Geometric Scale Factor Research Articles

New granular rock-analogue materials for simulation of multi-scale fault and fracture processes

AbstractIn this study, we present a new granular rock-analogue material (GRAM) with a dynamic scaling suitable for the simulation of fault and fracture processes in analogue experiments. Dynamically scaled experiments allow the direct comparison of geometrical, kinematical and mechanical processes between model and nature. The geometrical scaling factor defines the model resolution, which depends on the density and cohesive strength ratios of model material and natural rocks. Granular materials such as quartz sands are ideal for the simulation of upper crustal deformation processes as a result of similar nonlinear deformation behaviour of granular flow and brittle rock deformation. We compared the geometrical scaling factor of common analogue materials applied in tectonic models, and identified a gap in model resolution corresponding to the outcrop and structural scale (1–100 m). The proposed GRAM is composed of quartz sand and hemihydrate powder and is suitable to form cohesive aggregates capable of deforming by tensile and shear failure under variable stress conditions. Based on dynamical shear tests, GRAM is characterized by a similar stress–strain curve as dry quartz sand, has a cohesive strength of 7.88 kPa and an average density of 1.36 g cm−3. The derived geometrical scaling factor is 1 cm in model = 10.65 m in nature. For a large-scale test, GRAM material was applied in strike-slip analogue experiments. Early results demonstrate the potential of GRAM to simulate fault and fracture processes, and their interaction in fault zones and damage zones during different stages of fault evolution in dynamically scaled analogue experiments.

Investigation of inter-zonal heat transfer in large space buildings based on similarity: Comparison of two stratified air-conditioning systems

Stratified air-conditioning (STRAC) has been deployed in large space buildings to achieve vertical thermal stratification with significant energy-saving potential. This research focuses on two typical STRAC systems: floor-level sidewall air-supply system (FSAS) and nozzle sidewall air-supply system (NSAS). By employing experiment and CFD methods, airflow pattern and heat transfer between the unoccupied and occupied zone under the two air supply systems are investigated in a reduced-scale laboratory. The geometric models of the prototype building, with a geometrical scaling factor of 4:1, are established according to similarity principles and studied by CFD simulation. The results demonstrate that the two scales have similar indoor thermal performances. The numerical simulation results of the prototype building provide and compare commonly used inter-zonal heat transfer coefficients of actual large space buildings with the two typical STRAC systems. For FSAS, heat conduction caused by temperature gradient dominates the inter-zonal heat transfer. In NSAS, both heat conduction due to temperature gradient and heat convection due to airflow contributes equally to this heat transfer. The inter-zonal heat transfer coefficient Cb is affected by the airflow pattern and zonal division, and closely associated with local turbulence intensity.

A Compact Fractal-Shaped O-Ring Monopole Antenna for Modern Broadband Wireless Applications

In this letter, the design of a compact planar Fractal-shaped O-ring monopole antenna based on the Sierpinski carpet concept is studied and proposed for modern broadband wireless applications. The planar fractal-shaped O-ring monopole antenna is on the basis of Sierpinski category construction and then modifies the state of the plane inward with a radius of 27mm over the two iterations. The antenna structure is low profile and easy to be fabricated, and it has performed the simulation and measurement with the result VSWR ≤ 2 that can achieve a wide impedance bandwidth 636% from the frequency band 1.57GHz ~ 10GHz. The geometric scale factor of the Sierpinski fractal is according to the same scale element that defines the geometrical self-similarity. In our experiments, the results show that use of fractal-shaped O-ring into monopole antenna structure can effectively improve input impedance matching, and obtain a larger bandwidth and better radiation pattern, while also having predictable multi-band characteristics.

Corrected method for scaling the dynamic response of stiffened plate subjected to blast load

