Impact of Geometric and Petrographic Characteristics on the Variability of LA Test Values for Railway Ballast

Abstract

The Los Angeles test is one of the few mechanical test methods that provides information on the quality of railway ballast. However, the Los Angeles value is subject to large variability. Since important economic decisions depend on this value, the reasons for its variability are investigated. An extensive series of tests using four types of rock as well as an in-depth analysis of particle geometry and petrography are carried out. The impact of particle characteristics on the test results is investigated. The deviation of the petrographic composition within a given sample turns out to have a considerable impact on the Los Angeles test results, whereas the influence of the respective deviation of particle geometry is relatively small. The latter effect only comes into play in connection with petrographically homogeneous rock types. The distribution of the geometric features is similar in almost all of the rock types investigated. Due to the large deviation in particle shape and angularity, the sample mass of 10 kg (as provided in the standards EN 1097-2 and EN 13450) is not found to be representative. The necessary number of test repetitions in order to exclude the effect of deviation of particle geometry is estimated. The one result parameter according to the standard, the Los Angeles value, does not allow for discriminating between the amount of abrasion and the fragmentation occurring during the test. An additional result parameter for the estimation of the fragmentation rate is therefore proposed.

Appendices

Appendix A: Test on Homogeneity

Comparison of the rock types with regards to their geometric properties requires a nonparametric homogeneity test since the continuous geometric properties are not Gaussian. In the present study, the method proposed by Lung-Yut-Fong et al. (2012) is used. It is based on rank statistics similar to the univariate Wilcoxon Ranksum test, and it can be applied to more than two classes. Let X _ij for i=1,…,G and j=1,…,n _i be $\mathbb{R}^{p}$-valued random vectors, where G denotes the number of classes and n _i denotes the number of samples within a class i. All of the marginal distributions are assumed to be continuous. The homogeneity test addresses the hypotheses H ₀:X _ij ∀i,j are identically distributed random vectors against H ₁: at least two classes a,b∈{1,…,G} exist so that X _aj are distributed differently than X _bj . Let R _ijk be the rank of variable X _ijk for a fixed coordinate k=1,…,p, that is,

$$R_{ijk}=\sum_{l}^G\sum _{m=1}^{n_{i}} \mathbf{1}_{(X_{lmk}\leq X_{ijk})}. $$

Using the average rank of coordinate k in class i,

$$\overline{R}_i^k=\frac{1}{n_i}\sum _j R_{ijk} $$

the test statistic has the form

where $\overline{\mathbf{R}}_{i}'= (\overline{R}_{i}^{1}-0.5(n+1),\ldots,\overline {R}_{i}^{p}-0.5(n+1))$, n is the total number of random vectors (i.e., n=∑ _i n _i ), and a p×p covariance matrix with entries

$$s_{kk'} = \frac{4}{n}\sum_{i=1}^G \sum_{j=1}^{n_i} \biggl(\frac {R_{ijk}}{n}-0.5 \biggr) \biggl(\frac{R_{ijk'}}{n}-0.5 \biggr),\quad1\leq k,k'\leq p. $$

If H ₀ holds, the test statistic is asymptotically χ ² with (G−1)p degrees of freedom.

Appendix B: Abbreviations

(A) Raw data from Petroscope Size & Shape Analysis
Characteristic	Abbreviation
Long axis	L [mm]
Medium axis	I [mm]
Short axis	S [mm]
Minimum sieve size	d [mm]
Volume	V [mm3]
Flatness ratio S/I∈[0,1]	FR [–]
Elongation ratio I/L∈[0,1]	ER [–]
Proportion of Angles	PropA [%]
(B) Additional characteristics in the present analysis
Characteristic	Abbreviation
Mass of sample	m [g]
Aschenbrenner’s working sphericity ∈[0,0.96] (Eq. (1))	ψ′ [–]
Volume of Angles PropA⋅V	VoA [mm3]
Tensile stress in beam subject to point load F=1N (Fig. 4)	σ max [N/mm2]
Mean tensile stress	σ max,50 [N/mm2]
Particle count	N [–]
{Characteristic} prior to test	{Characteristic} P
{Characteristic} after test	{Characteristic} A
(C) Results from LA test
Characteristic	Abbreviation
LA value Proportion of particles with d<1.6 mm	LA RB [%]
Fragmentation ratio N P /N A for particles with d∈ ]4,50[ mm	FragR [%]
Loss of mass for d>31.5 mm (Eq. (3))	LoM 31.5 [%]
Fraction of LA value as result of rounding (Eq. (2))	$\mathit{FracLA}^{r}_{\mathrm{RB}}$ [–]