One of the failure mechanisms for water retaining structures is piping. Piping is an internal erosion mechanism creating hollow spaces (pipes) underneath, for example, a dike as a result of the transport of soil particles due to seepage. The formation of pipes can cause collapse of the structure once the erosion process reaches the outside of the dike. This study focusses specifically on the possibility of the occurrence of this failure mechanism in the Maasvallei area. The Maasvallei covers the area of the Maas roughly between the Dutch towns Roermond and Mook. The early signs of piping in the form of sand boils are frequently observed during periods of high water levels in the Dutch rivers. Although the total collapse of a dike in the Netherlands due to piping has not occurred in the past decades, the frequent observation of the early signs of the piping process has resulted in the inclusion of the piping failure mechanism in the Dutch legal safety assessment regulations for water retaining structures. During recent high-water periods in 2011 and 2012 sand boils were observed along several Dutch rivers except at the dikes along the Maas. The striking absence of sand boils in the Maasvallei area raised the question if the failure mechanism piping is relevant for this specific area. In the recent assessment of the Dutch dikes, many of the dikes along the Maas in Limburg were found to be insufficiently safe against piping. The dilemma then becomes clear: the lack of early signs of piping contradicts the outcome of the safety assessment. Resources could be saved if the dikes do not need to be reinforced for piping, however, the safety should not be compromised. Within the thesis this dilemma is studied. The main question that is answered is: Is dike-failure due to piping realistic in the Maasvallei?

Changes in the Earth’s climate system do have consequences for the river discharges. The development of the future climate is uncertain, which causes uncertainty in the future extreme river discharges. For flood protection considerations, it is important to quantify the climate uncertainties and its effects on extreme river discharges. In this study the uncertainty in extreme river discharges due to Climate Change is quantified. The results indicate the uncertainty in discharge return levels given a specific forcing scenario. Subsequently, the discharge return levels of the KNMI climate scenarios are compared with the found results for the forcing scenarios. The study also provides the consequences of the uncertainty in discharge return levels on the design water levels. The results give the uncertainty in the design water level and the additional height in design water level required to take account for this uncertainty.

The Netherlands is a country that is being threatened by water, both from the rivers and from the sea. The Dutch have built dikes to keep their lands from inundation. To ensure the strength and stability of these dikes, they are being assessed on the basis of several failure mechanisms. One of these failure mechanisms is Backward Erosion Piping, or piping for short. In piping, the current underneath a dike is strong enough to take soil particles with it. Tests on piping in tidal subsoil were conducted in the summer of 2021, where a pipe was found to have grown at greater depth than expected The occurrence of this deeper piping has rarely been seen before, let alone described. This lack of knowledge poses a potential safety risk, as it may underestimate the vulnerability of certain subsoil configurations. Therefore, the objective of this thesis is to develop a comprehensive understanding of deeper piping and identify the key parameters influencing its formation. To achieve this objective, a definition of deeper piping and its differentiation from conventional piping is established. Sub-mechanisms governing deeper piping are examined by analysing the forces responsible for grain movement and the forces that maintain grain stability. A Finite Element Model of the subsoil is constructed to quantify the driving forces within the subsoil, which, when combined with resisting forces, enables the determination of whether deeper piping can occur in a given subsoil configuration. To investigate the factors contributing to deeper piping, a series of simulations are conducted using this Finite Element Model. By varying the parameter values while keeping other factors constant, the influence of each parameter on the occurrence of deeper piping was examined. The analysis revealed that several key parameters significantly affect deeper piping formation, including cohesion force (𝑐), cohesion anisotropy (𝛼𝑐 ), permeability and thickness of the top layer (𝑘0 and 𝐷0, respectively), permeability of underlying layer (𝑘1), permeability anisotropy (𝛼𝑘 ) and representative grain diameter 𝑑𝑟𝑒𝑝. Also, it was found that the entrance configuration plays a large role in deeper pipe formation. These findings provide valuable insights into the mechanisms underlying deeper piping and enhance our ability to identify subsoil configurations that are prone to this phenomenon. These findings enhance the identification of subsoil configurations prone to deeper piping, thereby improving risk assessment and mitigation strategies associated with this failure mechanism.

