Determination of Spatial Variability in d
70
Grain
Size Values Using High Density Site
Measurements
ir. M.M. DE VISSER a, dr. ir. W. KANNING b, ing. R. KOOPMANS a, ir. J. NIEMEIJER a a
ARCADIS, the Netherlands b
Deltares, the Netherlands and Colorado School of Mines, USA
Abstract. Research to the failure mechanism piping (internal, backward erosion) in the Netherlands shows that the dikes require costly berms to meet the required safety standards. According to the Sellmeijer piping-formula, the d70 (70%-quantile of the
grain size distribution by weight) is an important parameter in the resistance against piping. Therefore a better insight in the d70
variability in the naturally deposited sand layers beneath dikes is of great importance. High density site measurements (5x5 meter spacing) give insight in local heterogeneity of the d70 and the implications for representative design values. Three test sites
were developed at locations with distinct geomorphological deposits. The spatial variability in the d70 appears to be large.
Despite the large amount of data at a very dense measurement grid, there is no obvious spatial correlation in the measurements. The sites have a similar or larger coefficient of variation than the much sparser regional datasets that are normally used to derive the representative d70. Current regulations prescribe the characteristic (5% lower bound) value as the design parameter in the
piping formula. Considering the large variation in d70 values this approach may not be appropriate. Given the influence of the d70
on dike dimensions, hence investment costs, establishing a method for determining a representative d70 value is important. We
recommend to develop more sites at distinct geomorphological deposits to gain insight in the spatial variability in grain size distribution and to determine design values with matching site sampling requirements. An important aspect of further research is the interaction between d70 variability and the physical development of the piping channel.
Keywords. grain size distribution, d70, seepage, piping, backward erosion, sand boils, dike, levee, spatial variability, site
measurements
1. Introduction
In the Netherlands, the attention for the failure mechanism piping has increased because recent research showed that the dikes (levees) along the rivers do not meet the required safety standards (ENW, 2010). Bringing the dikes up to standard will require costly berms if the current methodology would be used.
The current method in the Netherlands to calculate the safety against piping is with the formula of Sellmeijer in which the grain size (d70) is an important parameter (RWS, 2012; Kanning, 2012). Therefore a better insight in the d70 variation in the naturally deposited sand layers beneath dikes and the effect on its design value (d70 value used for piping assessment) is of great importance. For that reason, the Expertise Network for Flood Protection advised further research on the heterogeneity of the subsoil (ENW, 2013).
The goal of this research is to use high density site measurements in order to obtain insight in local heterogeneity of the d70 grain size and the implications for representative d70 input parameters (design values). This paper first addresses the piping safety assessment. Next, the measurements and locations of the test sites are described, followed by an analysis of the results. The paper concludes with sketching implications for design practice.
2. Grain Size for Piping Safety Assessment Piping, also called backward erosion, is progressive internal erosion in an aquifer under a dike and is considered to be an important failure mechanism of dikes with an underlying sand layer and a relatively thin top layer. Current regulations in the Netherlands prescribe the use of the piping formula by Sellmeijer (RWS, 2012), © 2015 The authors and IOS Press.
This article is published online with Open Access by IOS Press and distributed under the terms of the Creative Commons Attribution Non-Commercial License.
see eq. (1), in which the d70 is an important parameter in the resistance against piping.
= (, , , , , , ) (1) Where c is the critical hydraulic head [m], L
the seepage length [m], k the permeability of the sand layer [ms-1], D the thickness of the aquifer [m], White’s coefficient [-], angular resistance [°] and p the apparent volume weight
of the sand grains in water [kNm-3]. The d70 value is the 70%-quantile of the grain size distribution (by weight) of the top of the piping-sensitive layer.
According to the Sellmeijer-formula there is an inverse relation between the d70 and the required seepage length: the smaller the d70, the bigger the required seepage length. In general: smaller grains will erode sooner. The Sellmeijer-formula is validated using laboratory tests in uniform sands. However, the subsoil in the Netherlands (and most alluvial geologic regions) can be very heterogeneous.
The current Dutch design and safety assessment practice is to determine the d70 from a grain size distribution by taking samples from the subsoil every few hundred meters along the dike, which is referred to as ‘regional dataset’. The design value, also referred to as representative value, for the d70 as used in the piping-formula is a characteristic (5% lower bound) value (TAW, 1999).
3. High Density Grain Size Site Measurements 3.1. Description and Site Location
For this research, three test sites with a very dense measurement grid (5x5 meter spacing) were defined to determine d70 values at three locations with distinct geomorphological deposits and a thin cohesive top layer (which is a typical piping sensitive configuration) in the Netherlands. An analysis per site and an inter-site comparison is performed to assess the d70 spatial variability. The test setup and statistical analysis was similar for all sites.
