The Study on Portable Falling Weight Deflectometer Based on the Elastic Half-Space Theory

2011 ◽  
Vol 97-98 ◽  
pp. 156-161
Author(s):  
De Cheng Feng ◽  
Wen Xin Zuo ◽  
Yin Zhao ◽  
Peng Cao
Keyword(s):  
Half Space ◽  
Integral Transform ◽  
Elastic Half Space ◽  
Space Theory ◽  
Falling Weight Deflectometer ◽  
Empirical Formulas ◽  
Foreign Countries ◽  
Back Calculation ◽  
Boussinesq Solution ◽  
Falling Weight

As a quick, accurate and efficient inspecting equipment, the Portable Falling Weight Deflectometer (PFWD) is widely used in subgrade modulus evaluation in the foreign countries. However, most analysis methods used in the modulus back calculation of PFWD is based on the classical Boussinesq solution or empirical formulas, which could hardly reflect the resilient of subgrade accurately. In this paper, the elastic half-space theory is introduced into the analysis of modulus back calculation, and with the integral transform and the numerical analysis, this paper provides an approximate method to evaluate the elastic modulus of subgrade.

Falling weight deflectometer data interpretation using dynamic impedance

1996 ◽  
Vol 23 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Dieter Stolle ◽  
Farideddin Peiravian
Keyword(s):  
Data Interpretation ◽  
Angular Frequency ◽  
Elastic Half Space ◽  
Graphical Form ◽  
Falling Weight Deflectometer ◽  
Dynamic Impedance ◽  
Back Calculation ◽  
Actual Field ◽  
A Site ◽  
Falling Weight

This paper deals with the characterization of pavements and their supporting subgrade by comparing the measured dynamic impedance of a site, based on falling weight deflectometer data, with that of a two-layer, elastodynamic model. The pavement is modelled as a Kirchhoff plate and the subgrade as an incompressible, semi-infinite, elastic half space. The impedance of the two-layer problem is developed in graphical form as a function of a dimensionless angular frequency that depends on the pavement and subgrade properties. The characterization methodology outlined is applied to both simulated and actual field data. The effects of bedrock location and increasing subgrade stiffness with depth on dynamic impedance are addressed, and some limitations associated with the back calculation of system parameters are discussed. Key words: pavements, layer moduli, impedance, dynamic, back calculation.

Normal Stresses in a Granular Material under Falling Weight Deflectometer Loading

1996 ◽  
Vol 1540 (1) ◽  
pp. 24-28 ◽  
Author(s):  
P. Ullidtz ◽  
V. Askegaard ◽  
F. O. Sjølin
Keyword(s):  
Elastic Half Space ◽  
Vertical Force ◽  
Falling Weight Deflectometer ◽  
Normal Stresses ◽  
Dynamic Effects ◽  
Sand Fraction ◽  
Measured Stress ◽  
Actual Force ◽  
Boussinesq’S Equation ◽  
Falling Weight

The vertical normal stress under a falling weight deflectometer (FWD) was measured in a sand. The material had more than 90 percent falling within the sand fraction from 60 μm to 2 mm. The stress was measured with three different transducers. All transducers were installed at a depth of 280 mm. The sand was uniform to a depth of 700 mm and at a distance of 600 mm to either side of the centerline. An FWD was used to exert a known vertical force on the surface of the sand, using a loading plate 300 mm in diameter. The average stress under the plate was about 300 kPa. All the loads were imposed in the centerline of the three gauges, but at different horizontal distances from FWD to transducers. An integration of the measured stress on the plane of the transducers results in a force 10 to 14 percent larger than the peak force exerted by the FWD. The measured force is thus reasonably close to the actual force. When the measured stress is compared with the stress predicted using Boussinesq's equation for an elastic half-space, a very large difference is observed. At the centerline of the load, the measured stress is about twice the theoretical value. This difference cannot be explained by variation in material characteristics, including nonlinearity, or by dynamic effects.

Axisymmetric contact with friction of a rigid sphere with an elastic half-space

2009 ◽  
Vol 465 (2108) ◽  
pp. 2565-2588 ◽  
Author(s):  
O. I. Zhupanska
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Integral Transform ◽  
Elastic Half Space ◽  
Rigid Sphere ◽  
Analytical Treatment ◽  
Normal Contact ◽  
Exact Analytical Solutions ◽  
Single Integral ◽  
Toroidal Coordinates

The problem of normal contact with friction of a rigid sphere with an elastic half-space is considered. An analytical treatment of the problem is presented, with the corresponding boundary-value problem formulated in the toroidal coordinates. A general solution in the form of Papkovich–Neuber functions and the Mehler–Fock integral transform is used to reduce the problem to a single integral equation with respect to the unknown contact pressure in the slip zone. An analysis of contact stresses is carried out, and exact analytical solutions are obtained in limiting cases, including a full stick contact problem and a contact problem for an incompressible half-space.