Test on a small scaled model is an effective approach to predict the dynamic response of full scale structure under blast loadings. However, the geometric dimensions of specimens cannot simply comply with complete geometrical similarity due to manufacture or test restrictions. It would result in the difference structural performance between the full and small scaled models. This paper proposed a corrected similarity relationship of the dynamic behaviour between prototype and replica of stiffened plates subjected to blast load, in which both the thickness of the plate and the configuration (cross-sectional shape) of stiffeners are distortedly scaled-down (double distorted geometric scaling factors). Firstly, based on the mesh convergence study and comparing with results from experimental tests, a numerical method in predicting the confined blast load and dynamic response of structure was verified, which provides a reliable means to determine the dynamic behaviour of stiffened plate designed by the corrected similarity criterion of this paper. Then, the influence of altering the stiffener configuration on the dynamic response of stiffened plates was analysed and on the basis of it, a criterion for scaling the stiffener is proposed to help design a stiffener-distorted model from prototype structure. In addition, a method for scaling the double-parameter distortedly small scaled model is proposed to predict the dynamic response of the prototype. Finally, two sets of examples of both the small size and prototype stiffened structures subjected to blast load were analysed by using the presented method. It is shown that the replica developed by applying the present method is able to accurately predict the behaviour of the full-size stiffened plates, even when the thickness of the plate and the configuration of the stiffeners are distortedly scaling down with different factors.

A novel method to determine the coupling scaling laws of vibration characteristics for rotor-bearing systems

The purpose of this article is to study the coupling effects of support stiffness on geometric scaling factor powers of the rotor-bearing system and predict vibration characteristics of a prototype by scaled models accurately. Associated to the least-squares–based similitude method, the discrete iteration method proposed evaluates the estimated scaling laws under variable (instable) powers and further broadens the restriction of boundary conditions in scaling laws, which is the main finding in this article. The discrete iteration method does not need to establish a physical model but directly uses input and output parameters to establish output scaling laws. The complete scaled model and geometric distorted model are selected as study cases to prove the effectiveness and accuracy of the discrete iteration method. The vibration characteristics of the rotor-bearing system are obtained by the finite element method with validation by experimental test for the natural characteristics. The comparison between the prediction results and those without the discrete iteration method shows that discrete iteration method can significantly improve the accuracy for predicting the prototype.

EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE EFFECT OF SIZE IN POST-TENSIONED CONCRETE DECK SLABS

It is widely known that as the structure of the size increases, its nominal strength decreases. In this paper, the effect of size on punching shear has been quantified for transversely post-tensioned deck slabs cast between flanges of precast concrete girders. A 1:2 scaled model of the bridge was constructed in the laboratory, and experimental and numerical analyses were carried out. However, in order to apply these results on a real bridge, simply using the geometrical scale factors is not sufficient and a structural size effect has to be taken into account. Since a full-scale experimental study was not possible due to the costs involved, a numerical approach using finite element analysis software package TNO DIANA was used to model both the prototype and the real bridge, and a comparison was made to estimate the effect of size on the bearing capacity. It was found that increasing the transverse prestressing level had a positive effect on the punching shear strength of the deck slab. Furthermore, a lower size effect was observed with higher transverse prestressing levels. It is concluded that if a suitable size factor is used, either numerical or small-scale experimental studies can be reasonably used to investigate existing structures.

Characterization of velocity-gradient dynamics in incompressible turbulence using local streamline geometry

This study develops a comprehensive description of local streamline geometry and uses the resulting shape features to characterize velocity gradient ( ) dynamics. The local streamline geometric shape parameters and scale factor (size) are extracted from by extending the linearized critical point analysis. In the present analysis, is factorized into its magnitude ( ) and normalized tensor . The geometric shape is shown to be determined exclusively by four parameters: second invariant, ( ); third invariant, ( ); intermediate strain rate eigenvalue, ; and vorticity component along intermediate strain rate eigenvector, . Velocity gradient magnitude, , plays a role only in determining the scale of the local streamline structure. Direct numerical simulation data of forced isotropic turbulence ( ) is used to establish streamline shape and scale distribution, and then to characterize velocity-gradient dynamics. Conditional mean trajectories (CMTs) in – space reveal important non-local features of pressure and viscous dynamics which are not evident from the -invariants. Two distinct types of – CMTs demarcated by a separatrix are identified. The inner trajectories are dominated by inertia–pressure interactions and the viscous effects play a significant role only in the outer trajectories. Dynamical system characterization of inertial, pressure and viscous effects in the – phase space is developed. Additionally, it is shown that the residence time of – CMTs through different topologies correlate well with the corresponding population fractions. These findings not only lead to improved understanding of non-local dynamics, but also provide an important foundation for developing Lagrangian velocity-gradient models.