This research focusses on the d70 variability and not the hydraulic conductivity although
conductivity is the other main contribution to piping safety.
The site in Veessen (A) is situated at the location of a newly constructed dike along the IJssel River close to the village Veessen. riverine (fluvial)- and moraine (peri-glacial) deposits are both present at this location, which could result in a variable grain size. The site close to the village Veecaten (B) is situated further downstream along the IJssel River. The sand layer is considered to be an aeolian deposit and therefore expected to consist of relatively fine sand. The site close to the village IJzendoorn (C) is situated at the northern shore of the River Waal. The site is located just on a channel belt, which appears to be a holocene sand deposit. 3.2. Sites and Sampling Method
At each site of 75 by 75 meters, samples of the piping-sensitive layer were taken every 5 meters. The piping sensitive layer is the sand layer just below the cohesive top layer. From each sample the grain size distribution was determined by sieving (according to Dutch soil investigation standards). This resulted in 256 measurements per site. Measurement grids this extensive have not been realized before in the Netherlands.
4. Results
4.1. d70 Variability at Sites
The results of the dense d70 measurements are shown in top view scatter plots in Figure 1, Figure 2 and Figure 3. The average values of sites A and C are similar and are mainly described as medium to coarse sand. At site B mainly fine sand was found. In site A, the coarser sand is located on the northern side of the site; the southern side has finer sand. In site C, a different pattern is visible: the coarser and finer sand is more regularly divided throughout the site. The d70 in site B is very uniform, despite the two coarser samples in the south.
4.2. Statistical Analysis of the Measurements For each site the mean value of the d70, its standard deviation and its coefficient of variation
Figure 1. d70 measurements at Veessen (site A).
Figure 2. d70 measurements at Veecaten (site B).
Figure 3. d70 measurements at IJzendoorn (site C).
Table 1. Statistical characterization d70
Site Veessen (A) Veecaten (B) IJzendoorn (C) #samples [-] 256 256 256 Mean [10-6 m] 416 205 420 Standard dev. [10-6m] 215 25 108 Coeff. of variation [-] 0.52 0.12 0.26 Minimum [10-6 m] 127 153 162 Char. value [10-6 m] 173 172 248
(standard deviation divided by the mean) are determined. From these results the characteristic 5% lower bound value is determined, which is used as design value in the current design standards. Also the minimum value of the d70 in the site is listed.
The results of the statistical characterization are shown in Table 1. Site A shows a very large variation in d70, with a coefficient of variation of 0.52. In site B the coefficient of variation is 0.12 and in site C 0.26. The variation in site A and C is very large despite the extensive dataset in a very small area. Due to the large variation, the characteristic value is much lower than the average value. The characteristic values of sites A en B are similar, but the average value of site B is a factor 2 smaller than of site A. This is due to the large variation in site A and the small variation in site B.
4.3. Comparison to Traditional Assessment The site data are compared to available regional datasets that are normally used to derive the representative d70. Also, subsets of the data are analysed, see Section 4.4. The results are shown in Table 2, Table 3 and Table 4 for the respective sites.
The regional dataset around site A consists of 28 samples with higher average d70 (538μm= 538*10-6 m) than the site (416μm). The coefficients of variation of the regional data and the site are similar (0.56 regional and 0.52 in the site).
The measurements of the regional dataset around site B are unknown. However, in current safety assessments on comparable soil conditions in the region, characteristic values of 185μm and 210μm are used, based on expert judgement. These values are similar to the characteristic value of the site (169μm).
The regional dataset around site C has only 5 samples with a slightly higher average d70 (469μm) than the site (420μm). The coefficient of variation of the site is higher than the regional data (0.14 regional; 0.26 site) despite the large amount of data at a small location. The minimum value is measured in the site, not in the regional dataset.
4.4. Subsets
The influence of the spatial density of the measurements is explored by making subsets of the total dataset. The data is divided in four subsets with samples every 10 meters (64 samples per subset).
For site A, there are considerable variations between the different subsets. This results in a different characteristic value (162-183μm, difference of 13%) for each subset. For site B the average values of the subsets are very similar. The small difference in coefficient of variation results in comparable characteristic values (163-174μm; difference of 7%) for each subset. For site C the subsets are relatively similar and have roughly the same coefficient of variation, which results in comparable characteristic values (240-257μm; difference of 7%) for each subset. Hence, even with less dense data, the characteristic values remain similar for the three sites.