Elastic Half Space under Axisymmetric Surface Loading and Influence of Couple Stresses

2020 ◽  
Vol 897 ◽  
pp. 129-133
Author(s):  
Jintara Lawongkerd ◽  
Toan Minh Le ◽  
Suraparb Keawsawasvong ◽  
Suchart Limkatanyu ◽  
Jaroon Rungamornrat
Keyword(s):  
Half Space ◽  
Integral Transform ◽  
Couple Stress Theory ◽  
Elastic Field ◽  
Elastic Half Space ◽  
Small Scale ◽  
Internal Length ◽  
Stress Theory ◽  
Axisymmetric Surface ◽  
Small Scale Effect

This paper presents the complete elastic field of a half space under axisymmetric surface loads by taking the influence of material microstructures into account. A well-known couple stress theory is adopted to handle such small scale effect and the resulting governing equations are solved by the method of Hankel integral transform. A selected numerical quadrature is then applied to efficiently evaluate all involved integrals. A set of results is also reported to not only confirm the validity of established solutions but also demonstrate the capability of the selected mathematical model to simulate the size-dependent characteristic of the predicted response when the external and internal length scales are comparable.

Visco-Elastic Back-Calculation of Traffic Speed Deflectometer Measurements

2019 ◽  
Vol 2673 (12) ◽  
pp. 439-448 ◽  
Author(s):  
Christoffer P. Nielsen
Keyword(s):  
Calculation Procedure ◽  
Falling Weight Deflectometer ◽  
Calculation Algorithm ◽  
Structural Evaluation ◽  
Driving Speed ◽  
Back Calculation ◽  
Traffic Speed ◽  
Falling Weight ◽  
Calculation Procedures ◽  
Project Level

The traffic speed deflectometer (TSD) has proven a valuable tool for network level structural evaluation. At the project level, however, the use of TSD data is still quite limited. An obstacle to the use of TSD at the project level is that the standard approaches to back-calculation of pavement properties are based on the falling weight deflectometer (FWD). The FWD experiment is similar, but not equivalent, to the TSD experiment, and therefore it is not straightforward to apply the traditional FWD back-calculation procedures to TSD data. In this paper, a TSD-specific back-calculation procedure is presented. The procedure is based on a layered linear visco-elastic pavement model and takes the driving speed of the vehicle into account. This is in contrast to most existing back-calculation procedures, which treat the problem as static and the pavement as purely elastic. The developed back-calculation procedure is tested on both simulated and real TSD data. The real TSD measurements exhibit significant effects of damping and visco-elasticity. The back-calculation algorithm is able to capture these effects and yields model fits in excellent agreement with the measured values.

Dynamic Response of a Rigid Foundation Subjected to a Distance Blast

2012 ◽  
Author(s):  
Deji Ojetola ◽  
Hamid R. Hamidzadeh
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Integral Transform ◽  
Numerical Technique ◽  
Formal Solution ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Rigid Foundation ◽  
Transform Method

Blasts and explosions occur in many activities that are either man-made or nature induced. The effect of the blasts could have a residual or devastating effect on the buildings at some distance within the vicinity of the explosion. In this investigation, an analytical solution for the time response of a rigid foundation subjected to a distant blast is considered. The medium is considered to be an elastic half space. A formal solution to the wave propagations on the medium is obtained by the integral transform method. To achieve numerical results for this case, an effective numerical technique has been developed for calculation of the integrals represented in the inversion of the transformed relations. Time functions for the vertical and radial displacements of the surface of the elastic half space due to a distant blast load are determined. Mathematical procedures for determination of the dynamic response of the surface of an elastic half-space subjected to the blast along with numerical results for displacements of a rigid foundation are provided.

A practical approach to falling-weight deflectometer (FWD) data reduction

2005 ◽  
Vol 42 (2) ◽  
pp. 641-645 ◽  
Author(s):  
Dieter Stolle ◽  
Peijun Guo
Keyword(s):  
Mechanical Properties ◽  
Shear Modulus ◽  
Falling Weight Deflectometer ◽  
Layer System ◽  
Surface Loading ◽  
Back Calculation ◽  
Pavement Response ◽  
Subgrade Modulus ◽  
Falling Weight

The authors present a simplified methodology for preprocessing falling-weight deflectometer (FWD) data, which identify a pseudo-static pavement response to surface loading. This allows one to employ static analysis to back-calculate the mechanical properties of the pavement–subgrade system. It is shown that the subgrade modulus can be identified, independent of the details of the pavement structure itself, at least for a two-layer system. The quality of the effective shear modulus is sensitive to the value of Poisson's ratio selected.Key words: pavement–subgrade system, subgrade modulus, back-calculation, FWD.

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