Explanation:

- The question is asking about which test to use for checking the initial stability of a footing resting on fully saturated clayey strata.
- The answer is option 'C', which is unconsolidated non-drained test.
- Let's break down the reasons why this is the correct answer:

Unconsolidated non-drained test:

- This test is also known as the "quick" or "falling head" test.
- It is used to determine the shear strength of a soil under conditions where there is no drainage of water from the specimen during the test.
- This test is appropriate for fully saturated soils, which is the condition in the question.
- The test involves applying a load to a soil specimen, and measuring the time it takes for the specimen to deform or fail.
- The results of the test can be used to determine the shear strength parameters of the soil, which are important for assessing the stability of foundations or other structures.
- In the case of the question, since the footing is resting on fully saturated clayey strata, the unconsolidated non-drained test is the most appropriate for determining the initial stability of the foundation.

Consolidated undrained test:

- This test is also known as the "one-step" test.
- It is used to determine the undrained shear strength of a soil specimen under conditions of total confinement.
- The test involves applying a load to a soil specimen while maintaining the total confinement, and measuring the deformation or failure of the specimen.
- This test is not appropriate for fully saturated soils, as the specimen must be consolidated prior to the test, which would result in drainage of water from the specimen.

Unconsolidated drained test:

- This test is also known as the "triaxial" test.
- It is used to determine the drained shear strength of a soil specimen under conditions of partial confinement.
- The test involves applying a load to a soil specimen while allowing drainage of water from the specimen, and measuring the deformation or failure of the specimen.
- This test is not appropriate for fully saturated soils, as the drainage of water from the specimen would not be possible.

Unconsolidated undrained test with pore pressure measurement:

- This test is similar to the unconsolidated non-drained test, but with the additional measurement of pore pressure during the test.
- It is used to determine the pore pressure buildup in a soil specimen during deformation or failure.
- This test can be useful for assessing the stability of a foundation or other structure under conditions of high pore pressure, but it is not necessary for determining the initial stability of the foundation in the case of the question.