Centrifuge modelling of static liquefaction in submarine slopes: scaling law dilemma

The scaling laws for the centrifuge modelling of the initiation and propagation of static liquefaction in submerged slopes are investigated in this paper. A theoretical model is developed to analytically determine the scaling factor of fluid viscosity in simulating the onset of static liquefaction by detailed analysis of the hydromechanical processes at the grain scale. Based on this, a fluid with a viscosity of [Formula: see text]-times that of water ([Formula: see text]-fluid) is suggested, where N is the geometrical scaling factor in centrifuge modelling. A fluid with a viscosity of N-times that of water (N-fluid) was adopted for simulating dynamic events in the centrifuge; N-fluid is used and suggested by previous researchers. Centrifuge tests were designed to examine and verify the scaling factors for pore fluid viscosity in simulating the onset of static liquefaction and the post-liquefaction behaviour of subaqueous landslides. These tests were performed at 10g, 30g, and 50g conditions, with [Formula: see text]-fluid, N-fluid or water, where g is the Earth’s gravitational acceleration. Results confirm that the correct scaling factors (prototype/model) for pore fluid viscosity are [Formula: see text] and 1/N for investigating the onset of static liquefaction and the post-failure behaviour of the submarine slopes, respectively.

Small shaking table testing and numerical analysis of free-field site response and soil-structure oscillation under seismic loading

In this study, the accuracy level of geometric scaling factor (herein, λ = 45) selected for the shaking table test model represents the actual site conditions as discussed by comparing the results of both experimental data and numerical analysis obtained from the soil-structure oscillation and free-field response under seismic loads. The difficulty to be overcome in this experimental campaign was to investigate the limited soil size considered for this complex geodynamic problem due to the small capacity of the shaking table having payload of 2.5 kN and the geometry of testing platform of 1 m × 1 m, respectively. The superstructure used in the analysis of the soil-structure interaction is specified as six story building structure with height of 30 m resting on a silty sand soil with a shear wave velocity of 536 m/s. Within the frame of this work, the underlying soil is handled as a homogeneous single layer on the top of rigid bedrock. The diameter of the ground specimen and the bedrock depth were considered to be 26.23 m and 10 m, respectively. Special cylindrical flexible testing equipment was designed to hold the excavated soil volume in the container without deforming the experimental setup. In order to examine the seismic responses at the control points of the scaled test models under the nonlinear supporting effects, 2-D finite element analyses of the soil-structure system have been executed by using the PLAXIS simulation program. It is obviously seen that the soil layer parameters have significantly increased the free-field site response compared with the bedrock response under different seismic excitations. Based on the comparison of calculated results with experimental recordings, it is suitable to mention that small capacity shaking table experiments with appropriate scaled test models provides an alternative means of laboratory investigations even for such complex soil-structure coupling problems.

Dual‐energy extension of the uniform‐approximation approach

AbstractIn the talk an extension of the uniform‐approximation approach, that relies on the truncation of the elastic energy after a certain power of a geometric scaling factor, towards an analogous truncation of the dual energy is proposed. On the one hand, this allows for a derivation of fully defined boundary value problems including compatible displacement boundary conditions. On the other hand, the extension enables us to provide an a priori error estimate for the systematic error of the arising approximative models with respect to the exact three‐dimensional solution.The approach is compared to the approach of a fixed kinematic assumption for the displacement field which is widely used in engineering. We show that the later approach leads in general to a more complex model for a comparable approximation accuracy so that the consistent approximation approach is to prefer.

A priori estimation of the systematic error of consistently derived theories for thin structures

The consistent approximation approach is a dimension reduction technique for the derivation of hierarchies of lower-dimensional analytical theories for thin structural members from the three-dimensional theory of elasticity. It is based on the uniform truncation of the potential energy after a certain power of a geometric scaling factor that describes the relative thinness of the structural member. The truncation power defines the approximation order N of the resulting theory.In the contribution, we deal with the exemplary case of a slender, beam-like continuum with rectangular cross-section. We introduce an extension of the consistent approximation approach towards a simultaneous, uniform truncation of the complementary energy. We show that compatible displacement boundary conditions can be derived from the Euler-Lagrange equations of the complementary energy, whereas, field equations and stress boundary conditions follow from the Euler-Lagrange equations of the potential energy. Thus fully defined boundary value problems are obtained for all orders of approximation N.We provide an a priori-error estimate for the systematic error of the Nth-order theory. It states that the norm difference of the solution of the so derived boundary value problem of order N to the exact solution of the three-dimensional theory of elasticity declines like the geometric scaling factor to the power of N+1. Thus the approximation character of the approach is proved.Furthermore, we outline why the approach is to prefer over the - in engineering mostly used - approach of a fixed displacement field ansatz with unknown coefficients. We show that the later approach leads in general to theories of higher complexity without increasing the approximation accuracy compared to a consistent approximation.

