Grasping the Heterogeneity of the Subsurface:
Using Buildup Scenarios for Assessing Flood Risk
Marc HIJMA, Raymond van der MEIJ and Kin Sun LAM Deltares, The Netherlands, marc.hijma@deltares.nl
Abstract. The subsurface plays an important role when assessing flood risk and its build up has to be known in considerable detail to properly determine the chance of flood-protection failure. Currently, the subsurface below flood-protections is often characterized by geotechnical cross sections that are constructed using e.g. cone penetration tests (CPTs). In most cases, however, the available density of information is insufficient to account for the relevant heterogeneity of the subsurface. By ignoring this it is possible that buildups that have a negative impact on flood risk are missed and the strength of the flood protection is overestimated. In addition, due to the uncertainty about the buildup of the subsurface, the assessment criteria have to be conservative meaning that parts of flood protections will be assessed ‘unsafe’ unnecessarily. The existing uncertainty can be reduced significantly by incorporating additional, geological knowledge that exists about the general principles behind the buildup of the subsurface and to use both this knowledge and the measurements to make stochastic schematizations using subsurface buildup scenarios. The latter consist of a set of alternative buildup scenarios that characterize the subsurface in a certain segment. Each scenario has its own probability of encountering and is made up of stacked units that are described in terms of their geotechnical properties. The scenarios can be used in probabilistic assessments. The approach is flexible, meaning that scenarios can be easily expanded and adapted to incorporate additional data or information on the subsurface.
Keywords: heterogeneity, subsurface, stochastic, dike safety, flood risk, flood protection, scenarios, schematization
1. Introduction
The performance of flood protections such as dikes and dams during extreme events depends on local conditions such as the geometry of the protection and the subsurface. The latter forms an important part of any flood protection and its buildup has to be known in considerable detail to properly determine the probability of failure during high water by e.g. piping and stability issues such as slope failure and flow slides. Currently, the subsurface is often characterized using geotechnical cross sections, constructed by drawing lines between depth intervals with similar features in CPT graphs and borehole logs. The available density of information, however, is often insufficient to account for the relevant spatial variation in the subsurface. Ignoring this variation can easily result in missing buildups that have a negative impact on flood risk and overestimation of the strength of the defense system. Also, because the high uncertainty regarding the buildup of the subsurface is generally acknowledged, the assessment is designed to be conservative. Parts of flood protections will thus be assessed “unsafe”
unnecessarily and this will result in overly high strengthening costs.
These problems can be overcome by taking into account the system that exists in the buildup of the subsurface, i.e. the geological history of an area. In low lying coastal, fluvial or deltaic regions the subsurface generally consists of discrete depositional units with limited depth variation and a systematic internal structure. In this paper a method is presented that uses both the measurements as well as knowledge about the geometry of the depositional units to characterize the subsurface with scenarios. Each scenario represents a possible buildup of the subsurface. The method involves schematizing the subsurface of a certain area with scenarios that capture and represent the relevant features and variation in the subsurface. These scenarios, or only the normative scenarios, can then be used during the safety assessment. This approach minimizes the probability that critical buildups are missed and hence the assessment becomes more reliable. The method has similarities with the approach described in Fookes (1997) and was earlier discussed by Kruse (2011). Although the method was developed to assess flood protections in The Netherlands, it can be used
© 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. doi:10.3233/978-1-61499-580-7-924
globally in all projects where the heterogeneity of the subsurface has to be taken into account. The outcome of this method is flexible and can be used as input for different geotechnical purposes.
Below we kick-off with highlighting the benefits of stochastic schematizations with scenarios over common methods to characterize the subsurface. Next we describe how to construct a stochastic schematization. As a proof of concept we will then illustrate how a stochastic schematization is used during a flood-risk assessment.
2. Stochastic Schematization with Scenarios The relevant properties of the subsurface have to be schematized for a safety assessment of flood protections. With schematization we mean a characterization of the ‘actual’ subsurface into a few variables. To do this there has to be information about the subsurface (e.g. CPTs, boreholes, geophysics, lab tests), but also the application of the schematization, e.g. for piping or flow slide, has to be well known in order to focus on the relevant properties. A common practice is to use a subsurface during the assessment that is chosen from the available set of measurements. The chosen sequence can be an average or normative condition. Alternatively, horizontal interpolation between layers and properties between adjacent measurements is used to determine geotechnical cross sections. These cross sections are then used “as is”, deterministically, during subsequent assessments. There exists, however, considerable uncertainty with this common deterministic strategy on the spatial variation in the buildup of the subsurface, especially regarding variations that have not been encountered within the measurements. Also, local variation is often underestimated as in most cases the distance between e.g. CPTs along flood protections is at least hundreds of meters.
