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Approximate Stress Distribution method - Stress in Soil due to applied load, Soil Mechanics | Soil Mechanics Notes- Agricultural Engineering PDF Download

Approximate Stress Distribution method

In this method a 2:1 distribution of stress is assumed (as shown in Figure 6.2). If a rectangular area of B x L is loaded by uniformly distributed loadq, the vertical stress a depth of z below the loaded area can be determined as:

\[{\sigma _z}={{q(B \times L)} \over {(B + z) \times (L + z)}}\]                       (6.12)

The maximum stress is equal to average stress at depth equal to 2B. The maximum stress is greater than average stress if z < 2B and the maximum stress is less than average stress if z > 2B.

Approximate Stress Distribution method - Stress in Soil due to applied load, Soil Mechanics | Soil Mechanics Notes- Agricultural Engineering

Fig. 6.2. Approximate stress calculation method.

 Problem 1

Draw the vertical stress distribution due to a concentrated load (Q) of 50 kN acting on the surface of a soil for the following condition by using Boussinesq’s equation:

i) Variation of stress with depth for horizontal distance, r = 0 (points just vertically below the load) and r = 1m.

ii) Variation of stress with horizontal distance (either side of the load) for depth, z = 2m and z = 3m. 

Solution

Equation (6.4) is used to calculate the vertical stress at any depth at any horizontal distance from the point of application of the concentration load. Figure 6.3 shows the variation of vertical stress with depth at horizontal distance, r = 0 and r = 1m. Keeping r value constant, the stress is calculated for different z values upto z = 8m.  For example, at (r = 1m, z = 2m), the vertical stress is 4.22 kN/m2.      

Approximate Stress Distribution method - Stress in Soil due to applied load, Soil Mechanics | Soil Mechanics Notes- Agricultural Engineering


Fig. 6.3. Variation of vertical stress with depth.


Figure 6.4 shows variation of vertical stress with horizontal distance at depth z = 2m and z = 3m. It is observed that as the depth increases vertical stress decreases at the centre line. Same vertical stress is observed at different location with respect to depth and horizontal distance. For example, same vertical stress (2 kN/m2) is observed at (r = ± 1.5m, z = 2m) as well as at (r = ± 1 m, z = 3m). The line joining points with same vertical stress below ground level is called

Isobar.

Approximate Stress Distribution method - Stress in Soil due to applied load, Soil Mechanics | Soil Mechanics Notes- Agricultural Engineering

Fig.6.4. Variation of vertical stress with horizontal distance.

The document Approximate Stress Distribution method - Stress in Soil due to applied load, Soil Mechanics | Soil Mechanics Notes- Agricultural Engineering is a part of the Agricultural Engineering Course Soil Mechanics Notes- Agricultural Engineering.
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FAQs on Approximate Stress Distribution method - Stress in Soil due to applied load, Soil Mechanics - Soil Mechanics Notes- Agricultural Engineering

1. What is the approximate stress distribution method in soil mechanics?
Ans. The approximate stress distribution method in soil mechanics is a technique used to determine the stress distribution in soil due to an applied load. It involves simplifying assumptions and calculations based on empirical formulas to estimate the stress distribution within the soil.
2. How does the approximate stress distribution method work in agricultural engineering?
Ans. In agricultural engineering, the approximate stress distribution method is used to analyze the stress distribution in soil caused by various agricultural activities such as tillage, irrigation, and harvesting. By using this method, engineers can evaluate the impact of these activities on soil strength and stability.
3. What are the factors considered in the approximate stress distribution method?
Ans. The approximate stress distribution method takes into account several factors, including the load magnitude, load distribution, soil properties (such as cohesion and angle of internal friction), and the depth of the soil layer. These factors are used to estimate the stress distribution and its effects on the soil.
4. How accurate is the approximate stress distribution method in predicting stress in soil?
Ans. The accuracy of the approximate stress distribution method depends on the complexity of the soil and load conditions. While it provides a reasonable estimation of stress distribution, it may not capture all the intricacies of the actual stress distribution. It is recommended to validate the results with actual field measurements or more advanced analytical methods for critical applications.
5. Can the approximate stress distribution method be used to analyze stress in different soil types?
Ans. Yes, the approximate stress distribution method can be used to analyze stress in various soil types. However, the accuracy of the method may vary depending on the specific soil properties, such as cohesion, angle of internal friction, and compressibility. It is essential to consider the specific characteristics of the soil type when applying the approximate stress distribution method.
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