Introduction:
The long-term stability of an excavated clay slope is a critical consideration in geotechnical engineering. Triaxial tests are commonly used to assess the mechanical properties and stability of soils. Different types of triaxial tests can be conducted depending on the specific conditions and requirements of the slope.

Explanation:
The most appropriate triaxial test to assess the long-term stability of an excavated clay slope is the Consolidated Drained (CD) test. This test involves applying a confining pressure and allowing the soil sample to consolidate under this pressure before shearing is initiated. The drainage is allowed during the entire test, which mimics the long-term conditions of the slope.

Reasons:
There are several reasons why the Consolidated Drained (CD) test is the most appropriate for assessing the long-term stability of an excavated clay slope:

1. Realistic simulation: The CD test allows for the realistic simulation of long-term conditions by allowing drainage during the test. In an excavated slope, there may be pore water pressures that dissipate over time, and the CD test accounts for this drainage.

2. Consolidation effects: Excavated clay slopes often undergo consolidation due to the excavation process and subsequent loading. The CD test captures the consolidation effects by allowing the soil sample to consolidate under the applied confining pressure before shear is initiated.

3. Long-term stability assessment: The CD test provides information on the long-term stability of the clay slope by evaluating the shear strength parameters (such as cohesion and angle of internal friction) under drained conditions. This is important for assessing the potential for slope failure over time.

4. Shear strength behavior: The CD test allows for the measurement of shear strength parameters at various stress levels and strain rates, which is essential for understanding the behavior of the clay slope under long-term loading conditions.

In summary, the Consolidated Drained (CD) test is the most appropriate triaxial test to assess the long-term stability of an excavated clay slope. It provides a realistic simulation of long-term conditions, captures consolidation effects, and evaluates shear strength parameters under drained conditions. This information is crucial for assessing the stability and potential failure mechanisms of the slope over time.

In consolidated drained test, expulsion of pore water is permitted in both the stages. It is used for short-term and long-term stability analyses in saturated sands and long-term stability analysis in clays.