Differential stress
Encyclopedia
Differential stress is the difference between the greatest and the least compressive stress experienced by an object. For both the geological
and civil engineering
convention
is the greatest compressive stress and 
is the weakest,
.
In other engineering
fields and in physics
,
is the greatest compressive stress and 
is the weakest, so
.
These conventions originated because geologists and civil engineers (especially soil mechanicians
) are often concerned with failure in compression, while many other engineers are concerned with failure in tension. A further reason for the second convention is that it allows a positive stress to cause a compressible object to increase in size, making the sign convention self-consistent.
In structural geology
, differential stress is used to assess whether tensile or shear failure will occur when a Mohr circle (plotted using
and 
) touches the failure envelope of the rocks. If the differential stress is less than four times the tensile strength
of the rock
, then extensional failure will occur. If the differential stress is more than four times the tensile strength of the rock, then shear failure will occur.
Geology
Geology is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which it evolves. Geology gives insight into the history of the Earth, as it provides the primary evidence for plate tectonics, the evolutionary history of life, and past climates...
and civil engineering
Civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...
convention
is the greatest compressive stress and is the weakest,.In other engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
fields and in physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
,
is the greatest compressive stress and is the weakest, so.These conventions originated because geologists and civil engineers (especially soil mechanicians
Soil mechanics
Soil mechanics is a branch of engineering mechanics that describes the behavior of soils. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids and particles but soil may also contain organic solids, liquids, and gasses and other...
) are often concerned with failure in compression, while many other engineers are concerned with failure in tension. A further reason for the second convention is that it allows a positive stress to cause a compressible object to increase in size, making the sign convention self-consistent.
In structural geology
Structural geology
Structural geology is the study of the three-dimensional distribution of rock units with respect to their deformational histories. The primary goal of structural geology is to use measurements of present-day rock geometries to uncover information about the history of deformation in the rocks, and...
, differential stress is used to assess whether tensile or shear failure will occur when a Mohr circle (plotted using
and ) touches the failure envelope of the rocks. If the differential stress is less than four times the tensile strengthTensile strength
Ultimate tensile strength , often shortened to tensile strength or ultimate strength, is the maximum stress that a material can withstand while being stretched or pulled before necking, which is when the specimen's cross-section starts to significantly contract...
of the rock
Rock (geology)
In geology, rock or stone is a naturally occurring solid aggregate of minerals and/or mineraloids.The Earth's outer solid layer, the lithosphere, is made of rock. In general rocks are of three types, namely, igneous, sedimentary, and metamorphic...
, then extensional failure will occur. If the differential stress is more than four times the tensile strength of the rock, then shear failure will occur.