Civil Engineering Formulas

All the Formulas and calculation used in technical & design calculation in Civil Engineering and the related fields of Civil Engineering are incorporated in this Book.

Author: Tyler Gregory Hicks

Used this Book only for Study and Practices.

Civil Engineering Formulas




              A hard foundation laid below ground level to support, strengthen, stabilize and renovate an existing Building or any other Structures is called Underpinning.

Methods And Construction Techniques

               The Rehabilitation of an existing building, mostly 40 to 50 years old, motivated by a change of use or structural damage, which may be a consequence of insufficient Soil Bearing Capacity, may require an underpinning project.

This type of work requires skilled labour, not only constructors, but also in the planning stage, since there is not an universal solution applicable to all cases. In fact, the underpinning solution depends on many factors, among which are the mechanical properties of the support stratum of soil, the conservation conditions of the foundation elements and, above all, the restrictions imposed during this operation.



                   Micropiles are presented as a variant of deep foundations, and consist of piles of small diameter between 75mm and 350mm, cast in situ, vertical or executed with an angle. These elements, when compressed, transmit their forces to the ground primarily by lateral friction (floating piles), although there is a small contribution from the bearing resistance.. In general, the execution of micropiles is divided into the following stages.

  • ·         Drilling to the specified depth.
  • ·         Placement of the reinforcement.
  • ·         Gravity fill injection of grout.
  • ·         Pressure postgrouting injection, when applicable.

 Pre-Stressed Connection

                   The use of this GEWI type systems results, firstly in the installation of a certain normal stress at the interface between the beam and the underpinned element. Moreover, the load transfer to the micropiles produces, according to the strut and tie method, tensions that can be absorbed at the expense of the resistance of these steel bars.


 Jet grouting

                  Jet grouting The physical process of jet grouting technique can be summarized in the following steps

  •  Soil fracture: the initial structure of the soil is broken and the soil particles or fragments are dispersed by the action of one or more horizontal jets.
  •  Mixing and partial replacement: a part of the particles or fragments of soil is replaced and the other part is mixed with the injected grout.
  •  Cementation: the remaining soil particles are bonded together as the grout sets and hardens, forming a single body.

This technique can be applied to both incoherent and cohesive soils, as a result of the conversion of the potential energy, obtained from pumping the grout, into kinetic energy.


Underpinning Tips

Normally, this process needs to be designed or lead by a structural engineer for better results, but here are a few tips that will help you during the underpinning process.
The underpinning process must be started from the corners and the working inwards.
Underpinning must be made only on load-bearing walls.

  • Do not underpin below non-load bearing walls.
  • Start underpinning under a strip of footing. It is recommended to start with at least 3 feet long, two feet wide and two feet in depth.
  • After the excavation has been completed, add concrete to the cavity. Concrete should be mixed using one part cement, three parts sand, and six parts aggregates.
  • Remember to use formwork on the edges.
  • Allowed concrete placed to set for at least two days.
  • Use a rod bar ensuring that the cavity under the existing foundation is filled up.
  • Ensure that the concrete is cured thoroughly before loading it.
  • Once the concrete has gained sufficient strength, break off the projecting footing.
  • Cut the concrete with the mass of concrete surface.
  • Backfill and compact. If you are having problems achieving the required consolidation, use a hose to add water to the soil.

Foundation: Types, Use and Objectives

images (1)

Foundation: Types, Use, Objectives


Definition & Introduction

                    Foundation are structural elements, which transfer loads to the soil from columns, walls or lateral loads from earth retaining structures.                 

                        A structure essentially consists of two parts, namely the super structure which is above the plinth level and the substructure which is below the plinth level. Substructure is otherwise known as the foundation and this forms the base for any structure. Generally about 30% of the total construction cost is spent on the foundation.The soil on which the foundation rests is called the “foundation soil”.Shallow FootingDeep Foundation

Types of Foundation

         The two main types of foundation are :

  • Shallow foundation/Footings
  • Deep foundation

Shallow Foundation

                     Shallow Foundation are usually located no more than 6 ft below the lowest finished floor OR Depth (D) of foundation is less than or equal to its width (B). When the soil bearing capacity of soil upto low depth is sufficient to take the structure load then it is provided.


