Newmark's sliding block
Encyclopedia
The Newmark's sliding block analysis method is an engineering method used to calculate the permanent displacements of soil slopes (also embankments and dams) during seismic loading. It is also simply called Newmark's analysis or Sliding block method of slope stability
analysis.
as the name suggests in 1965 in the British Geotechnical Association's 5th Rankine Lecture
delivered by him in London and published later in the Association's scientific journal Geotechnique. The original inventor of the idea was Nicolas Ambraseys
whose doctoral thesis on the seismic stability of earth dams at Imperial College London
in 1958 formed the basis of the method. At his Rankine Lecture, Newmark himself acknowledged Ambraseys' contribution to this method through various discussions between the two researchers while the latter was a Visiting Professor at the University of Illinois.
method which considered the seismic slope failure only at limiting conditions (i.e. when the Factor of Safety, FOS became equal to 1) and providing information about the collapse state but no information about the induced deformations. The new method points out that when the FOS becomes less than 1 "failure
" does not necessarily occur as the time for which this happens is very short. However, each time the FOS falls below unity, some permanent deformations
occur which accumulate whenever FOS < 1. The method further suggests that a failing mass from the slope may be considered as a block of mass sliding (and therefore sliding block) on an inclined surface only when the inertial force (acceleration x mass) acting on it, is equal or higher than the force required to cause sliding.
Following these assumptions, the method suggests that whenever the acceleration (i.e. the seismic load) is higher than the critical acceleration
required to cause collapse, which may be obtained from the traditional pseudo-static method (such as Sarma method
), permanent displacements will occur. The magnitude of these displacements is obtained by integrating
twice (acceleration is the second time derivative
of displacement
) the difference of the apllied acceleration and the critical acceleration with respect to time.
on slopes. In the special case of earth dams
, it is used in conjunction with the shear beam method which can provide the acceleration time history at the level of the failure surface. It has been proved to give reasonable results and quite comparable to measured data.
However, Newmark's sliding block assumes rigidity - perfect plasticity
which is not realistic. It also cannot really take account of pore water pressure
built-up during cyclic loading which can lead to initiation of liquefaction
and different failures than simple distinct slip surfaces. As a result, more rigorous methods have beed developed and are used nowadays in order to overcome these shortcomings. Numerical methods such as finite difference
and finite element analysis are used which can employ more complicated elasto-plastic constitutive models simulating pre-yield elasticity.
Slope stability
The field of slope stability encompasses the analysis of static and dynamic stability of slopes of earth and rock-fill dams, slopes of other types of embankments, excavated slopes, and natural slopes in soil and soft rock...
analysis.
History
The method was proposed by Nathan M. NewmarkNathan M. Newmark
Nathan Mortimore Newmark was an American structural engineer and academic. He was awarded the National Medal of Science for engineering.-Early life:...
as the name suggests in 1965 in the British Geotechnical Association's 5th Rankine Lecture
Rankine Lecture
The Rankine Lecture is hosted in March each year by the British Geotechnical Association. It is widely viewed as the most prestigious of the invited lectures in Geotechnics.The lecture commemorates W. J. M...
delivered by him in London and published later in the Association's scientific journal Geotechnique. The original inventor of the idea was Nicolas Ambraseys
Nicolas Ambraseys
Professor Nicolas Neocles Ambraseys Dip.Eng DIC PhD FICE FREng is a Greek Engineering Seismologist...
whose doctoral thesis on the seismic stability of earth dams at Imperial College London
Imperial College London
Imperial College London is a public research university located in London, United Kingdom, specialising in science, engineering, business and medicine...
in 1958 formed the basis of the method. At his Rankine Lecture, Newmark himself acknowledged Ambraseys' contribution to this method through various discussions between the two researchers while the latter was a Visiting Professor at the University of Illinois.
Method
According to Kramer, the Newmark method is an improvement over the traditional pseudo-staticStatic
Static has several meanings:* Static electricity, a net charge of an object** The triboelectric effect, e.g. from shoes rubbing carpet* White noise, a random signal with a flat power spectral density** Noise , a type of radio interference...
method which considered the seismic slope failure only at limiting conditions (i.e. when the Factor of Safety, FOS became equal to 1) and providing information about the collapse state but no information about the induced deformations. The new method points out that when the FOS becomes less than 1 "failure
Failure
Failure refers to the state or condition of not meeting a desirable or intended objective, and may be viewed as the opposite of success. Product failure ranges from failure to sell the product to fracture of the product, in the worst cases leading to personal injury, the province of forensic...
