5.3 Newmark's influence charts
4 min read•august 16, 2024
Newmark's influence charts simplify stress calculations in soil masses. These graphical tools, developed in 1935, estimate vertical stresses due to surface loads based on Boussinesq's theory. They're super useful for quick stress estimates under various loading conditions.
Engineers use these charts for foundation analysis, embankment design, and settlement calculations. They're great for preliminary designs and checking complex numerical analyses. However, they assume simple soil conditions, so they might not work for all real-world situations.
Newmark's Influence Charts: Concept and Purpose
Development and Theoretical Basis
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- Graphical tools estimate vertical stresses in soil masses due to surface loads
- developed these charts in 1935 to simplify stress calculations
- Based on Boussinesq's theory of stress distribution in elastic, homogeneous, and isotropic half-space
- Provide influence values (I) representing the ratio of vertical stress at a point to applied surface pressure
- Allow quick estimation of stresses under various loading conditions (point loads, line loads, uniformly distributed loads)
- Particularly useful for determining stresses at depths below corners of rectangular loaded areas
- Serve as practical alternative to complex mathematical calculations
- Valuable tools for geotechnical engineers in preliminary design stages
Applications in Geotechnical Engineering
- Used to analyze stress distribution under foundations (spread footings, mat foundations)
- Apply to embankment design and stability analysis
- Assist in settlement calculations for various structures
- Help evaluate stress changes in soil due to construction activities (excavations, tunneling)
- Aid in the design of retaining walls and earth support systems
- Support the analysis of slope stability problems
- Facilitate quick stress estimates for geotechnical reports and feasibility studies
Interpreting Newmark's Influence Charts
Chart Structure and Components
- Consist of concentric circles and radial lines representing influence values for different load configurations
- Presented in dimensionless form with horizontal distances expressed as ratios of depth to point of interest
- Provide influence values for various ratios of length to width (L/B) of rectangular loaded areas
- Include separate charts for different loading scenarios (point loads, line loads, rectangular areas)
- Contain isobar lines connecting points of equal influence values
- Feature depth ratios (z/B) along the vertical axis and horizontal distance ratios (x/B) along the horizontal axis
- Incorporate a legend explaining the meaning of different line types and symbols used in the chart
Using the Charts for Stress Determination
- Identify location of interest relative to loaded area and determine corresponding influence value (I)
- Calculate vertical stress by multiplying influence value by applied surface pressure
- Apply principle of superposition for rectangular loaded areas by considering stress contributions from all four corners
- Interpolate between chart values for points not directly on provided
- Use chart directly for point loads to determine influence value at desired depth and radial distance
- Treat line loads as series of point loads and apply superposition to calculate total stress
- Approximate irregularly shaped loaded areas with rectangles and calculate stresses using superposition
Applying Newmark's Influence Charts for Stress Calculation
Stress Calculation Procedures
- For uniformly distributed loads over rectangular areas sum contributions from all four corners
- Determine stress under center of uniformly loaded rectangular area using simplified equation based on influence value
- Analyze stress distribution under foundations, embankments, and other surface loads in geotechnical projects
- Apply charts to each layer separately when dealing with layered soils considering stress distribution from layer above
- Calculate stress increase at a point due to multiple loaded areas by summing individual contributions
- Determine stress distribution along a vertical line by applying the chart at various depths
- Estimate stress changes with depth to evaluate potential for soil or settlement
Practical Examples and Applications
- Calculate vertical stress increase at depth of 5m below corner of 10m x 20m foundation loaded with 200 kPa
- Estimate stress distribution under a long strip footing (line load) supporting a retaining wall
- Determine stress increase at various depths below center of circular tank foundation
- Analyze stress distribution in soil layers beneath an embankment with varying geometry
- Evaluate stress changes in soil due to excavation by considering negative loading
- Calculate stress increase at a point due to multiple building foundations in close proximity
- Estimate stress distribution along potential failure surface in a
Advantages vs Limitations of Newmark's Influence Charts
Advantages and Practical Benefits
- Provide simplicity, speed of use, and ability to generate quick estimates for various loading conditions
- Particularly useful in preliminary design phase and for checking more complex numerical analysis results
- Allow easy visualization of stress distribution patterns in soil masses
- Facilitate rapid parametric studies by varying load configurations or soil properties
- Serve as effective teaching tools for understanding stress distribution concepts in geotechnical engineering
- Enable quick hand calculations in the field or during client meetings
- Provide a standardized method for stress estimation across the geotechnical engineering industry
Limitations and Considerations
- Assume elastic, homogeneous, and isotropic soil conditions which may not accurately represent all real-world situations
- Do not account for soil layering, anisotropy, or non-linear stress-strain behavior affecting stress distribution in complex soil profiles
- Decrease in accuracy with increasing depth and distance from loaded area
- Lack information on horizontal stresses or shear stresses which may be critical in certain geotechnical analyses
- May require supplementation or replacement by advanced numerical methods (finite element analysis) for complex loading scenarios or soil conditions
- Do not consider effects or time-dependent soil behavior
- Limited in their ability to model three-dimensional stress distributions in highly irregular geometries
Key Terms to Review (15)
Consolidation: Consolidation refers to the process by which soil decreases in volume over time due to the expulsion of water from its pores under sustained load. This process is critical in understanding how soils behave under load and is closely linked to factors such as soil-water interaction, effective stress, and drainage conditions.