The method described in this paper presents an alternative approach using subsurface buildup scenarios to characterize the subsurface for flood-risk assessments. It combines data from CPTs and boreholes with knowledge of the natural pattern in the buildup of the subsurface. This is relevant, because it makes a difference if
the sediments were deposited in a dynamic river-mouth area or at the bottom of the lagoon. The environment in which the sediments were deposited gives information about what buildup to expect, how much variation is possible and over what distances relevant changes in buildups can occur. The lateral and vertical stacking of units and the depth intervals occupied are thus directly related to the spatial and temporal variation in deposition and erosion of sediment in the area. The method thus requires close cooperation between geologists and engineers and it provides a direct, rational path from the same available measurements as in the common method, supplemented by expert knowledge, to the input for subsequent analysis, including probabilistic assessments.
Figure 1. Photo of a tidal area in The Netherlands to illustrate the variability of depositional environments over short distances. Landscapes likes these lie buried in many coastal areas.
3. Constructing a Stochastic Schematization 3.1. Data and Knowledge
The subsurface measurements along flood protections generally consist of CPTs, borehole logs and in some cases geophysical data. Where available, detailed terrain elevation data (e.g. LIDAR), geological maps, and published information can be used. When constructing buildup scenarios these measurements require interpretation in terms of relevant geotechnical parameters and geological setting. The importance or added value of geological insight increases with decreasing data densities, because even with relatively little information the
geological setting and hence the buildups that can be expected can be determined.
Preferably, the subsurface data are made available in digital form. This allows for streamlined, efficient data handling and interactive analysis. In The Netherlands we have used the open-source software package iMOD (http://www.deltares.nl/en/software/1029519/imo d1/1029521, Figure 2) for such analysis.
3.2. Identifying Relevant Units
Each scenario represents a possible buildup of the subsurface for a certain segment of the flood protection and consists of a stack of soil units. These units are used to describe soil that has similar lithological and geotechnical properties. In many cases this means that the units represent sediments from a certain paleoenvironment, e.g. a lake, a river channel or a tidal basin. For example, in Figure 3 Unit A stands for a flood-plain clay, Unit B for a flood-basin clay and Units C and D for different sandy fluvial deposits. For each region and application the units that are relevant can differ, depending on the application and the geological history. For e.g. a piping-risk assessment, the focus of schematization may lie on different types and depths of sand bodies, while for e.g. a stability assessment the focus
will lie on the thickness and depths of weak layers. Based on the available information, the properties of the units (e.g. grain size, density, permeability) are stored in a database to use during the assessment. If only a few measurements of these properties are available, default values can be assigned to the required parameters. In The Netherlands specialized software is being developed to facilitate these steps.
3.3. Constructing Relevant Segments 3.3.1. High Data Densities
Even in countries with abundant information about the subsurface along the flood protections, the data density is in most cases not enough for reliable deterministic schematizations. The abundance does allow dividing the flood protections into segments based on the measurements. The divisions between the segments indicate relevant changes in the buildup of the subsurface. Examples are changes in the thickness of peat layers, the depth of a consolidated substrate or changes in the proportion of sand layers versus clay layers. For each segment buildup scenarios are constructed.
0 2000 4000 6000 8000 -5 -10 -15 -20 0
Distance along dike (m)
Depth (m
O.D.) Borehole
CPT
Figure 2. Visualization of subsurface information along a flood protection using iMOD. All boreholes and CPTs in a certain perpendicular distance from the dike are plotted. This distance can be varied. By clicking on a measurement, the borehole log or CPT-values will be shown. The background is formed by a 3D-geological model from the Geological Survey of The Netherlands (GeoTOP) that in this case shows the geological units. The red dashed lines indicate the boundaries of the different segments. O.D. is the Dutch Ordnance Datum (NAP) that lies just below mean sea level.
