Amsterdam quays under pressure

Modelling and testing of historic canal walls

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Amsterdam faces the challenge of maintaining a domain of 200 km historic quay walls, which is a vital part of the city’s historical landscape. Many quays are currently in poor condition and require renovation or replacement in the near future, significantly impacting the city. The quay walls can be up to 300 years old and their structure consists of a masonry cantilever wall on top of a timber floor, which is supported by headstocks founded on multiple vertical timber pile rows. In recent years, quay walls have shown signs of damage, partial collapse, and early warnings of such events. The most recent and severe incident was the collapse of the Grimburgwal in 2020, where approximately 20 meters of quay wall suddenly collapsed, plunging into the canal within a matter of seconds. Consequently, it is important to be able to predict the resistance of these structures and understand their potential failure mechanisms. The most common and severe failure mechanism observed in Amsterdam’s city centre is the lateral failure of the pile foundation. Calculating the resistance against this mechanism with existing models, leads to estimates of insufficient strength and safety. It seems that these models are too conservative, because in reality, the majority of the existing structures that proof unsafe on paper is performing quite well in practice. The discrepancy between the models and reality arises from uncertainties in the working principles of historic quay walls, geometrical unknowns, as well as uncertainties in soil and structural properties.

This thesis provides a comprehensive understanding of the lateral failure of the pile foundation by full-scale quay wall experiments and it proposes a computational model to predict the resistance against this failure mechanism.

To gain a comprehensive understanding of the lateral failure mechanism, an unique and extensive experimental program has been conducted on an existing historic quay wall, founded on timber piles. The quay is located at Amsterdam Overamstel and dates back to 1905. Experiments have been conducted at three different system levels. At level 1, four-point bending experiments have been performed on individual piles to obtain the bending material properties. At level 2, lateral pile group experiments have been conducted on two 3x4 pile groups to study the pile-soil-pile interactions. At level 3, proof load experiments have been carried out on entire full scale quay wall sections, to study the overall behaviour of the quay. As part of the experimental program, an extensive geotechnical site investigation has been performed. The experimental approach chosen enables a stepwise validation and calibration for computational quay wall models.

Through the experimental program, it is demonstrated that among all potential failure mechanisms, the lateral failure mechanism is most likely to occur when a quay wall is subjected to large surface loading at its backside. Examples of such loads in practice are parked or moving cars, heavy vehicles or goods. The mechanism is triggered by an increase in soil stresses at the backside of the quay, which pushes the foundation towards the water. This, in turn, results in the bending of the timber piles, accompanied by the development of bending stresses. State-of-the-art models (ABAQUS, PLAXIS and spring models) were used to predict the failure surface load of the Overamstel quay, with an estimated value of approximately 20kPa. However, in reality, the quay demonstrated significantly greater strength, as failure was not observed even for loads as high as 55kPa. While part of this underprediction can be attributed to experiment-specific effects not considered in the prediction analysis, the substantial underprediction of the failure load still emphasizes the conservatism in current modelling approaches.
Clear indicators of the lateral failure mechanism include the inclined position of the top of the piles, broken piles, settlements at the backside of the quay, and lateral deflection of the foundation. These indicators can effectively be monitored, as demonstrated by the employed monitoring plan in the experiments. Elements of this plan, such as inclination sensors mounted on the pile caps, can be implemented in Amsterdam’s city centre to detect signs of lateral failure. The foundation piles experience fracture when they reach a state of full yielding, which occurs when the bending stresses in the timber surpass the modulus of rupture across the entire cross-section of the pile. Bending experiments conducted on timber piles indicate a substantial variance in both the modulus of rupture (variation coefficient of 0.26) and the modulus of elasticity (variation coefficient of 0.3). Consequently, the piles exhibit a wide range of flexural stiffnesses and bending moment capacities. These discrepancies stem from natural variability and biological degradation of the timber, which lead to the formation of a weakened outer layer or “soft shell” starting at the perimeter of the piles, going inward. The soft shell thickness is approximately 10% of the external pile diameter and it does not contribute to the structural strength of the piles.

The substantial variations in load carrying capacities within a timber pile group can be primarily attributed to the variations in pile stiffness and bending capacity. Surprisingly, typical pile group effects such as in-line, side-by-side, pile free height, and pile diameters do not have a large contribution to the variations in individual lateral pile resistances found. When multiple piles are considered together, significant variations between individual piles compensate each other, leading to a group resistance that was almost identical in the two pile group experiments. This finding is advantageous from a computational modelling and risk assessment standpoint. Within the tested pile groups at the Overamstel site, with 200-300 mm diameter piles, partial yielding starts at approximately 100 mm of group deflection. The first pile breakages are expected to initiate at 140 mm of deformation; however, due to the redistribution of lateral loads among the piles, it does not directly result in group failure. Nevertheless, when deformations exceed 200 mm, a majority of the piles will break, leading to group failure. It is vital to emphasize that the transition from the initial onset of yielding to group failure requires merely a slight additional lateral load of 15%.