Shallow Footing

Types of Shallow foundation

  1. Isolated  spread footing 
  2. Combined footing
  3. Cantilever or strap footings
  4. Wall footings
  5. Raft or Mat foundation
Combined footing
Combined Footing

Use of Shallow Foundation

            A shallow foundation system generally used when

  1.   The soil close the ground surface has sufficient bearing capacity
  2.   Underlying weaker strata do not result in undue settlement. The shallow foundations are commonly used most economical foundation systems.
Isolated Footing
Isolated Footing

Deep Foundations

           The shallow foundations may not be economical or even possible when the soil bearing capacity near the surface is too low. In those cases deep foundations are used to transfer loads to a stronger layer, which may be located at a significant depth below the ground surface. The load is transferred through skin friction and end bearing.Deep Foundation

Types of Deep foundation 

  1. Pile foundation
  2. Pier foundation
  3. Types of Pile foundation :
  4. Friction pile
  5. Load bearing pile
Foundation Load Mechanism
Pile Cap. Pile. Imposed Load (P) Skin Friction (Pf) End bearing (Pb) P = Pf + Pb.

Objectives of a foundation

  • To distribute the total load coming on the structure on a larger area.
  • To support the structures.
  • To give enough stability to the structures against various disturbing
  • forces, such as wind and rain.
  • To prepare a level surface for concreting and masonry work.



Types of Soil & Suitable Soil for Foundations Bed

Type of Soil (

In this article you will learn about different types of Soil and Suitable soil for any structure’s foundation bed.


Soil is sediments or other unconsolidated accumulations of solid particles produced by the chemical and physical disintegration of rocks which may or may not contain organic matter.

Types of Soil

The soil on which the foundations of various types of structure is to be constructed are classified into:

(1) Sand

The grain size of Sand varies between 0.075mm to 2mm. The shape of the grains may be angular, rounded or irregular and silica is the major constituents of sand.

Image result for sand for construction

Properties of Sand

  • It doesn’t shrink when dry.
  • It doesn’t swell when wet.
  • It is cohesionless.
  • It doesn’t affected by the action of frost.
  • It doesn’t allow water to rise up by capillary action.


Coarse sand provides a good foundation bed. Since it is angular shape that’s why it prevent the structures from slipping and also from escaping from under surface of the foundation concrete. Fine and saturated sand are not suitable for foundation use.

(2) Gravel and Shingle

This type of soil consists of mostly big size particles of coarse material resulting from the disintegration of rocks and often transported by water from their original source. Size of the particles varies from 3 mm to 200 mm. The stone particles having size more than 200 mm are termed as boulders.

Image result for gravel and shingle in construction

Properties of Gravel and Shingle

  • It is not affected by freezing of water.
  • It doesn’t swell when wet.
  • It doesn’t shrink when dry.
  • It has great power and strength of load bearing.
  • It doesn’t settle over the load.


Gravel and Shingle provides a good foundation bed and is suitable for foundation of almost all types of structures.

(3) Clay

It consists of particles having grain less than 0.002. It is composed of microscopic and sub-microscopic particles of weathered rocks. It consists of particle having grain size less than 0.002 mm.

Wet Clay

Properties of Clay

  • Clay can retain it shape vertically when hard but flows down when wet and exert pressures.
  • It consolidates under load and may cause settlement of the structure.
  • It is cohesive type of soil.
  • It shrinks and cracks when dry.
  • It swells and heaves when wet.


It is suitable for foundation of ordinary and light structures. But when heavy structure is to be constructed then must check through various laboratory tests because it is can settle down when saturated. It is also difficult to excavate when dry or when heavily saturated.

(4) Silt

It is finer variety of soil having grain size of 0.002 mm to 0.6 mm.

Silty Soil

Properties of Silt

  • It has slight tendency towards swelling and shrinkage.
  • It is relatively impervious.
  • It is not as superior is sand.
  • It is generally found in beds of river, canals and reservoirs.


It is not considered as a good foundation material.

(5) Alluvial Soil

This soil is transported by water forces and mixed with soils of different origin. When velocity of water reduced then large size particles are start settling down. On further reduction of the velocity of water, still smaller fraction separates out. Thus the alluvial soils are deposited according to the grains sizes.

Alluvial Soil Deposit

Properties of Alluvial Soil

  • It is a cohesive soil.
  • It is plastic but consolidate under load.
  • It Cracks on Drying.


This type of soil are suitable for light Structures.

(6) Black Cotton Soil

This type of soil is inorganic in nature. It is also called peat and bungum.

Black Cotton Soil

Properties of Black Cotton Soil

  • It swell when confined between walls.
  • It can withstand a high pressure in dry state.
  • It becomes so soft during rains that even mam cannot walk through it.
  • It is dark, grey or black in color.


It is the most unreliable soil for foundation bed.

(7) Reclaimed soil

This is also known as made-up soil. This types of soil consist of ballast or brick bats, ashes, old iron pieces etc used for filling the low lying areas or back filling

Properties of Reclaimed Soil

  • Its bearing strength is very low.
  • It is usually porous in nature.


This type of soil is not suitable for laying or constructing structure over it.

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