Due to climate change, a new water management policy is considered in the Netherlands. The shift towards greater extremes in both wet periods and dry periods requires a more dynamic policy. It is investigated what effect the placement of a permanent water barrier in the Rijnmond has on the water levels in the Rhine branches, and if this can be an opportunity to help the drought prone area in the east of the Netherlands.This study shows that replacing the Maeslantkering with a permanent barrier has no influence on the water levels upstream of Nijmegen in the Waal at average to low Rhine discharges (2000 - 600 m^3/s), and thus has no effect on the water distribution at the Pannerdensche Kop. If the fresh water demand to stop the salt wedge is eliminated, a different water distribution over the Rhine branches is possible, but structural changes at the bifurcation point have to be made in order to achieve this. River water can be used to supply the east of the Netherlands with water. In this study, three options to do so are examined. The most promising options of these is placing a pumping station in the Rhine nearby Lobith and supplying the streams in the area with water, many of which fall dry in summer. From there, the water can be used for irrigation, infiltration, and other fresh water demands, relieving the stress on the groundwater during dry spells. Building a permanent storm surge barrier is not a requirement, but because it increases the navigability of the Waal river, water can be extracted more often with a permanent barrier. A solution to combat drought in the east of the Netherlands seems to be more urgent than a solution to mitigate sea level rise. However, a permanent barrier can help in mitigating the effect of drought on groundwater levels in the east of the Netherlands by allowing for more flexibility in using river water extraction.

In the Netherlands, a new assessment method for the required safety level of primary flood defences is introduced in the Water Act. It is estimated that currently roughly 1900 kilometres of flood protection does not meet the safety requirements for the future (Jonkman, Jorissen, Schweckendieck & Van den Bos, 2017). Past flood defence projects show that integrating reinforcement measures is a difficult assignment. It is specifically focused on dike reinforcement projects in this thesis. A deficiency in the design process is identified in the role that the influence on the existing situation has on the evaluation and selection of design alternatives that are input for the Environmental Impact Assessment. The difficulty for improving the importance of the existing situation in the surroundings, in the design process is that the subject experts on these themes are typically assessing the consequences of proposed interventions (Aalberts, 2018). The research objective is set to develop a method that allows to include the influence on the existing situation within the evaluation and selection of design alternatives in dike reinforcement projects. This method aims for providing information to compare the spatial integration of reinforcement designs in early stages of reinforcement projects. Subject experts should assess the provided information, and determine whether a reinforcement design provides a satisfying influence on the project area. It is focused on dike reinforcement projects in rural area. A research through design study is used to develop the method to compare design alternatives. The study included the identification of technical design measures to increase the strength of dikes in rural area, and the decomposition of rural areas in functional characteristics that can be valued. A conceptual evaluation model is developed to express the relation between functional characteristics and design alternatives for dike reinforcements. It is studied how a method can be provided to compare the outcome of the conceptual evaluation model for a large variety of design alternatives. The value of the developed method is assessed in a case study, which is the dike reinforcement project “Wolferen-Sprok”. The resulting method is able to compare design alternatives on the influence on the existing situation by following seven steps. It is providing design measures for the identified safety problem of the dike in a certain project area. Simultaneously, the characteristics of the project area should be identified and visualized on maps. This provides the required information to apply the conceptual evaluation model that identifies effects of design alternatives on the existing situation. The retrieved data is visualized to compare design alternatives. It is concluded that the developed method focusses mainly on natural, cultural, and social economic functions in rural project areas. This means that influence of design alternatives on costs, maintainability, and landscape values should be addressed separately, in the evaluation and selection of design alternatives. It is recommended to study how the influence on these topics can evaluated in a similar method. The developed method can be applied to include the existing situation in the project area in the evaluation and selection of design alternatives in dike reinforcement projects in rural areas. It is expected that application of the method in design teams provides new input for further improvement of the method.

