight motion of a plumb bob string, which occurs when using a tape to measure a distance. The tape is generally held above the ground and the plumb bob is used to transfer the measurement from the ground to the tape.

4) Personal errors

Wrong reading, wrong recording, reading from wrong end of chain etc., are personal errors. These errors are serious errors and cannot be detected easily. Care should be taken to avoid such errors.

Precautions against Errors and Mistakes

• The point where the arrow is fixed on the ground should be marked with a cross (×).
• The zero end of the chain or tape should be properly held.
• During chaining the number of arrows carried by the follower and leader should always tally with the total number of arrows taken.
• The chainman should call the measurement loudly and distinctly and the surveyor should repeat them while booking.
• Ranging should be done accurately.
• No measurement should be taken with the chain in suspension.

Adjustment of Chain

Chains are adjusted in the following ways.

i) When the chain is too long, it is adjusted by

   a) Closing up the joints of the rings

   b) Hammering the elongated rings

   c) Replacing some old rings by new rings

ii) When the chain is too short, it is adjusted by

   a) Straightening the bent links

   b) Opening the joints of the rings

   c) Replacing the old rings by some larger rings

Most Probable Value

If two or more measurements of the same quantity are made, random errors usually cause different values to be obtained. As long as each measurement is equally reliable, the average value of the different measurements is taken to be the true or the most probable value. The average (the arithmetic mean) is computed simply by summing all the individual measurements and then dividing the sum by the number of measurements.

The 90 Percent Errors

Using appropriate statistical formulas, it is possible to test and determine the probability of different ranges of random errors occurring for a variety of surveying instruments and procedures. The most probable error is that which has an equal chance (50 percent) of either being exceeded or not being exceeded in a particular measurement. It is sometimes designated as E90.

In surveying, the 90 percent error is a useful criterion for rating surveying methods. For example, suppose a distance of 100.00 ft is measured. If it is said that the 90 percent error in one taping operation, using a 100 ft tape, is ± 0.01 ft, it means that the likelihood is 90 percent that the actual distance is within the range of 100.00 ± 0.01 ft. Likewise, there will remain a 10 percent chance that the error will exceed 0.01 ft. It is sometimes called maximum anticipated errors. The 90 percent error can be estimated from surveying data, using the following formula from statistics. 

Where, 

       Δ = Delta, the difference between each individual measurement and the average of n measurements.

                  n = the number of measurements

To measure the distance, we have to use the tape several times; there would be nine separate measurements for 900ft distance, each with a maximum probable error of ± 0.01 ft. It is tempting simply to say that the total error will be 9 × (±0.01) = ± 0.09 ft. But this would be incorrect. Since some of the errors would be plus or some would be minus, they would tend to cancel each other out. It would be very unlikely that errors would completely cancel and so there still be a remaining error at 900 ft. A fundamental property of accidental or random errors is that they tend to accumulate or add up, in proportion to the square root of the number of measurements in which they occur. This relationship, called the law of compensation, can be expressed mathematically in the following equation.

Where 

              E = the total error in n measurements

              E₁ = the error for one measurement

              n = the number of measurements

From the above example, E = ± 0.01√9 = ± 0.01 × 3 = ± 0.03 ft. In other word, we can expect the total accidental error when measuring a distance of 900 ft to be within a range of ± 0.030 ft, with a confidence of 90 percent. It must be kept in mind that this type of analysis assumes that the series of measurements are made with the same instruments and procedures as for the single measurement for which the maximum probable error is known. 

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Chain Surveying

Chain Surveying is the simplest and oldest form of land surveying of an area using linear measurements only. It can be defined as the process of taking direct measurement, although not necessarily with a chain. In chain surveying the linear measurements are only made and no angular measurements are taken. Chain survey is suitable for the survey of areas that are fairly flat and small areas with simple details. This method is generally known as chain surveying because the principle instrument or equipment used in this method is the chain. The term taping can also be used for measurements with a tape. Tapes are more accurate and easier to carry and use than chains. However, chain surveying is ideally suited for rough use in difficult terrains.