Applicability of the 1g similitude law to the physical modeling of soil-track interaction

This study aimed to investigate the applicability of the 1g similitude law to the physical modeling of soil-track interaction. Model track experiments were performed using four physically modeled soil-track systems with different geometric scale factors, under three different relative densities of the model ground. Based on the modeling of the model technique, the results of the physical models were compared in terms of the largest physical model scale. The soil-track interaction behaviors showed similar tendencies on the whole, but slight differences were also observed depending on the geometric scale factor. Such differences, however, were not significant compared to the differences in relation to other soil-structure interaction problems. Moreover, considering that the shearing action on the soil-track interface is a large replica of the shearing process in the direct shear tests of the soil, the differences among the physical models were attributed to the specimen size effect observed in the direct shear test of the soil, rather than to the similitude relationships. Therefore, it can be concluded that the 1g similitude law can be applied to the assessment of the soil-track interaction behavior, provided that the mechanical boundary restraint of the shearing action on the soil-track interface is properly accounted for.

Laboratory Flume Experiments on the Formation of Spanwise Large Wood Accumulations: Part II—Effect on local scour

AbstractIn this second companion paper, hydraulic model tests were conducted to analyze local scour due to natural spanwise large wood (LW) accumulations. Spanwise accumulations were modeled using a vertical barrier, similar to a LW retention rack in prototype. The flume experiments were conducted according to Froude similitude in a scale of 1:30 for various approach flow conditions (subcritical and supercritical flow) and different uniform bed material (2.7–13.1‐mm model dimensions). The findings allow the estimation of local scour depth due to spanwise LW accumulations as a function of unit discharge, sediment diameter, and wood volume. Higher unit discharge, finer bed material, and increasing wood volume lead to an increased scour depth. The scour length can be estimated based on the scour depth and a geometrical scaling factor. The longitudinal shape of the cross‐sectional scour depth can be described with a Gaussian normal distribution. Based on the results of both scour depth and length, the design of LW retention structures can be significantly improved. At the same time, the results demonstrate that LW accumulations strongly affect the geomorphic conditions and may consequently create more heterogeneous morphological structures.

Toward "plug and play" prospective motion correction for MRI by combining observations of the time varying gradient and static vector fields.

The efficacy of a Wireless Radio frequency triggered Acquisition Device (WRAD) is evaluated for high frequency (50 Hz) prospective motion correction in a 3-dimensional spoiled gradient echo pulse sequence. The device measures the rate of change in the gradient vector fields (slew) using a 3-dimensional assembly of Printed Circuit Board (PCB) inductors and the direction of the static magnetic field using a 3-axis Hall effect magnetometer. The slew vector encoding is highly efficient, because the Maxwell-term position encoding is observable, allowing overconstrained pose measurement using 3 sinusoidal gradient pulses lasting 880 μs. Since small offsets in the magnetometer can introduce bias into the pose estimates, sensor/system biases are tracked using a lightweight Kalman filter. The only calibration required is determining a geometric scaling factor for the pickup coils, which is specific to the device and will therefore be valid in any scanner. The device was used to perform prospective motion correction in 3 subjects, resulting in an increase in Average Edge Strength (AES) for involuntary and deliberate motion. The WRAD is simple to set up and use, with well-defined measurement variance. This could enable "plug and play" prospective motion correction if pulse sequence independence is achieved.

First measurements of the vertical beam size with an X-ray beam size monitor in SuperKEKB rings