In the last century, approximately 100,000 people lost their lives during a flood event and over 1.4 billion people were affected. As the population and economic activities grow in flood-prone areas and the frequencies and intensities of flood events increase due to climate change, damage due to flooding is expected to increase. To limit and control the potentially increased risks, in many locations flood defences, such as levees, are built and existing flood defences are reinforced. It is thus important to be able to properly estimate the reliability of these levees and to understand their potential failure mechanisms. In particular, there are significant uncertainties associated with the occurrence of geotechnical failure mechanisms such as slope instability and piping. The hindcasting of levee failures can provide valuable information about the factors and uncertainties that dominate levee performance and reliability. Systematic forensic engineering approaches to evaluate failed structures and methods of hindcasting have been developed in the field of structural engineering, but these are not well applicable to failed levees. This is mostly due to the scarcity of relevant information prior to, during or after the levee failure, which leaves multiple scenarios and alternative model choices possible to characterize the event. This thesis proposes and demonstrates methods for systematic analysis of levee failures at the individual section and system level. These methods of hindcasting are expected to contribute to the overall quality, repeatability, transferability, transparency and recognisability of the analysis of levee failures. In this thesis, existing approaches for evaluating structural failures have been adapted to analyse levee failures using both deterministic and probabilistic techniques. This thesis focuses on the levee failure mechanism of slope instability of the inner slope. Firstly a deterministic method is proposed which is applied to a slope failure. In this method, the uncertainties in possible causes and computational models are modelled by defining possible scenarios explaining the failure based on all the information available. The influence of the identified scenarios and possible alternatives in model choices are analysed through a sensitivity analysis. Results of the computations are confirmed or refuted by observation information of the failure such as the shape of the failure surface. To illustrate the method, it is applied to the levee failure near Breitenhagen (2013), in Germany in Chapter 2 of this dissertation. The levee near Breitenhagen is located at the intersection of the Saale and the Elbe and it failed due to instability of the slope at the polder side of the levee. Unexpected saturation of the levee, steep slope of the levee, and the influence of the tree roots were identified to cause of the levee failure by previous reports. However, in the present study, an old breach was found to be there (the first proxy was a pond likely caused by this old breach next to the levee; the old breach was later confirmed with archive research). This old breach and pond resulted in a scenario with low strength and high water pressures in both levee and the aquifer and was identified to be the most likely scenario explaining the failure. The results indicate that locally low values of shear strength (low values of pre-overburden pressure or cohesion) explain the failure. Other scenarios that were evaluated resulted in a situation that was not likely to fail or, resulted in a slip surface that differs from the observed failure surface. The deterministic method does not quantify uncertainties explicitly. That makes it difficult to uniquely identify the most likely scenario to explain the failure. Therefore the deterministic method is advanced by making it probabilistic and by including Bayesian techniques in Chapter 3. Thereby a better insight is provided into the relative likelihoods of the various scenarios explaining the failure. Failure observations (water level at failure, the shape of the slip surface, etc.) and a-priori levee information (soil layering, shear strength etc) are systematically taken into account to quantitatively identify the most likely scenario explaining the failure and the most representative model choices to most accurately characterise the failure. The Bayesian techniques are also used for updating the scenario and possible alternatives in model choices using the observations of the actual failure (if present) such as the shape of the slip surface. To illustrate the method, it is also applied to the levee failure near Breitenhagen (2013) in Germany. Similar to the deterministic method, the old breach resulting in a scenario with locally weak soil and aquifer connection is found to be the most likely scenario. Further, the Limit equilibrium using Spencer’s approach and undrained soil response is identified to be the most representative model choices. The shear strength ratio is identified as the 6 most dominant contributor to the failure. Compared to the “deterministic method” introduced in chapter 2, the probabilistic method adds the possibility to quantitatively substantiate the identification of the most likely scenario explaining the failure as well as the most representative model choices. Both methods of hindcasting have had little application and validation. Therefore both methods have been applied to a large-scale levee failure experiment. The levee of the Leendert de Boerpolder, in the Netherlands, was brought to failure under controlled circumstances. As a result, very detailed information is available. The levee was brought to failure by gradually lowering the water level in an excavated ditch at the polder side of the levee. Since the water level drawdown is known at the time of failure, this information is used to validate the outcome of both methods of hindcasting. The available levee information was used in two steps. In the first instance, only basic information was used in the hindcasting. In the second step, the geometry of the observed slip surface is also included. The probabilistic method using Bayesian techniques required some adjustment, to account for the survival of previous load phases during a stepwise increase of the load. Both methods of hindcasting identified the same water level drawdown at the moment of failure, but different model choices. In addition, the identified water level drawdown is confirmed by the observed water level drawdown at the time of the failure, i.e. 1.6 m. Finally, this thesis introduces a method to quantify the influence of deviating conditions on the failure rate of a levee by looking at failures on a system level. The annual failure rate of a levee section is assessed based on information from historical floods. The return period of past events is also taken into account. The presence of deviating conditions at failed and survived levee sections is analysed based on satellite observations. Bayesian