General Procedure in Chain Surveying

a) Reconnaissance: Walk over the area to be surveyed and note the general layout, the position of features and the shape of the area.

b) Choice of Stations: Decide upon the framework to be used and drive in the station pegs to mark the stations selected.

c) Station Marking: Station marks, where possible should be tied into a permanent object so that they may be easily replaced if moved or easily found during the survey. In soft ground wooden pegs may be used while rails may be used on roads or hard surfaces.

d) Witnessing: This consists of making a sketch of the immediate area around the station showing existing permanent features, the position of the stations and its description and designation. Measurements are then made from at least three surrounding features to the station point and recorded on the sketch. The aim of witnessing is to re-locate a station again at much later date even by others after a long interval.

e) Offsetting: Offsets are usually taken perpendicular to chain lines in order to dodge obstacles on the chain line.

f) Sketching: Sketching the layout on the last page of the chain book, together with the date and the name of the surveyor, the longest line of the survey is usually taken as the base line and is measured first.

Equipment Used in Chain Surveying

The equipment used in chain surveying can be divided into three, namely

1. Those used for linear measurement. (Chain, steel band, linear tape)
2. Those used for slope angle measurement and for measuring right angle (e.g. Abney level, clinometer, cross staff, optical squares)
3. Other items (Ranging rods or poles, arrows, pegs etc.).

1) Chain

It is used to measure the distance between two points on the ground. The chain is composed of 100 or 150 pieces of galvanized mild steel wire 4mm in diameter called links. The ends of each link are bent into a loop and connected together by means of three rings. The ends of the chain are provided with brass handles for dragging the chain on the ground, each with a swivel joint so that the chain can be turned round without twisting. The length of the chain is measured from the outside of one handle to the outside of the other. Metallic tallies are fixed at various distinctive points of the chain to facilitate quick reading of a chain in surveying measurements.

Chain is designed for hard usage and is sufficiently accurate for measuring the chain lines and offsets of small surveys. Chains are made up of links which measure 200mm from centre to centre of each middle connecting ring and surveying brass handless are fitted at each end. To avoid confusion in reading, chains are marked similarly from both end (E.g. Tally for 2m and 18m is the same) so that measurements may be commenced with either end of the chain.

Types of chains

Generally, chains are of two types

1. Metric Chain
2. Non-metric Chain

1) Metric Chain

Metric chains are either 20m or 30m in length. A metric chain is prepared with 100 or 150 pieces/ links of galvanized mild steel wire of diameter 4mm. One metre is divided into 5 links each of 0.2m. The least count of metric chain is 0.2m. The ends of the pieces are bent to form loops and connected together by means of three oval shaped rings which gives flexibility to the chain. Two brass handles are provided at the two ends of the chain with swivel joints so that chain can be turned round without twisting. The outside of the handle is the zero point or the end point of the chain. The length of the chain is measured from the outside of one handle to the outside of the other. The length of a link is the distance between the centres of the two consecutive middle rings as shown in the Fig.1. The end links include the length of handle. Tallies are provided for marking 5m, 10m, etc for chains of 20m and 30m lengths and marked with letter “m” to distinguish the metric chain from non-metric chain. Small brass rings are provided at every meter length, except where tallies are attached. In metric chains readings are started from ends, increasing towards the centre. The length of chain whether 20m 0r 30m is indicated on the handle for easy identification.

Fig. 1 Metric Chain

2) Non – Metric Chain

In this type of chains other than metrics unit are used. Nowadays metric chains are used everywhere, therefore this type of chains become obsolete. Generally, these chains are 3 types.

a) Engineer’s Chain

The Engineer’s chain is 100ft. long and consists of 100links, each link being 1ft long. It is used in all engineering surveys.

b) Gunter’s Chain/Surveyor’s Chain

The Gunter’s chain is 66ft. long and is divided into 100 links each 0.66ft long. It is very convenient for measuring distances in miles and furlongs.

   10 Gunter’s chain = 1 furlong
   50 Gunter’s chain = 1 mile

   10 square Gunter’s chain = 1 acre

c) Revenue Chain

The standard size of this type of chain is 33ft. The number of links are 16. This chain is commonly used in cadastral survey.

Suitability of Chains

The chains are suitable for the following cases.