An analytical quay wall model has been developed to predict the resistance against lateral failure of historic quay walls. This model comprises a framework of elastic beams embedded in an elastic foundation, which is externally loaded by a linear elastic soil model based on Flamant’s theory. The framework is made up of multiple Euler-Bernoulli beams, connected to each other by boundary and interface conditions. The stiffness of the connection between piles and headstock is described by a pile-headstock interface model. The elastic foundation is represented by a series of independent p-y springs, approximated with a bilinear elastic-perfect-plastic model. A method is developed to include the pile-soil-pile interaction and the influence of a sloping surface by adjusting the plastic branch of the p-y springs. This method has been validated through multiple experiments documented in literature in which steel piles were used, eliminating material property uncertainties. The analytical quay wall model has been validated and calibrated with the Overamstel quay wall experiments, employing the stepwise approach. In the first step, the bending properties of the timber piles were obtained from the level 1 bending experiments. Subsequently, in the second step, the model’s capability to describe laterally loaded pile groups was validated through the level 2 pile group experiments. Finally, the Flamant soil model and the model’s ability to describe a historic quay were validated using the level 3 quay experiments. As a final step, the model was compared with finite element computations, demonstrating a good agreement in displacements and forces. The analytical quay wall model accurately predicts lateral displacement, pile bending moments, and bending stresses at various depths, allowing for the assessment of pile fracture under specific surface loads. Its key advantages over state-of-the-art finite element modelling software include robustness, computational speed, feedback loops (e.g. force and displacement-dependent pile-headstock connection stiffnesses), minimal input requirements, and no numerical stability issues at large deformations. The model is highly suitable for trend analysis, sensitivity studies, and probabilistic analysis due to its short computational time in seconds, compared to complex three-dimensional FEM software that takes minutes to hours. The effectiveness and potential of the validated analytical quay wall model have been demonstrated in two “follow up” studies, described below.

In the first study, the quay model has been employed to investigate the failure of the Grimburgwal. With the model it was demonstrated that bending stresses in the timber piles exceeded the modulus of rupture as a consequence of local deepening of the canal in front of the quay. It therefore provides valuable insights for Amsterdam’s historical centre. The analyses have served as an additional validation step for the analytical quay wall model developed in this thesis, specifically for applications to the quay walls of Amsterdam’s historical centre.

In the second study the quay model has been used to effectively showcase the potential of Bayesian updating by incorporating evidence of survived loading situations and corresponding deformations. This approach enables refinement of the reliability predictions and parameter distribution uncertainties, leading to a more accurate prediction of the resistance against the lateral failure mechanism of quay wall foundation piles. Depending on the type of evidence, an a-priori reliability prediction for a quay wall that fails to meet safety standards can be updated to any of the three consequence classes (CC3, CC2, and CC1b) outlined in NEN8700. In a fictive case study, a quay wall with an a-priori reliability of β = 1.5 has been increased to β = 3.2 by including evidence of an extreme survived load of 10 kN/m2 that resulted in displacements of less than 4mm. This is a decrease in failure probability by two orders of magnitude, showing the potential impact of using observational information in combination with Bayesian updating

The main practical implication of this thesis has been the improvement in modelling accuracy, as a result of the Overamstel experiments. The revised “gain” in modelling accuracy for bending moments and deflection was 43% and 37% respectively. This improvement can be attributed to advancements in modelling techniques, such as accurately simulating pile-soil-pile interaction and modelling the pile-headstock connection, as well as utilizing precise location-specific geotechnical and structural material properties as model input. The improved modelling accuracy results in a less conservative evaluation of the quay walls, leading to a reduction in the number of unnecessarily rejected quay walls for the Amsterdam quay wall domain.

The most practical recommendations for Amsterdam are: a) to develop accurate techniques for mapping quay wall configurations, b) to implement comprehensive quay wall monitoring systems in the city centre, c) to utilize the analytical model in future studies and assessments, d) prioritize geotechnical site investigations before making model predictions, and e) perform non-destructive tests in the city centre and incorporate this information in the assessment.

The methods and insights developed in this dissertation enhance the understanding of the lateral failure of historic quay walls and enable more precise predictions of their resistance against such failures. As such, the model can be effectively used to support decisions on their safe use, remaining service life, and the need for their replacement.