techniques and likelihood ratios are used to update the average failure rate as a function of the presence of a deviation. The river system of Sachsen-Anhalt, Germany, is used as a case study. It experienced severe floods with many levee failures in the years 2002 and 2013 resulting in the failure of 41 levee sections due to internal erosion, instability or overflow. It is found that the presence of geological deviations has a significant influence on the observed failure rate and that the failure rate increases with the magnitude of the hydraulic loading. The results show that in the case of the occurrence of a visually identifiable geological deviation in the subsurface, the updated failure rate of a section is about 14 times high than when there is no visually identifiable deviation. The presence of other deviations, such as bushes or trees, or permanent water near the levee also results in a somewhat higher failure rate (20–30% higher) than the calculated average annual failure rate. It is also discussed how the expected number of failures in a system during a high water event with a certain magnitude can be estimated. The results of this research can be used to further optimize soil investigations, calibrate the results of more advanced reliability analyses, and complement risk assessments. The method offers opportunities in particular in environments where little data is available. Overall, the methods and insights developed in this thesis can contribute to a better understanding of the performance and reliability of flood defence systems.@en

In most current dike assessments only the stationary water levels are investigated in the assessment of the stability of the inner slope, while there are differences for all kind of dikes between the stationary and transient pore water pressures and therefore in the stability. This results in a conservative probability of failure, while determination of a probability of failure should not be conservative but should be as realistic as possible. When time dependency is included in a calculation, an average flood duration is used, while the flood duration is highly variable. The following research question is defined to address the problem: “What is the influence of the flood duration on slope stability and in what degree affects the flood duration the design?” The degree of influence of time dependency on the pore water pressures and slope stability depends on dike characteristics, flood wave characteristics and the delay in failure. The basis for answering the research question is the software SEEP/W to model the time dependent pore water pressures and the software SLOPE/W to calculate the safety factor for the stability of the inner slope. In the research theoretical dike are used and there is focused on the flood waves in the Rhine and Meuse. A correlation analysis is performed to get insight in the contribution of different flood wave shape variables to the safety factor. And a probabilistic analysis is performed using transient and stationary water levels to know the differences in probability of failure between taking the shape of a flood wave into account or not. In both probabilistic analyses is varied in the permeability and the strength of the material; the shape of the flood waves is varied in the transient analysis. In this way the contribution of the flood to the probability of failure can be quantified. Dike characteristics The differences in pore water pressure are especially large for dikes that consist of an impermeable material such as clay. When only the subsoil consists of clay, larger differences are expected than when only the dike body consist of clay. However, large differences in pore water pressures do not necessary lead to large differences in the safety factor. The largest differences in safety factor are obtained when uplifting of the hinterland takes place during the stationary state and/ or during the passage of a flood wave. A transient calculation is therefore most useful for dikes with an aquifer and a thin (thinner than 5 m) weak (low POP values) hinterland. Flood wave characteristics The differences in safety factor during a permanent water level and the passage of a flood wave are large when no stationary conditions are reached during the passage of a flood wave. This is the case for high and short flood waves. Both in the Rhine and Meuse, the amount of short waves (< 7days) is high, which increases the influence of a time dependent calculation. Also, the importance of a time dependent calculation increases when the response to the increased pore water pressures is delayed caused by the permeability of the material. The influence of the height of a flood wave on the stability increases when the soil is permeable. Delay in failure Time dependency causes failure of the embankment to not occur simultaneously with the maximum wave height. The flood wave is decisive for the dike failure, but the permeability and the strength of the dike determines the moment of failure. Influence on design Taking time dependency into account leads to higher safety factors and lower probabilities of failure with exception for dikes that consist completely out of sand. For these types of dikes, the probability of failure and safety factors are the same order of magnitude. This could affect the design, because the dikes are safer when time dependency is considered. The strength of the material is the largest contributor to the distribution of safety factors and therefore to the probability of failure (60-95%). Whereas the contribution of the permeability to the probability of failure is small (2-12%), the variation in the height and duration of a flood wave contribute for 2-20% to the probability of failure. In a permeable dike this contribution is mainly determined by the height of a flood wave, while in an impermeable dike the duration of a flood wave is of importance. Considering the influence of time in stability probabilities of failure, this research proved that probabilities of failure taking the duration into account differ significantly from stationary calculations. It is therefore useful to take time dependency into account when determining the correct safety factor for impermeable dikes, but it is not useful in determining the correct safety factor for permeable dikes, because a stationary calculation is sufficient. In clay dikes it is useful to take the variation in height and duration into account, while for a sand dike it is sufficient to only consider the variation in height of a flood wave. When the variation of the duration of a flood wave is not considered, it is recommended to use a representative duration of a flood wave; that results in the same total probability of failure as when the variation of the duration is included. At Lobith the duration of the representative flood wave varies from 13 - 16 days. At Borgharen the representative duration varies between the 10 – 11 days for different dike types.