3.3.2. Low Data Densities
In areas with very low data densities a different strategy has to be followed to create segments. For those areas the emphasis lies on the available knowledge on the regional geological history. This usually involves establishing parameters that have influenced the sediment distribution patterns in a region, e.g. tidal range, wave activity, morphology (remote sensing), sediment inputs, main river courses and the like. Using values for these parameters, information from similar regions elsewhere, and the available measurements, the regional distribution and depths ranges of the various units can be determined. In practice the first step is to register depth intervals of well recognizable units within the available measurements. The next step is to plot the measurements in map view and to determine the spatial extent of each unit in e.g. a few kilometers wide zone along the flood protection. Expert knowledge on the spatial extent and general distribution patterns of units can improve the spatial resolution significantly. Based on overlapping regions for the different units, segments can be constructed. The units that occur in the segment are then used to construct the buildup scenarios.
3.4. Constructing Scenarios
The buildup scenarios should capture all relevant variation within a segment for a certain failure mechanism. For the construction of the scenarios the available information has to be analyzed in detail to cluster the measurements into scenarios. In this step the application determines the number and detail of the scenarios. In a high-data density area the measurements weigh heavy in constructing the scenarios. In a lower-density situation the possible vertical stack of units can be constructed by combining the overlaps of delineated zones and note the alternatives in scenarios that result from the units that can occupy the same or overlapping depth interval (see above). The end-depth of the scenarios can vary, depending on the application, the height of the flood protection and e.g. the depth to a sufficiently stiff substrate, but is generally in the order of tens of meters below the surface.
3.4.1. Assigning Depths to the Units
Depth of boundaries between units can be given as representative or, depending the application, as likely or as normative values. For e.g. stability assessments the latter could encompass depths chosen to maximize the thickness of the weak layers within the possible range.
3.4.2. Probability of Encountering
The probabilities of encountering the scenarios are based upon the probabilities of encountering the individual units within the scenario (Figure 3). The latter probabilities are based upon i) the relative frequency of the soil unit being encountered in the measurements; ii) the characteristic width of the unit in the segment (e.g. a tidal channel of a certain width) relative to the length of the segment and iii) the possible occurrence of a unit within a segment or in other words: how many tidal channels can be present, based on geological insight, within a certain segment? Probabilities are given in fractions representing probability classes. For example, “a low probability being encountered” can be expressed as 5%. In some cases it is necessary to add scenarios that represent buildups that have not been encountered in measurements, but, based on geological insight, still have a relevant probability of encountering.
3.5. An Example
Figure 3 shows a fictitious example where Unit A represents an omnipresent, relatively stiff, flood-plain clay. Below Unit A lies either organic flood-basin clay (Unit B, 40%) or a sandy channel deposit (Unit D1, 60%). In most cases the base of the channel reaches Unit C (Unit D2), a coarse grained fluvial deposit. If not, Unit B lies in between Units D1 and C. The probability of encountering the different scenarios is based on the probabilities of encountering of the individual units (Figure 3). The sum of the probabilities of the scenarios should add up to 100%. The names of the units in the example are illustrative; during a project it is often helpful to use names that have a link with the sediment properties.
The units were recognized in CPTs and boreholes and were chosen based on similar
characteristics (e.g. grain size, organic content, friction ratios, etc). Both the measurements and geological considerations indicated that in more than half of the segment a shallow sandy deposit (Unit D1) was found and therefore a 40/60% division between Units B and D1 was chosen. All measurements penetrating the sandy deposit indicated that the sandy deposit lay embedded within Unit C (Unit D2). However, based on knowledge of nearby areas the possibility that the sandy deposit was separated from Unit C by Unit B was included as this is relevant for e.g. piping and stability assessment.
If one of these scenarios is assessed unsafe this could mean that the entire segment has to be strengthened. When this scenario has a low probability, it may be worthwhile to pinpoint the locations where this scenario occurs with additional soil investigations (see also section 4.3).
Figure 3. The left panel shows segment x with three possible scenarios. Each unit has its own probability of encountering (upper right panel). Units A and C occur everywhere, while Unit B has a probability of 40% and Unit D1 60%. Below Unit D1, Unit D2 occurs in 90% and Unit B in 10% of the cases. This leads to probabilities of encountering of 40%, 54% and 6% for scenarios I, II and III respectively (lower right panel).
4. Flood-Risk Assessments using Stochastic Schematizations
4.1. Probabilistic Analysis
To determine the probability of failure of a flood protection, one can calculate the probability of failure of each subsurface scenario for each failure mechanism. Assuming the scenarios and mechanisms are not correlated, the weighted sum of all scenarios and mechanisms gives the
probability of failure of the entire segment (Figure 4). If needed, aspects like length-effects and correlation between scenarios and mechanisms should be taken into account.
