The critical depth is defined as the maximum depth of excavation of soil that can be performed without any failure. Critical depth is one of the essential considerations of design used to study and analyze the stability of unsupported trenches or excavations. An open excavation performed beyond the critical depth of the given soil type, results in the dissipation of residual stress, aiding to the instability of the soil mass.

Critical depth is a parameter that studies the need for excavation support systems for the construction of structures. As per OHSAS(Occupational Health and Safety Assessment Series), all the trenches or excavation with a depth that exceeds 5 feet need shoring or bracing or any other excavation support systems. Instead of providing structural support, the excavated walls can be sloped to avoid collapse.

The article explains the parameters that must be studied to determine the critical depth of the open excavation of a particular soil type.

**Critical Depth in Open Excavation**

The determination of critical depth in open excavation for homogeneous soils is given by Taylor’s method. Taylor developed a series of design curves based on the total stress conditions, to establish an approximate value of factor of safety (FS).

Taylor hence developed a relation involving the unit weight of soil, the critical height of excavation (Hc), cohesion value of soil ‘c’ and Stability number 'Ns' as:

Factor of Safety(FS) is the ratio of resisting forces to the driving forces. These forces can also be resisting moments and driving moments. An **FS** less than or equal to 1 results in the failure of the slope. A theoretically stable slope has an **FS** value greater than 1. The usual **FS** required is between 1.3 to 1.5.

Factor of Safety for a slope is studied by the following information:

- The soil and Water Profile
- The kinematics of slope failure
- The strength of soil
- The weight of soil

The factor of safety can be determined in terms of height as the ratio of the maximum height of slope ( critical depth ) to the actual height of the slope. Therefore,

**FS = Hc/H Eq.2**

**Determination of Stability number (Ns)**

Taylor developed a graph showing the relationship between the stability number (Ns), the slope angle (B), and the angle of friction of the soil (Eq.1). Given the slope angle and the angle of friction of the soil, the stability number is calculated from the graph below.

The value of stability number varies with the types of slope failures of the given soil.

## Determination of **Critical Depth in Open Excavation**

The formula below can determine the critical depth (Hc) in open excavation

The calculation can be understood by an example below:

**Example 1**

A soft clay is excavated with a slope angle of 75 degrees with the horizontal. The stability number is 4.55. The soil cohesion value is 650psf. The unit weight of the soil is 110pcf. Determine the maximum depth up to which the excavation can be carried out? What is the F.S of the slope against sliding or failure, if the depth excavated is 10feet?

**Solution:**

**Given,**

- Ns=4.55
- C= 650 psf
- Unit weight ( Gama) = 110 pcf

Note: The unit pcf is pound per cubic foot. 1pcf = 16.02kg/m3

The equation for Critical depth is given by, Eq.3,

By substituting the values, Hc = [4.55 x 650]/110 = 26.9ft

As per the question, if the depth excavated is 10ft, the Factor of safety F.S is given by Eq.2,

**F.S = Hc/H**

Where, Hc =26.9ft and H = 10ft

Then, F.S = 26.9/10 = 2.69 >1

As the FS is greater than 1, the slope excavated is stable.

## Safe Heights for Open Excavation

From the chart shown above, the theoretical safe heights for homogeneous clay cut slope that is subjected to vertical side cutting are tabulated below.

Open excavation that demands to dig deeper than critical depth requires temporary slope protection, to prevent the collapse of the soil materials, excavation hazards, and for the safety of workmen.

### Frequently Asked Questions

**How deep can I conduct open excavation without support?**

As per OSHAS (Occupational Safety and Health Act), all the trenches or excavation with a depth that exceeds 5 feet need shoring or bracing or excavation support systems. Instead of providing structural support, the excavated walls can be sloped to avoid collapse.

Open excavation that demands to dig deeper than critical depth requires temporary slope protection to prevent the collapse of the soil materials, excavation hazards, and for the safety of workmen.

**What is the formula to determine the critical depth of open excavation?**

Critical depth of open excavation (Hc) is given by the formula:

Where Ns is the stability number, 'c' is the value of cohesion of soil, and Gama is the unit weight of the soil.

**What are the different methods to support open excavation beyond critical depth?**

Different methods of supporting excavation include temporary support structures, shoring, adequate sloping, etc.

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