Levees are earthen structures that are designed to protect land from flooding and are commonly composed of impervious soils and built on sandy foundations. They are sensitive to an erosion process that is known as piping. After several years of investigation into piping, Sellmeijer proposed design rules by curve fitting results of a numerical model. The design rule are currently applied in the assessment of levees, despite being obtained under the assumption of uniform and homogenous subsoils. Consequently, the design rules seem to be fine for standard consultancy, but it is insufficient for heterogeneous and anisotropic. In this thesis, the effects of anisotropy and heterogeneity are analysed in a elementary and a realistic numerical model study in order to improve the design rule of Sellmeijer. In the elementary study, several aquifers compositions are created by adding an artificial element with a different permeability to the body or by varying the permeability of the body depending on direction. The realistic study is a modification of the elementary study since stratified aquifer compositions have been implemented. After each simulation, the critical head computed in the elementary or realistic composition is compared to the critical head computed with Sellmeijer design rules which requires one calculation value of the bulk permeability. To improve the design rules an alternative method to determine the bulk permeability is proposed that assumes that there is curved or radial flow towards the exit point instead of the Dupuit method which assumes that there is only horizontal flow. As a consequence, the bulk permeability is calculated as the geometric or logarithmic mean of the vertical and horizontal permeability. Based on both studies, it can be concluded that both anisotropy and heterogeneity in the aquifer greatly increase the critical head so that heterogeneous and anisotropic aquifers are significantly more resistant to piping. In some cases, the aquifer can withstand a 45% higher water level. Furthermore, Sellmeijer’s design rules more accurately approach the heterogeneous and anisotropic aquifer, if the bulk permeability is determined with the new approach.

In this thesis, the effects of the foreshore and heterogeneities of the subsoil on the piping safety analysis are determined. The effects are searched for by use of the numerical model D-Geo Flow. The results of this research give more insights in when and how a foreshore has to be included in the safety analysis. It is also concluded that heterogeneous soils are more resistant to piping than homogeneous soils, which are currently used in the safety analysis.

In 2010 a large flash flood hit El Arish City, killing at least 6 people and causing a lot of damage. This was not the first time the Sinai was affected by these flash floods, more than 40 flash floods have been recorded in the El Arish watershed in the last 100 years. The enormous amount of water and the flow velocity of these floods are a hazard to its surroundings and to the rehabilitation plan of the Weather Makers. On the other hand the water is scarce in the arid Sinai and the flash floods could contribute to the plan to create a robust water cycle. The underlying goal of this research is to investigate whether a robust water cycle can be created by reducing the flash flood hazard and increasing the available water for the creation of biomass. Measures will have to be taken to start the transition and tackle issues such as drought, unfertile soil, water regulation and to properly address the social benefits to involve the inhabitants of the area. It is therefore essential to assess the hazards of the current and future situation of the Sinai and to apply appropriate measures on the hazardous locations.                The goal of this research is to propose a strategy to reduce the flash flood hazard, by first identifying hazard prone areas and then propose measures to counter these hazards. This strategy takes into account a scenario on change in catchment hydrology, gives guidance on land use for the region and will propose feasible measures to reduce flash flood hazards. It does not involve the design of the feasible measures nor a cost benefit analysis.                