• It is suitable for ordinary or preliminary works as its length alters due to continuous use.
• Its length gets shortened due to bending of links and gets lengthened by flattening of the rings.
• Being heavier, a chain gets sagged considerably when suspended at the ends.
• It can be easily repaired in the field.
• Measurement readings can be taken very easily.
• It is only suitable for rough works.

Merits of Chains

• They can be read easily and quickly.
• They can withstand wear and tear.
• They can be easily repaired or rectified in the field.

Demerits of Chains

• They are heavy and take too much time to open or fold.
• They become longer or shorter due to continuous use.
• When the measurement is taken in suspension the chain sags excessively giving incorrect measurements.

2) Steel Bands

This may be 30m, 50m or 100m long and 13mm wide. It has handles similar to those on the chain and is wound on a steel cross. It is more accurate but less robust than the chain. The operating tension and temperature for which it was graduated should be indicated on the band.

Fig. 2 Steel Band

3) Tapes

Tapes are used where greater accuracy of measurements are required, such as the setting out of buildings and roads. They are 15m or 30m long marked in metres, centimetre and millimetres. Depending upon the material tapes are classified as the following.

a) Cloth or Linen Tape

Linen tapes are closely woven linen and varnished to resist moisture. They are generally 10 metres to 30 metres in length and 12mm to 15 mm in width. These tapes are liable to stretch in use and should be frequently tested for length. They should never be used on work for which great accuracy is required. Cloth tapes are generally used for measuring offset measurements only due to following reasons.

• It is easily affected by moisture and shrunk.
• Its length gets altered by stretching.
• It is likely to twist and tangle.
• It is not strong as a chain or steel tape.
• It is light and flexible and it does not remain straight in strong wind.
• Due to continuous use, its figures get indistinct.

b) Metallic Tape

A linen tape reinforced with brass or copper wires to prevent stretching or twisting of fibres is called a metallic tape. As the wires are interwoven and the tape is varnished, these wires are not visible to naked eyes. These tapes are available in different lengths but tapes of 20m and 30m lengths are very common. These are supplied in leather case with winding machine. Each metre is divided into decimeters and each decimeter is sub-divided into centimeters.

c) Steel Tape

These are much more accurate and are usually used for setting out buildings and structural steel works. Steel tapes are available in various lengths up to 100m (20m and 30m being the most common) encased in steel or plastic boxes with a recessed winding lever or mounted on open frames with a folding winding lever. Steel tapes are available with different accuracy of graduation. At the end of the tape a brass ring is provided. The length of metal ring is included in the length of tape. A steel tape of lowest degree of accuracy is generally superior to a metallic or cloth tape for linear measurements.

d) Invar Tape

Invar tapes are made of an alloy of nickel (36%) and steel (64%) having very low co-efficient of thermal expansion (0.000000122 per 1ºC). These are 6mm wide and are available in length of 30m, 50m and 100m. These tapes are used for high degree of precision required for base measurements.

e) Fibre Glass Tapes

These are much stronger than lines and will not stretch in use.

4) Arrows

Arrow are made of tempered steel wire of diameter 4mm. One end of the arrow is bent into a ring of diameter 50 mm and the other end is pointed as shown in Fig.2. Its overall length is 400mm. Arrows are used for counting the number of chains while measuring a chain line. Generally, 10 arrows accompany a chain. A piece of coloured cloth, white or red ribbon is usually attached or tied to the end of the arrow to be clearly seen on the field.

Fig. 3 Arrow

5) Pegs

Pegs are used to mark definite points on the ground. These are made of hard timber and are tapered at one end. They are usually 15cm length with 3 to 5cm diameter circular in shape (or) 3 to 5cm square in shape. The pointed end of peg is covered by iron shoe for easy driving into the ground. Wooden pegs usually 2.5cm square and 15cm deep are used to mark the position of survey stations. Pegs are driven with a mallet and nails are set in the tops.

Fig. 4 Pegs

6) Ranging Rod

Rods, which are used for ranging a line are known as ranging rod. Such rods are made of seasoned timber or seasoned bamboo or steel tubular rods. Sometimes GI pipes of 25mm/30mm diameter are also used as ranging rods. They are generally circular in section of diameter 25mm/30mm and length 2m / 3m. These are used for marking a point in such a way that the position of point can be clearly and exactly seen from some distance away. The rod is divided into equal parts of 20cm each and the divisions are painted black and white or red and white alternatively so that the rod is visible from a long distance. The lower end of the rod is pointed or provided with an iron shoe. Sometimes these are used to mark the permanent points. When they are at a considerable distance, red and white (or) while and yellow flags about 25cm square should be fastened at the top.

