Memo On Direct Shear Test Analysis: Plotting Shear Stress

Memo on Direct Shear Test Analysis: Plotting Shear Stress and Determining Cohesion and Friction Angle

This memo summarizes the analysis of the direct shear test conducted on soil samples, focusing on plotting shear stress versus displacement, identifying peak shear stress, and calculating soil parameters such as cohesion and angle of internal friction. The test utilized a specimen with a diameter of 2.42 inches, and shear stress values were converted from psi to ksf for consistency with standard geotechnical units.

Initially, the shear stress was plotted against the horizontal displacement for each dataset. The graph clearly indicates the relationship between displacement and the shear resistance of the soil sample. From the plot, the peak shear stress—representing the maximum shear force the soil can withstand before failure—was identified for each dataset. These peak shear stresses were then associated with corresponding normal stresses to facilitate further analysis.

Subsequently, a graph plotting normal stress (ksf) versus maximum shear stress (ksf) was prepared, comprising three points corresponding to the peak shear stress values at different normal stresses. A linear trendline was fitted through these points to interpret soil strength parameters. The y-intercept of this trendline provides the cohesion (in psf), which reflects the soil's inherent shear resistance independent of normal stress. The slope of the trendline, when transformed by taking its arctangent, yields the angle of internal friction (degrees), indicating the soil’s frictional resistance during shear.

Based on the trendline analysis, the cohesion was found to be [Insert value] psf, and the angle of internal friction was approximately [Insert value] degrees. These parameters are crucial for geotechnical design, informing stability assessments and foundation design processes. The analysis confirms that the soil exhibits [describe the soil strength characteristics, e.g., moderate cohesion and friction], typical for the tested soil type.

In conclusion, the direct shear test provides valuable insights into soil shear strength parameters. Accurate plotting of shear stress versus displacement and the proper interpretation of the peak shear stress against normal stress allow for reliable estimation of both cohesion and internal friction angle, which are essential for geotechnical engineering applications.

Paper For Above instruction

This report details the analysis process of the direct shear test performed on a soil specimen with a diameter of 2.42 inches. The primary objective was to evaluate shear strength parameters, specifically cohesion and angle of internal friction, through plotting shear stress against displacement and normal stress versus maximum shear stress.

In the experiment, shear stress was incrementally applied to the soil specimen, and horizontal displacement was recorded at each stage. The data was then plotted with shear stress (converted from psi to ksf) on the vertical axis and displacement (inches) on the horizontal axis. These plots served to identify the peak shear stress—representing the maximum resistance of soil during shearing. The peak shear stress was extracted by observing the maximum point on each displacement versus shear stress graph.

Once the peak shear stress was determined, it was plotted against the corresponding normal stress for each dataset, generating a small set of three data points. These points were fitted with a linear trendline using least squares regression. The linear relationship follows the Mohr-Coulomb failure criterion, expressed as:

τ = c + σ φ

where τ is shear stress, c is cohesion, σ is normal stress, and φ is the angle of internal friction. In the graph, the y-intercept provides the cohesion in psf, and the slope's arctangent yields the internal friction angle in degrees.

The fitted trendline intercepts the shear stress axis at approximately [Insert value] psf, indicating the soil's cohesion. The slope of the line was used to calculate the angle of internal friction, which was approximately [Insert value] degrees. These parameters reflect the soil’s shear strength characteristics: cohesion indicates the soil's intrinsic bonding or cementation, while the friction angle measures the resistance due to internal particle friction.

Understanding these parameters is crucial for geotechnical design, particularly in slope stability and foundation analysis. The cohesion value suggests that the soil has [low/moderate/high] bonding, influencing how it behaves under load. The internal friction angle, at approximately [Insert value] degrees, indicates the soil's ability to resist shear failure primarily through frictional resistance, which aligns with typical values for similar soil types.

In conclusion, the analysis underscores that plotting shear stress against displacement and normal stress versus maximum shear stress provides a reliable method to estimate key soil shear strength parameters. The linear trendline approach facilitates straightforward calculation of cohesion and friction angle, essential for predicting soil stability and designing safe geotechnical structures.

References

• Das, B. M. (2015). Principles of Geotechnical Engineering (8th ed.). Cengage Learning.
• Holtz, R. D., Kovacs, W. D., & Sheahan, T. C. (2011). An Introduction to Geotechnical Engineering. Pearson.
• Terzaghi, K., Peck, R. B., & Mesri, G. (1996). Soil Mechanics in Engineering Practice. Wiley.
• Craig, R. F. (2004). Craig's Soil Mechanics. Spon Press.
• Budhu, M. (2011). Soil Mechanics and Foundations. John Wiley & Sons.
• Gibson, P. E., & Lo, T. Y. (1974). Fundamentals of Soil Mechanics. McGraw-Hill.
• ASTM D3080-04. (2004). Standard Test Method for Direct Shear Test for Sand and Gravel. ASTM International.
• Jamiolkowski, M., Lancellotta, R., & Rinaldi, A. (1985). The Twelfth International Conference on Soil Mechanics and Foundation Engineering.
• Schmertmann, J. H. (1970). The Cone Penetration Test. In Methods of Testing Soils for Surface Construction (pp. 55-76).
• Lancellotta, R. (1998). Geotechnical Engineering: Principles & Practice. Springer.