Table 2. Comparison Veessen (site A) d70 results with
regional and subset data
Site Veessen (A) Site Regional Site Subset 1 2 3 4 #samples [-] 256 28 64 64 64 64 Mean [10-6 m] 416 538 429 394 443 398 Standard dev. [10-6 m] 215 299 245 183 226 204 Coeff. of variation [-] 0.52 0.56 0.57 0.46 0.51 0.51 Minimum [10-6 m] 127 173 127 184 188 186 Char. value [10-6 m] 173 187 162 180 183 166
Table 3. Comparison Veecaten (site B) d70 results with
regional and subset data
Site Veecaten (B) Site Regional Site Subset 1 2 3 4 #samples [-] 256 64 64 64 64 Mean [10-6 m] 205 203 207 206 203 Standard dev. [10-6 m] 25 20 27 32 18 Coeff. of variation [-] 0.12 0.10 0.13 0.16 0.09 Minimum [10-6 m] 153 164 163 153 167 Char. value [10-6 m] 169 185-210 172 170 163 174
Table 4. Comparison IJzendoorn (site C) d70 results with
regional and subset data
Site IJzendoorn (C) Site Regional Site Subset 1 2 3 4 #samples [-] 256 5 64 64 64 64 Mean [10-6 m] 420 469 407 424 429 419 Standard dev. [10-6 m] 108 71 103 116 110 101 Coeff. of variation [-] 0.26 0.15 0.25 0.27 0.26 0.24 Minimum [10-6 m] 162 352 163 162 165 166 Char. value [10-6 m] 248 322 245 240 257 246
5. Discussion for Implementation 5.1. Sources of Uncertainty
There are multiple sources that may cause measured high variability (Phoon and Kulhawy, 1999; Schweckendiek, 2014), of which inherent natural variability, measurement uncertainty and transformation uncertainty (i.e. the construction and interpretation of sieve curves) seem the most applicable. Measurement uncertainty may be a factor if the soil samples are not taken deep enough in the sand layer and clay from the top blanket is included. This could also be considered human error. If measurement error were a relatively high contributor, and if it were unbiased (not systemic), this would result in averaging of uncertainty of many measurements.
However, given the standardization of the measurement procedure, we assume that measurement and transformation uncertainties are negligible, and that the main contributor to the variability is the natural variability of the d70. 5.2. Spatial Correlation of the Measurements Three types of sites can be distinguished: spatially homogeneous (site B), heterogeneous (site C) and composite (site A, which is coarse and heterogeneous in the north but fine and homogeneous in the south). The spatial variability of the d70 at the sites appears to be large despite the large amount of data at a very dense measurement grid. Furthermore, there is no evident spatial correlation within the sites based on visual observation of the data.
Interestingly, the sites have a similar (A and B) or larger (C) coefficient of variation than the much sparser regional data. The subsets show the same variability. This leads to the hypothesis that there is lack of spatial correlation and all samples are from a random population. Which could imply that, given samples from the same geologic unit, the spatial density of the measurements does not matter. Also, the mean and the standard deviation would converge to the same value given sufficient measurements according to the student-t distribution.
5.3. Geological Influence on Spatial Variability The large variability at site A could be explained from a geological perspective: this site is situated on both fluvial and moraine deposits. Here, the regional dataset seems to describe the average d70 and the variability well, which leads to a similar characteristic d70 as the site. Site B is situated on aeolian deposits, which explains the small grain size and low variability. Given the spatial homogeneity in Figure 2 and the correspondence in magnitude, the characteristic d70 of the nearby regional dataset seems representative. Only for site C the characteristic d70 is smaller than the regional value due to the higher variability of this site. Apparently, site C contains a smaller grain size fraction that is not present in the regional dataset.
Based on these results, the perception that more samples result in a more accurate d70 and therefore a less conservative calculation of necessary berm width is not valid. Less data can give a favourable view because smaller grains are not sampled, but also an unfavourable view with a smaller d70.
The d70 variability will at least partially be caused by the relatively small scale (meters and less) geomorphological processes that were involved in depositing these sand layers.
The variability might be dependent on geologic units: low variability in homogeneous deposits (B) and high variability in case multiple geologic units were mixed (A). This would lead to the conclusion that the characterization of geologic units is important. To assess this hypothesis, further research is needed to the correlation between specific geological units and characteristic d70.
The results of each test field are representative for similar geological deposits and should not just be extrapolated to the rest of the Netherlands. However, the deposits present in the test fields are typical for the eastern side of the Netherlands and therefore there will be more locations with these characteristics.