Fig. 5 Ranging Rod

7) Ranging Poles

These are similar to ranging rods except that they are heavier in section of length 4m to 6m. They are used for ranging very long lines in undulating ground. Their length varies from 4 m to 8 m and diameter from 60 mm to 100 mm. Ranging poles are commonly used to highlight the ends of survey lines, so that line of sight can be easily seen for extending lines or setting right angles with an optical square.

8) Offset Rod

It is similar to the ranging rod but is usually 3m long. The top is provided with a stout open ring recessed hook for putting or pulling the chain through a hedge or other obstruction like bushes etc. It is used for aligning the offset line and measuring short offsets. They are made up of hard wood and are provided with iron shoe at one end. At height of eye, two narrow slits at right angles to each other are also provided for using it for setting right angles.

9) Plumb Bob

It is used to transfer the end points of the chain onto ground while measuring distances in hilly terrain. It is also used for testing verticality of ranging poles, ranging rods etc. It is used while measuring distances on sloping ground and transfer to the levelled ground. It is made of steel in a conical shape with a thread connected at the centre. Plumb bobs come in a variety of shapes, sizes and weights, as shown in Fig. 6.

Fig. 6  Types of Plumb Bob

10) Cross Staff

This instrument is used for finding the foot of the perpendicular from a given point to a line, and setting out a right angle at a given point on a line. It consists of two pairs of vanes set at right angle to each other with a wide and narrow slit in each vane. The instrument is mounted upon a pole, so that when it is set up it is at normal eye level. It is also used for setting out lines at right angle to the main chain line. To set out a right angles the following three type of cross staffs are used.

   a) Open Cross Staff
   b) French Cross Staff

   c) Adjustable Cross Staff

11) Optical Square

It is used to set out right angles. It is a small compact hand instrument. It consists of a circular metal box about 5cm in diameter and 1.25cm deep. It is protected by a metal cover, which slides round so as to cover the openings and thus protects the mirrors from dust when not in use. H and I are the two mirrors placed at an angle of 45˚ to each other. It is used where greater accuracy is required. There are two types of optical square, one using two mirrors and the other a prism.

Fig. 7 Double Prism Optical Square

11) Clinometer

This instrument is used for measuring angles of ground slopes (slope angle). They are of several form, the common form is the Watking’s Clinometer, which consist of a small disc of about 60mm diameter. A weighted ring inside the disc can be made to hang free and by sighting across this graduated ring angle of slopes can be read off. It is less accurate than Abney level.

12) Abney Level

This instrument is generally used to obtain roughly the slope angle of the ground. It consists of a rectangular, telescopic tube (without lenses) about 125mm long with a graduated arc attached. A small bubble is fixed to the Vernier arm, once the image of the bubble is seen reflected in the eyepiece the angle of the line of sight can be read off with the aid of the reading glass.

Fig. 8 Abney Level

13) Hammer

It is used to give blows to fix the peg on the ground.

14) Laths

Laths are 0.5 to 1.0 m long sticks of soft wood. They are sharpened at one end and are painted with white or light colours. They are used as intermediate points while ranging or while crossing depressions.

15) Whites

Whites are the pieces of sharpened thick sticks cut from the nearest place in the field. One end of the stick is sharpened and the other end is split. White papers are inserted in the split to improve the visibility. Whites are also used for the same purpose as laths.

Necessary Precautions in Using Chain Surveying Instruments

• After use in wet weather, chains should be cleaned and steel tapes should be dried and wiped with an oily rag.
• A piece of coloured cloth should be tied to arrow (or ribbon – attached) to enable them to be seen clearly on the field.
• Ranging rods should be erected as vertical as possible at the exact station point.
• The operating tension and temperature for which steel bands/tapes are graduated should be indicated.
• Linen tapes should be frequently tested for length (standardized) and always after repairs.
• Always keep tapes reeled up when not in use.