" does not necessarily occur as the time for which this happens is very short. However, each time the FOS falls below unity, some permanent deformations
Deformation
In materials science, deformation is a change in the shape or size of an object due to an applied force or a change in temperature...
occur which accumulate whenever FOS < 1. The method further suggests that a failing mass from the slope may be considered as a block of mass sliding (and therefore sliding block) on an inclined surface only when the inertial force (acceleration x mass) acting on it, is equal or higher than the force required to cause sliding.
Following these assumptions, the method suggests that whenever the acceleration (i.e. the seismic load) is higher than the critical acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...
required to cause collapse, which may be obtained from the traditional pseudo-static method (such as Sarma method
Sarma method
The Sarma method is a method used primarily to assess the stability of soil slopes under seismic conditions. Using appropriate assumptions the method can also be employed for static slope stability analysis. It was proposed by Sarada K...
), permanent displacements will occur. The magnitude of these displacements is obtained by integrating
Integration
- Sociology and economy :*Social integration*Racial integration, refers to social and cultural behavior*Economic integration, refers to trade unification between different states*Educational integration of students with disabilities*Regional integration...
twice (acceleration is the second time derivative
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
of displacement
Displacement
-Physics:*Displacement , the difference between the path of the initial and final position covered by a moving object**Particle displacement, a measurement of distance of the movement of a particle in a medium as it transmits a wave...
) the difference of the apllied acceleration and the critical acceleration with respect to time.
Modern alternatives
The method is still widely used nowadays in engineering practice to assess the consequences of earthquakesEarthquake
An earthquake is the result of a sudden release of energy in the Earth's crust that creates seismic waves. The seismicity, seismism or seismic activity of an area refers to the frequency, type and size of earthquakes experienced over a period of time...
on slopes. In the special case of earth dams
Dam
A dam is a barrier that impounds water or underground streams. Dams generally serve the primary purpose of retaining water, while other structures such as floodgates or levees are used to manage or prevent water flow into specific land regions. Hydropower and pumped-storage hydroelectricity are...
, it is used in conjunction with the shear beam method which can provide the acceleration time history at the level of the failure surface. It has been proved to give reasonable results and quite comparable to measured data.
However, Newmark's sliding block assumes rigidity - perfect plasticity
Plasticity
Plasticity may refer to:Science* Plasticity , in physics and engineering, plasticity is the propensity of a material to undergo permanent deformation under load...
which is not realistic. It also cannot really take account of pore water pressure
Pore water pressure
Pore water pressure refers to the pressure of groundwater held within a soil or rock, in gaps between particles . Pore water pressures in below the phreatic level are measured in piezometers...
built-up during cyclic loading which can lead to initiation of liquefaction
Liquefaction
Liquefaction may refer to:* Liquefaction, the general process of becoming liquid* Soil liquefaction, the process by which sediments become suspended* Liquefaction of gases in physics, chemistry, and thermal engineering* Liquefactive necrosis in pathology...
and different failures than simple distinct slip surfaces. As a result, more rigorous methods have beed developed and are used nowadays in order to overcome these shortcomings. Numerical methods such as finite difference
Finite difference
A finite difference is a mathematical expression of the form f − f. If a finite difference is divided by b − a, one gets a difference quotient...
and finite element analysis are used which can employ more complicated elasto-plastic constitutive models simulating pre-yield elasticity.
See also
- Slope stabilitySlope stabilityThe field of slope stability encompasses the analysis of static and dynamic stability of slopes of earth and rock-fill dams, slopes of other types of embankments, excavated slopes, and natural slopes in soil and soft rock...
- Slope stability analysisSlope stability analysisThe slope stability analyses are performed to assess the safe and economic design of a human-made or natural slopes and the equilibrium conditions. The term slope stability may be defined as the resistance of inclined surface to failure by sliding or collapsing...
- Earthquake engineeringEarthquake engineeringEarthquake engineering is the scientific field concerned with protecting society, the natural and the man-made environment from earthquakes by limiting the seismic risk to socio-economically acceptable levels...
- Finite element analysis