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Compressive strength is the ability of a structure or material to endure pushing forces exerted axially. The test involves determination of materials behaviour under crushing loads. The material, referred to as specimen, is subjected to compressive forces and the progressive deformation recorded at various loads. The data collected form basis for calculating the material’s compressive stress and strain. These are then plotted as stress-strain diagrams that are used in the determination of yield strength, yield point, proportional limit, elastic limit, and the compressive strength of the material under investigation.

Different materials exhibit different modes of deformation when subjected to compression testing. Some materials do show compressive instability due to work-softening. Others show homogeneous compression with no friction at the contact surfaces. Shearing and buckling modes of deformation occur in materials having large length to width ratios.

Generally, the compressive strength of a material is the value of the compressive stress achieved at the point of failure of a material. The apparatus used in compressive test is similar to that used in tensile test. The difference occurs in the application of uniaxial compressive loads rather than uniaxial tensile loads. The stress-strain curve for a typical specimen resembles the one below:

From the diagram, the compressive strength corresponds to the end point of the curve. After loading, the material follows Hooke’s Law represented by the linear region. The region shows stress as directly proportional to strain and is used to calculate the compression Young’s Modulus (E).This is as shown below:

At the end of the linear region is the yield point. Further compression of the material leads to plastic deformation; the material cannot achieve its original dimensions after removal of the load.

Stress is calculated by dividing force applied by the cross section area of the specimen. However, engineering stress differs from uniaxial stress. Engineering stress utilizes the original specimen area in its calculations. On the other hand, uniaxial stress utilizes the area under given force as the area of the specimen is a function of the compression force.

Engineering stress is given by:

Where F is the applied load in Newton (N); and A_{o} is the original cross-section of the specimen in square meters (m^{2}).

Engineering strain is given by:

Where *l* is the current length of the material under test in meters (m); and *l _{o}* is the original length of the material in meters (m).

The compressive strength of a specimen is taken at the point before crushing. Therefore, the engineering stress and strain is calculated by considering the specimen’s length and the force applied just before the crush.

## Compressive Strength of Gravel, Gabbro and Limestone

To determine the compressive strength of the three materials, specimens were selected of similar dimensions so that comparison could be drawn from the results. A compressive load was then applied to each specimen till occurrence of failure. The load at the point of failure and the corresponding length of the specimens were measured and recorded. It also included records of the initial and final cross-section area of the specimen. These were used in calculating engineering stress and strain.

The specimens selected for the test were cubes of 150 x 150 x 150mm. They were moulded using ordinary Portland cement and subjected to conventional curing. The compression test led to the following results:

## Compressive strength of specimens

Specimen |
Force at fracture (×10^{3}kN) |
|||

3 days | 7 days | 14 days | 28 days | |

Gabbro | 2.85 | 4.55 | 6.24 | 6.79 |

Limestone | 2.28 | 3.58 | 5.02 | 5.69 |

Gravel | 2.36 | 3.73 | 5.53 | 6.21 |

Specimen | Length at fracture l (m) |
Force at fracture (×10^{3}kN) |

Gabbro | 0.148 | 6.79 |

Limestone | 0.147 | 5.69 |

Gravel | 0.446 | 6.21 |

Where: Original cross-section of all specimen, A_{o} = 2.25 × 10^{-2}m^{2}; and

Original length of all specimen *l _{o}* = 0.15m.

## Analysis and Discussion

From the results, engineering stress at the point of fracture for the three specimens was calculated at 28 days as follows;

Engineering strain was also calculated as follows;

From the tests, it is evident that Gabbro has higher compressive strength compared to gravel and limestone. On the other hand, gravel has a higher compressive strength compared to limestone. The comparison of the compressive strengths can be demonstrated by the graph below:

The stress-strain diagram can be compared to the three specimens from the onset of loading to the point of crushing. The calculated values of the engineering stress and strain for specimen were tabulated below:

Stress (MPa) | Strain (e) | |

Gabbro | 320 | 0.013 |

Gravel | 276 | 0.027 |

Limestone | 253 | 0.02 |

From the tabulated values above, a graph was plotted to compare the compression Young’s Modulus for the specimens. The test assumed that the compression followed Hooke’s Law.

## Engineering Stress-Strain Graph for the Three Specimen

The high compressive strength of Gabbro makes it suitable for use as facing stone in buildings. Usually, it is in the form of polished slabs. Gabbro is dense granite found mainly in Russia. It is a greenish or dark plutonic rock. It contains Plagioclase Feldspar and Quartz.

The lower strength of limestone is attributed to its nature. Limestone is composed mainly of aragonite and calcite minerals. These are different crystal formations of calcium carbonate. It is a sedimentary rock. Most are formed by coral and foraminifera marine organisms. The rock is soluble in water and weak acid solutions. The rock has numerous uses that range from building materials, as chemical feedstock, and filler product in paints or toothpaste.

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Gravel is a composition of unconsolidated rock fragments. It explains it’s low compressive strength compared to the other rocks. The particles range from granule to bolder size fragments. The use of gravel falls into two main divisions. The construction industry uses some of it where it may be mixed with other materials or used as it is. Gravel is also used in industrial processes to aid in the production of other materials. The resources of gravel are very large and are mainly found as deposits along glacial and river flood plains.

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