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Responsibilities, Role and Tasks of a Surveyor

Surveying is classified as a learned profession because the modern surveyor needs a wide background of technical training and experience and must exercise independent judgement. A surveyor is a semi-professional who is the leader of a small, but expert team, usually consisting of the surveyor with one or more survey assistants. A surveyor must have a thorough knowledge of mathematics, particularly geometry and trigonometry and calculus, a solid understanding of survey theory and instruments. They must also have a thorough knowledge of methods in the areas of geodesy, photogrammetry, remote sensing, cartography and computers, with some competence in economics (including office management), geography, geology, astronomy and town planning, and a familiarity with laws pertaining to land and boundaries. They are governed by a professional code of ethics. The surveyor, as the leader of the team, will be required to make most of the decisions necessary for the smooth running of the team to ensure that the required tasks are fulfilled.

Responsibilities of a Surveyor

The responsibilities of the surveyor are many and varied, but can generally be reduced to the following.

i) Responsibility to the Task

The surveyor is responsible for completing the task required in the most efficient manner and in the time available. All effort must be made to ensure that the information supplied by the surveyor is as accurate as is possible to complete the task. Not all tasks require the same order of accuracy. By an understanding of the task the surveyor must decide on the accuracy to be achieved.

ii) Responsibility to the Client or Employer

The surveyor has a responsibility to the client or employer to produce what the client requires, within the budget restraints. This may need patience and tact in explaining to the client the limitations to a task.

iii) Responsibility to the Community

The surveyor has a responsibility to the community in general, to ensure that work undertaken by his team does not damage property or interfere with members of the community. Permission must be sought before accessing private property or before removing trees or shrubbery to enable survey measurements. The surveyor has a responsibility to protect the public in the purchases and sales of land.

iv) Responsibility to the Team

The surveyor, as the leader of the survey team, has a responsibility to the members of that team and must ensure that their needs are met regarding their leave, pay etc. The surveyor has a responsibility to ensure that all members of the team receive the training needed, not only to complete the task at hand, but also to enable them to advance within their chosen professions.

Role of a Surveyor

The role of the surveyor is that of the leader of the team. With that role come the responsibilities outlined above. The role of the surveyor is to perform the measurements necessary to complete any task required.

Tasks of a Surveyor

The tasks performed by a surveyor will depend on which branch of surveying they practice in. The most common tasks involve the determination of height and distances. For the Cadastral Surveyor, the main tasks involve the determination of property boundaries. For the Topographical Surveyor, the main tasks involve the location of detail on the earth’s surface for the production of maps. For the Engineer Surveyor, the main tasks include the setting out of buildings, sewers, drains, bridges and roadways; determining areas and volumes of regular and irregular figures; the preparation of detailed drawings and plans. For the Mine Surveyor, the main tasks include the setting out of mine lease boundaries and the calculation of end-of-month volumes.

Responsibilities, Role and Tasks of a Survey Assistant

The survey assistant is an important and integral part of any survey party. Most measurements performed by a surveyor require the assistance of another person, be it levelling with a staff man or distance measurement with a chainman.

Responsibilities of a Survey Assistant

The main responsibility of the survey assistant is to assist the surveyor in performing his or her tasks.

Role of a Survey Assistant

As mentioned above, most surveys require at least two people, the surveyor and another, to be able to undertake the necessary measurements. The role of the Survey Assistant is to be that second person in the performance of survey measurements.

Tasks of a Survey Assistant

The tasks performed by the Survey Assistant will depend on what the surveyor is undertaking. The primary task for the Survey Assistant will be as a chainman and a staff man, although he/she may also be required to make sure that the equipment is kept clean and ready to be used. The Survey Assistant will also look after the vehicle, making sure that it is refueled, cleaned and correctly packed for use. Each morning the Survey Assistant will pack the vehicle with the survey equipment needed for the day. While on the work site, the Survey Assistant will also perform the manual labour, such as clearing lines of sight of vegetation and clearing around survey control points. While traversing, the Survey Assistant will also work ahead of the Surveyor, plumbing tripods and targets over control points for the Surveyor to observe to. In general, the Survey Assistant will perform whatever task is needed to help the surveyor to complete their work.

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