4.2. Semi-probabilistic analysis
If a full probabilistic analysis is not necessary (or too complex), it is possible to perform semi-probabilistic calculations that are representative for one mechanism in a segment. Proper partial factors derived from the required safety level do need to be available. The engineer can choose only to test a representative scenario. In that case, the engineer must judge which subsurface scenario is representative for a certain mechanism. Only that scenario needs to be analyzed and compared to the required safety factor that belongs to the given mechanism and required safety level. This then equals an analysis with a deterministic schematization, but the major difference is that in the path towards the analysis all other subsurface scenarios have been considered as well.
Alternatively, it is possible to derive a safety factor for each individual subsurface scenario (Schweckendiek and Calle, 2010). The required safety factor is, in that case, also dependent upon the probability of the scenario.
4.3. Effect on Further Investigations
If the semi- or full probabilistic analysis does not result in a safety level that adheres to the norm, the subsurface scenarios can help in choosing and prioritizing dedicated soil investigation. In a probabilistic analysis, the subsurface scenario with the largest probability of failure contributes most to the total failure probability. The soil investigation must therefore localize this scenario spatially and precisely define the layering. The general width of the relevant units within the scenario and the length of the segment help in defining the amount of needed investigation points. This may lead to a new segment with a more precise probability of failure. If the new segment adheres to the norm, further investigation is not required. The same holds for the remaining of the initial segment.
In a semi-probabilistic approach, a similar tactic can be followed, prioritizing any need for
soil investigation. If, for example, a scenario with a high peat layer determines the safety level, only the extent of this peat layer needs to be determined in detail. Investigation methods that specifically target locating this layer can be used. Once the location and the thickness are known in sufficient detail, the effect of this scenario can be reassessed. If the safety suffices with this extra information, the entire segment adheres to the norm. If the safety is below the norm, the area where this peat layer can occur must be strengthened.
Figure 4. Below the dike four subsurface scenarios are possible in a segment of the dike, but their exact locations cannot be ascertained. Each has its own chance of encountering (P) and its own probability of failure (F). The combined probability of failure is the weighted mean.
5. Discussion and Conclusion
Stochastic schematization with scenarios for flood-risk assessments has been successfully applied in The Netherlands and the method is expected to be very useful in other countries as well. It is designed to overcome the problem of having considerable uncertainty about the buildup of the subsurface due to an insufficient amount of measurements. With this approach the measurements can be handled in a rational and objective manner that matches the nature of the
buildup of soil in coastal and riverine lowlands. It also provides a direct link to application in geotechnical applications. The approach is flexible, meaning that scenarios can be easily expanded and adapted to incorporate additional data or information on the subsurface. Adding borehole or CPT information will in general result in detailing the spatial variation along the segments, making certain scenarios locally more likely, or even exclusive, and others less likely in a part of a segment. Verification and validation of the approach can, apart from theoretical considerations, be found in the fact that thus far it has described the subsurface very well for locations where since the scenarios were constructed highly detailed soil investigation data have become available. The method also aids in prioritizing soil- and laboratory investigations during a safety assessment.
Starting in 2017, the approach described here will be used to construct stochastic schematizations of the subsurface to assess the safety level of all main water flood protections of The Netherlands, including over 3500 km of dike. A next step will be an approach in which the stochastic schematizations can be updated easily when new measurements become available during e.g. an extreme event. Together with continuous monitoring of variables like water pressure this will give excellent opportunities for mitigation actions during and preceding high water events.
Acknowledgments
We would like to thank Gerard Kruse for discussion and input for this paper.
References
Fookes, P.G. (1997) The First Glossop Lecture 'Geology for Engineers: the Geological Model, Prediction and Performance'. Quart. Journal of Eng. Geol. 30, pp 293-431.
Kruse, G. (2011) Deriving scenarios for stochastic characterization of the subsurface. In: A feeling for soil and water – A tribute to Prof. Frans Barends (edited by M. Van, E. den Haan & J. van Deen. Deltares Select Series 07/2011 ISSN 1877-5608.
Schweckendiek, T. and Calle, E.O.F., 2010. A Factor of Safety for Geotechnical Characterisation. Proceedings of the 17th Southeast Asian Geotechnical Conference Tapei, Taiwan.