To assess the hazards in the El Arish watershed, the USACE method is used. The USACE method uses HEC-HMS for the hydrologic modelling and HEC-RAS for the hydraulic modelling. With a DEM sub basins and wadi channels are delineated and measured, precipitation data is collected from the TRMM and analyzed, the retention of the soil is simulated with curve numbers and transmission losses are estimated. The sensitivity of the hydrological model is checked and is used to simulate the 2010 flash flood to compare with imagery of the event. Measures usable in arid areas like the Sinai to reduce flash flood hazards are analyzed on their feasibility and their effects are modelled with the hydrologic model.The current flash flood hazard is assessed by simulating an extreme event and the region with the highest relative hazard is selected. Measures are proposed based on their applicability and the physical attributes of the surface with a decision tree. The following measures are suggested: spreading dams in flat wadis (<2%), impervious dams in mild sloping wadis (2-5%) and pervious dams on steep sloping wadis (>5%). The effect of these measures combined on the peak discharge is estimated to be 70-75% for an extreme precipitation event. The measures decrease the total- and peak discharge but they also spread the flash flood making the duration of the flow longer. To check whether the suggestions are future-proof a scenario of change in the hydrological cycle is considered by increasing the extreme precipitation with 15%. This causes the peak discharge to increase with 30-35% if no measures would be applied. By applying measures the peak discharge decreases with 60-65%, which is a smaller percentage than without an increase of extreme precipitation (70-75%).Challenges of the research are that measurement data was lacking to calibrate the conceptual hydrological HEC-HMS model, the large amount of uncertain parameters therefore cause equifinality. The estimated values of the parameters and the results of the simulation are however consistent with literature and gives a good indication on the hazard.This research shows that the flash flood hazard in the El Arish watershed can be reduced by using feasible measures. The proposed method to reduce the flash flood hazards can contribute to the plan of the Weather Makers to rehabilitate the Sinai by slowing down the flood and to enhance the infiltration. It also creates suitable locations for vegetation by capturing sediment and water this could help to create a robust water cycle.

The water levels along the dike of Kampen are affected by the magnitude of the discharge on the IJssel and the water level set-up caused by the wind characteristics on the IJsselmeer. The Kampereiland has been assigned as a retention area to reduce the water levels near Kampen during a storm. This area should store excess water during a storm at the IJsselmeer of a magnitude corresponding to an annual exceedance probability of 1/500, to prevent this water from flowing in the direction of Kampen. The Kampereiland is protected by dike trajectory 225 and a part of this trajectory has been made resistant to the overflow of water. According to new insights, the crest of this dike section seems too high and the Kampereiland inundates less frequently. Furthermore, not sure is whether the water level at Kampen benefits from the inundation of the Kampereiland and what the consequences are for surrounding dikes. The Kamperzeedijk is one of these surrounding dikes and protects the city IJsselmuiden, along with the polder behind. The influence of the crest height of this overflow resistant part on the water levels at Kampen and at IJsselmuiden is investigated. The most important assumptions are that dikes do not breach and that the water level at Kampen remains constant after water flows into the Kampereiland. The influence on the water levels at Kampen and at the Kamperzeedijk is evaluated for multiple crest heights of the overflow resistant dike section. Eventually, these water levels are processed with a statistical model to compute multiple water level exceedance frequency lines for each location and for various chosen crest heights of trajectory 225. The results show that higher crest heights of trajectory 225 lead to increased maximum water levels at the Kamperzeedijk and to lower maximum water levels at Kampen, and vice versa. The water levels in front of the overflow resistant dike section remain unaffected. The return periods for overflow at Kampen and IJsselmuiden are derived by comparing the water level exceedance frequency lines to their individual crest heights. Concluded is that the inundation of the Kampereiland does not immediately lead to a load increase in front of the Kamperzeedijk. A delay is observed as a result of the storage capacity of the Kampereiland. As soon as water from the Kampereiland flows into the Ganzendiep, the loads rapidly increase. Furthermore, concluded is that the Kampereiland is capable of reducing the water levels at Kampen. Based on the results from this research, a crest height of 2.7m +NAP leads to equal return periods for overflow at trajectories 10-2 and 11-2. The reduction of the crest height by ten centimeters increases the return period for overflow at Kampen from 30,000 years to 45,000 years. At the Kamperzeedijk, the return period is reduced from 80,000 years to 45,000 years. In reality, these return periods are also affected by other failure mechanisms. A full dike assessment has to elaborate on this. Furthermore, trajectory 225 is assessed whether it meets its safety standard. It would be more legitimate to assess trajectory 225 by explicitly quantifying its consequences on trajectories 10-2 and 11-2