This paper reports first measurements of the vertical beam size using an X-ray Beam Size Monitor (XRM) for each of the SuperKEKB rings (Low Energy Ring, LER, and High Energy Ring, HER) during Phase 1 and 2 commissioning of SuperKEKB. The XRM device is dedicated to measuring the e−/e+ vertical beam size using X-ray synchrotron radiation, and will eventually have the capability for single-shot (single bunch, single turn) measurements. The preparation of a deep Si detector and high-speed readout electronics for single-shot measurements is underway. In the meantime for Phase 1 and 2, we used a scintillator screen and CCD camera for multi-bunch measurements. The XRM has been installed in each ring and images X-rays from a bending magnet that pass through optical elements (a single pinhole and coded apertures). Several studies (geometrical scale factors, emittance control knob, and beam lifetime study) were carried out during the commissioning. In Phase 1 (February–June 2016), the measured vertical emittances εy are ∼10 pm for LER (consistent with the optical estimation) and ∼35 pm for HER (3.5 × greater than the optical estimation). Analysis of the beam size and lifetime measurements suggests unexpectedly large point spread functions (PSF), particularly in the HER. The spatial resolution of the imaging system (defect of focus, diffraction, and spherical aberration) and scattering in the beamline (EGS5 simulation) contribute ∼6µm of PSF, which does not adequately account for the observed PSF. The Phase 2 commissioning commenced in May–July 2018, with thinner Be filters, new optical elements, scintillator, and CCD camera with the purpose to reduce the PSF in HER. The Phase 2 study results suggest the PSF σs∼6.6µm in HER (corresponding to the spatial resolution of the imaging system and scattering in the beamline), which is ∼5 × smaller than in Phase 1. The overall performances of XRMs in LER and HER are accurate. The XRM in LER will be able to measure the design beam size at the zero current (14µm). For the HER, the PSF that we observed during the Phase 2 indicates that the minimum measured beam size corresponds to the emittance at the design current (12.9 pm) and the XRM will be able to measure the design beam size at the zero current (7 µm).

ICARE-VEG: A 3D physics-based atmospheric correction method for tree shadows in urban areas

Many applications dedicated to urban areas (e.g. land cover mapping and biophysical properties estimation) using high spatial resolution remote sensing images require the use of 3D atmospheric correction methods, able to model complex light interactions within urban topography such as buildings and trees. Currently, one major drawback of these methods is their lack in modeling the radiative signature of trees (e.g. the light transmitted through the tree crown), which leads to an over-estimation of ground reflectance at tree shadows. No study has been carried out to take into account both optical and structural properties of trees in the correction provided by these methods. The aim of this work is to improve an existing 3D atmospheric correction method, ICARE (Inversion Code for urban Areas Reflectance Extraction), to account for trees in its new version, ICARE-VEG (ICARE with VEGetation). After the execution of ICARE, the methodology of ICARE-VEG consists in tree crown delineation and tree shadow detection, and then the application of a physics-based correction factor in order to perform a tree-specific local correction for each pixel in tree shadow. A sensitivity analysis with a design of experiments performed with a 3D canopy radiative transfer code, DART (Discrete Anisotropic Radiative Transfer), results in fixing the two most critical variables contributing to the impact of an isolated tree crown on the radiative energy budget at tree shadow: the solar zenith angle and the tree leaf area index (LAI). Thus, the approach to determine the correction factor relies on an empirical statistical regression and the addition of a geometric scaling factor to account for the tree crown occultation from ground. ICARE-VEG and ICARE performance were compared and validated in the Visible-Near Infrared Region (V-NIR: 0.4–1.0 µm) with hyperspectral airborne data at 0.8 m resolution on three ground materials types, grass, asphalt and water. Results show that (i) ICARE-VEG improves the mean absolute error in retrieved reflectances compared to ICARE in tree shadows by a multiplicative factor ranging between 4.2 and 18.8, and (ii) reduces the spectral bias in reflectance from visible to NIR (due to light transmission through the tree crown) by a multiplicative factor between 1.0 and 1.4 in terms of spectral angle mapper performance. ICARE-VEG opens the way to a complete interpretation of remote sensing images (sunlit, shade cast by both buildings and trees) and the derivation of scientific value-added products over all the entire image without the preliminary step of shadow masking.

Towards a general prediction-model for the current-induced mobilisation of objects on the sea floor

The aim of this work was to quantify the physical conditions, required for the mobilisation of unexploded ordnance devices (UXO) on the sea floor. As a basis for this, the hydrodynamic processes around UXO were measured in the wind tunnel and the flume tank in terms of conditions, especially Reynolds numbers. From these experiments, the typical shape of a sandy sea floor in the close vicinity of an object, due to current-induced burial was determined. Knowing this, the model for current-induced mobilisation of objects was developed. The model assumes a critical dimensionless Moment Factor MF=a⋅Reb, where the parameters a and b had to be investigated. This was accomplished by performing a total number of 287 numerical simulations, wind-tunnel testings and flume tank experiments at different geometric scale factors (1:10, 1:5, 1:2 and 1:1). With the parameter values so determined, the model describes the critical situation of an arbitrary shaped cylinder-like object regarding the incident flow velocity, the immersed mass and the burial depth, as well as the length and the volume-averaged diameter of the object.