Distance to the Point of Interest: Distance to the point of interest refers to the specific measurement of how far a particular location is from a designated reference point where analysis or observation is focused. This distance plays a critical role in various geotechnical analyses, particularly when assessing the impact of soil behavior and external loads at different locations.
Dynamic loading: Dynamic loading refers to the application of loads that change over time, typically involving forces that vary in magnitude and direction. This concept is crucial in understanding how structures respond to different types of stresses, such as those caused by earthquakes, wind, or moving vehicles. It highlights the importance of analyzing not just static conditions but also the effects of time-varying loads on soil and structural integrity.
Earthquake engineering: Earthquake engineering is a field of engineering that focuses on designing structures and infrastructure to withstand seismic activity and minimize damage during earthquakes. It encompasses a range of techniques and analyses that aim to reduce the risks associated with earthquakes, ensuring safety and resilience in built environments. This discipline draws from various scientific principles, including geotechnical engineering, to create solutions for earthquake-prone regions.
Finite Element Method: The Finite Element Method (FEM) is a numerical technique used for solving complex engineering and mathematical problems by breaking down a larger system into smaller, simpler parts called finite elements. This method is particularly useful in analyzing physical phenomena such as seepage, stress distribution, and slope stability, allowing engineers to predict how structures will respond under various conditions.
Influence Lines: Influence lines are graphical representations used in structural engineering to show how the reaction or internal forces at a particular point in a structure vary as a moving load traverses the structure. They are essential for analyzing structures subjected to moving loads, helping engineers to understand the maximum and minimum effects of these loads on various points of interest.
Limit Equilibrium Analysis: Limit equilibrium analysis is a method used in geotechnical engineering to assess the stability of slopes, retaining structures, and other soil masses. It focuses on determining the balance between driving forces that may cause failure and resisting forces that help maintain stability, typically using methods like factor of safety calculations to ensure safety in construction and design.
Liquefaction: Liquefaction is the process by which saturated or partially saturated soil substantially loses strength and stiffness in response to applied stress, often due to seismic shaking, transforming it temporarily into a fluid-like state. This phenomenon significantly impacts the stability of structures and ground during earthquakes and is crucial to understanding various geotechnical challenges.
Load Magnitude: Load magnitude refers to the size or intensity of a load acting on a structure or soil, measured in force per unit area. Understanding load magnitude is crucial for analyzing the behavior of structures and foundations, as it influences stress distributions and potential deformations in the underlying soil or material.
Nathan M. Newmark: Nathan M. Newmark was a prominent engineer and educator known for his contributions to the fields of civil engineering and structural analysis. He is particularly recognized for developing Newmark's influence charts, which are used to analyze the effects of loads on structures, especially in geotechnical engineering applications, demonstrating his lasting impact on engineering education and practice.
Newmark's Influence Method: Newmark's Influence Method is a technique used in geotechnical engineering to analyze the settlement of foundations and earth structures under applied loads. This method utilizes influence charts to estimate the vertical displacements caused by point loads at various locations, allowing engineers to understand how different factors affect ground movement. By using these charts, practitioners can simplify complex problems involving soil mechanics and foundation design.
Settlement analysis: Settlement analysis refers to the process of evaluating the vertical displacement of the ground surface that occurs due to loading, typically from structures or soil consolidation. Understanding this concept is crucial in predicting how structures will behave over time and ensuring their stability and integrity under various conditions.
Shear Strength: Shear strength is the maximum resistance of a soil or rock to shear stress, which is critical in understanding how materials behave under loading conditions. This concept is essential in various aspects of geotechnical engineering, as it influences stability, load-bearing capacity, and the overall performance of structures in contact with soil.
Slope stability analysis: Slope stability analysis is a method used to determine the safety and stability of slopes, assessing the potential for landslides or other failures due to gravitational forces acting on soil and rock materials. This analysis incorporates various factors such as the effective stress within the slope, external loads, and material properties to predict whether a slope will remain stable or if it is at risk of failure under certain conditions.
Static loading: Static loading refers to the application of a constant load or force on a structure or material that does not change over time. This type of loading is important in geotechnical engineering as it affects the stability and performance of foundations and other structures. Understanding static loading is crucial for predicting how materials will behave under steady conditions, and it serves as a baseline for analyzing more complex loading scenarios like dynamic loading.