5.4. Representative d70 Based on Measurements
The representative value (design value) for the d70 in current regulations is a characteristic (5% lower bound) value, which is used in the piping
formula (RWS, 2012). However, with the large variation in d70 values the question arises whether this is an appropriate approach.
The 5% lower bound was intended as a safe value that is representative for a dike section. However, as this research shows, there is very high local variability, which does raise the question: what is a safe representative value of the d70. Which should be answered by the question: what does determine piping resistance?
Several hypotheses are possible. Without taking into account the heterogeneity, the lowest d70 value of the dike section may be proposed. Which should be characterized based on statistical distributions and acceptable safety levels. However, the piping erosion path needs to develop from the inside to the outside, encountering multiple d70 values. This may result in the criterion that the piping resistance is determined by the maximum d70 in the erosion path. The erosion path in its simplest form may be the path of the weakest d70 (Kanning, 2012). This can be implemented as a search algorithm and results in Figure 4 for site C.
Figure 4. Path of the weakest d70 for site IJzendoorn (C)
However, not only d70 determines the erosion path, but also flow velocities which may force the erosion path more straight and through areas of high d70. Limited research by Kanning (2012) suggests that representative d70 values may be closer to the mean than to the lower bound.
5.5. Impact of d70 on Design
The value of the representative d70 has a substantial influence on the design of a dike, as addressed in the required seepage length according to Sellmeijer. This is demonstrated in
an example for which the aquifer permeability (5.8*10-4ms-1), thickness of the aquifer (40m), thickness of the cohesive top layer (2m) and head difference (6.5m) are set as standard values. For given values of the d70 for site C, the additional required seepage length is determined relative to seepage length (193m) that would be required based on the regional characteristic d70 value (Figure 5). The 23% lower characteristic d70 of the densely sampled site results in 12% additional required seepage length (24m), and thus a 24 m longer berm. This research shows that the required seepage length, and thus the investment costs of dike improvement projects cannot easily be reduced by the amount of measurements, if the current regulation (characteristic values) for the d70 is used. Thus, establishing a method for determining a plausible d70 value is important.
Figure 5. Additional required seepage length (Ladd) for
various d70 values relative to seepage length that would be
required based on the regional characteristic d70 value, site
IJzendoorn (C).
6. Conclusions and Recommendations
Sites with high density measurements (5x5 meter spacing) were developed at three locations with distinct geomorphological deposits in the Netherlands to obtain insight in local heterogeneity of the d70 grain size. The spatial variability in the d70 can be large, despite the large amount of data at a very dense measurement grid and there is no obvious spatial correlation in the measurements. Three types of sites can be distinguished: spatially homogeneous, heterogeneous and composite. The sites have a similar or larger coefficient of variation as the much sparser regional datasets that are normally used to derive the representative d70.
Current regulations prescribe the characteristic (5% lower bound) value as the design parameter in the piping formula. Considering the large variation in d70 values the question arises whether this is an appropriate approach.
Other possible methods for deriving representative values of the d70 need further research. Possible lines of research are the maximum values in the weakest path (Kanning, 2012) or characterization of the d70 for geological units. Given the influence of the d70 on the dike dimensions, and thus the investment costs, establishing a method for determining a representative d70 value is important. We recommend to develop more sites at distinct geomorphological deposits to gain more insight in spatial variability in grain size distribution. Such sites can also yield data to improve methods on how to determine representative input parameters with matching site sampling requirements. An important aspect of further research is the interaction between d70 variability and the physical development of the piping channel.
Acknowledgements
We thank the waterboards Waterschap Groot-Salland, Waterschap Rivierenland and Waterschap Vallei en Veluwe for supplying the data.
References
ENW (2010). Piping, Realiteit of Rekenfout, Expertise Network for Flood Protection, the Netherlands. ENW (2013). Advies inzake concept-TRZandmeevoerende
wellen, ENW-13-01, Expertise Network for Flood
Protection, the Netherlands.
Kanning, W. (2012). The Weakest Link, Spatial Variability in
the Piping Failure Mechanism of Dikes, Delft
University of Technology, the Netherlands.
Phoon, K.K. and Kulhawy, F.H. (1999). Characterization of Geotechnical Variability, Canadian Geotechnical
Journal, 36, pp 612-624.
RWS (2012). Onderzoeksrapport Zandmeevoerende wellen, Rijkswaterstaat Waterdienst, the Netherlands.
Schweckendiek, T. (2014). On reducing Piping Uncertainties,
A Bayesian Decision Approach, Delft University of
Technology, the Netherlands.
TAW (1999). Technical Report on Sand Boils (Piping), Technical Advisory Committee on Flood Defences, the Netherland