The role of instability-enhanced friction on ‘anomalous’ electron and ion transport in Hall-effect thrusters

Using a self-consistent 2D particle-in-cell (PIC) simulation, we investigate the electron transport in Hall-effect thrusters. The PIC simulation is explicit in time and models the axial and azimuthal directions of a thruster without using any artificial parametric or geometric scaling factors. The applied discharge voltage and external magnetic field causes electrons to drift in the azimuthal direction, and this drives an instability in the plasma that produces large amplitude oscillations in both the plasma density and azimuthal electric field. A Fourier transform in time and space shows that the oscillations follow a dispersion relation similiar to that for an ion acoustic instability (in agreement with a recent kinetic theory). Correlated with the presence of this instability is an enhanced electron cross-field transport; even in the absence of electron-wall collisions and secondary electron emission. The amplitude of plasma density oscillations (but not electric field oscillations) is found to decrease significantly in a region just downstream of the thruster exit (before then increasing again), and reaches levels similar to those measured experimentally with collective light scattering techniques. By taking relevant velocity moments of the electron distribution function in the PIC simulations, we reconstruct each term in the electron momentum conservation equation and demonstrate that ‘anomalous’ electron transport can be explained entirely due to an instability-enhanced friction force between electrons and ions. This friction force acts as an additional momentum loss allowing electrons to cross the magnetic field, and as an accelerating force causing ions to rotate azimuthally in the same direction as the electrons. Clear evidence of ion-wave trapping in the instability electric field is observed.

Particle separation by phase modulated surface acoustic waves.

High efficiency isolation of cells or particles from a heterogeneous mixture is a critical processing step in lab-on-a-chip devices. Acoustic techniques offer contactless and label-free manipulation, preserve viability of biological cells, and provide versatility as the applied electrical signal can be adapted to various scenarios. Conventional acoustic separation methods use time-of-flight and achieve separation up to distances of quarter wavelength with limited separation power due to slow gradients in the force. The method proposed here allows separation by half of the wavelength and can be extended by repeating the modulation pattern and can ensure maximum force acting on the particles. In this work, we propose an optimised phase modulation scheme for particle separation in a surface acoustic wave microfluidic device. An expression for the acoustic radiation force arising from the interaction between acoustic waves in the fluid was derived. We demonstrated, for the first time, that the expression of the acoustic radiation force differs in surface acoustic wave and bulk devices, due to the presence of a geometric scaling factor. Two phase modulation schemes are investigated theoretically and experimentally. Theoretical findings were experimentally validated for different mixtures of polystyrene particles confirming that the method offers high selectivity. A Monte-Carlo simulation enabled us to assess performance in real situations, including the effects of particle size variation and non-uniform acoustic field on sorting efficiency and purity, validating the ability to separate particles with high purity and high resolution.

Vibration response characterisation and fault-size estimation of spalled ball bearings

Research efforts have increased to investigate the ability to quantify localised bearing faults, ie spalls. These efforts revolve around extending the useful service life of the bearing after the detection of spalls. A number of studies have investigated a linear correlation between the size of spalls and three geometric points that may be recognised in the vibration response: the entry into the spall; the exit from the spall; and a third impact point between the first two. The time difference between these points, calculated using different signal processing techniques, has been widely exploited for quantifying spall size. Currently, there are two main challenges: the first is to enhance the entry point, which typically has weak excitation; the second is to distinguish the impact and the exit points investigated in the literature based on the spall size. However, for practical applications, there is no prior rough estimation of the fault size (ie small or large) and a method is needed for the interpretation of responses. This paper provides insights into the movement of the rolling element within the spall region and shows that the rolling element strongly strikes the bearing races at a minimum of two points. A new technique is then presented to quantify the spall and determine the inherent scaling factor without comparison to any reference data. The technique is based on evaluating two root-mean-square (RMS) energy envelopes, one for the vibration signal and one for a numerical differentiation of this signal. A geometric scaling factor is then used to give a generalised quantification for the small and large spalls. Serviceable estimations of spall size have been achieved for several seeded faults measured on two dissimilar test-rigs provided by the German Aerospace Centre (DLR) and the University of New South Wales (UNSW).