# Max HendriksDelft University of Technology | TU · Department of Engineering Structures

Max Hendriks

Professor

## About

191

Publications

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2,047

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Introduction

Additional affiliations

November 2011 - present

August 2007 - January 2022

## Publications

Publications (191)

To date, there is no comprehensive approach available that can explicitly model the complete transient waveforms of acoustic emissions (AE) induced by fracture processes in brittle and quasi-brittle materials like concrete. The complexity of AE modelling arises from the intricate coupling between the local discontinuity of material fracturing and t...

This paper proposes a new mechanical model to describe the dowel action with the aim of using the model to gain a deeper understanding of the unstable dowel splitting cracking observed in shear experiments of beams without shear reinforcement. The model was developed by combining beam on elastic foundation (BEF) theory and fracture mechanics. The p...

Assessment of existing reinforced concrete (RC) structures after an earthquake is a challenging task that must somehow relate qualitative and quantitative observations in the plastic hinge regions and the associated residual deformation capacity of damaged structures. Having an estimate available for the remaining drift capacity will result in more...

Cultural heritage sites all over the world are increasingly threatened by regional-scale subsidence. Addressing this issue necessitates a deep understanding of how ground settlements impact structural integrity. Traditional approaches, primarily reliant on in-situ investigations, are not only costly but also constrained by their installation in ant...

As the existing bridge stock is ageing, assessment of existing bridges becomes increasingly important. In the Netherlands, the shear capacity of reinforced concrete slab bridges is found to be insufficient. In particular, the shear and punching shear capacity of reinforced concrete slab bridges subjected to concentrated loads from the design tandem...

Coda wave interferometry (CWI) holds promise as a technique for concrete stress monitoring. This is because the coda, which consists of multiply scattered arrivals, is the result of propagation through the medium over large distances. As such, it is sensitive to both minute structural changes and small velocity changes in that medium. Previous stud...

Based on literature a constitutive equation for drying of concrete and key input parameters were identified (addressing Tasks 1.1 and 1.2 of project ICD 521). The key input parameters are the desorption isotherm and the moisture diffusivity, both in the relevant range of relative humidity (75% to 100% RH). Models describing desorption isotherms and...

Bond deterioration is one of the major consequences of reinforcement corrosion in reinforced concrete (RC) structures. In this paper, a two-phased numerical modelling approach is presented that aims to determine the constitutive behaviour (bond-slip) at the reinforcement-concrete interface at a certain corrosion level. The novelty of the approach i...

Monitoring or identifying structural cracks is crucial for assessing the health of existing concrete structures. Key information about structural cracking encompasses the location of the crack and its kinematics, which include movements perpendicular and parallel to the crack face. Acoustic emission (AE) is a sensitive technique for detecting the l...

This paper presents a systematic comparison between implicit and explicit solution procedures for simulating the fracture processes in reinforced concrete. Implicit procedures are known to suffer from convergence problems due to negative softening stiffness, bifurcations and snap-backs. Explicit techniques have the potential to overcome those, but...

Typically precast girders are designed and utilized as simple supported members. Alternatively, the precast girders can be made continuous at the intermediate support using cast-in-place concrete topping. Once the girders are made continuous, time-dependent restraint moments will occur. The magnitude of the restraint moment is mainly affected by th...

Concrete, as the most widely used construction material, is associated with a high environmental impact. Within the present study, structural optimization is the method of choice to counter this issue. The entire process, from optimization, to design, experiments and numerical simulation is outlined. Embedded in the framework of a design competitio...

Frost salt scaling of concrete is related to cyclic freezing and melting of a few millimeter thick deicer solution on the surface of the concrete. It is almost absent when pure water is freezing and reaches a maximum at a so-called pessimum concentration that for NaCl is around 3%. Different mechanisms have been suggested to explain this pessimum a...

To assess the structural capacity of reinforced concrete structures, identifying the internal cracks is important. Acoustic emission (AE) is promising to estimate the location of internal cracks. However, the localization is influenced by many factors like arrival time picking error, presence of crack, etc., resulting in localization error. The err...

Corrosion and shear cracking are frequently observed near supports of pretensioned bridge girders in coastal climates, so non-linear finite element analysis was used to study the effect of corrosion on shear performance in a real case study. Varying degrees of corrosion and various locations (top strands, bottom strands, vertical stirrups and girde...

This study investigated the effect of fire on the ultimate load‐bearing capacity of reinforced concrete (RC) slabs. The structural response of RC circular specimens subjected to static load conditions after exposure to a hydrocarbon fire on one side of the specimen was examined. Two fire exposure times were considered (60 and 120 min) in addition t...

Sequentially Linear analysis (SLA), an event-by-event solution strategy in which a sequence of scaled linear analyses with decreasing secant stiffness is performed, representing local damage increments; is a robust alternative to nonlinear finite element analysis of quasi-brittle structures. Since it is based on a fixed smeared crack constitutive m...

There are a large number of precast girder bridges in the Netherlands that are made continuous utilizing cast in situ layers and cross beams. When controlled by the Eurocode minimum shear reinforcement requirement, the majority of these bridges that were constructed before the 1970s have insufficient amount of transverse reinforcement, which could...

For reinforced concrete members without shear reinforcement, the shear failure is characterized by the formation of a critical flexural shear crack. Recently experimental observations making use of Digital Image Correlation (DIC) by many researchers suggested the significance of geometric characteristics and kinematic conditions of critical shear c...

Strut-and-Tie modelling (STM) has been widely applied to design D-regions of reinforced concrete structures. For economic and environmental reasons there is a need for optimized Strut-and-Tie models. How to optimize Strut-and-Tie models considering multiple load combinations has not been investigated extensively in the literature. In order to addre...

We simulate the glue-spall stress due to mechanical interactions between a frozen saline solution (brine-ice composite) and a non-air entrained concrete surface including the impact of the micro-structure of the frozen solution. The presence of brine channels at the ice/concrete interface was found to be a prerequisite to induce stress during freez...

Alkali–silica reaction (ASR) in concrete causes expansion and degradation of the material, which might give adverse structural consequences. From the structural engineer point view, the greatest concern is if ASR leads to loss of structural integrity. Two natural questions arise when assessing existing concrete structures affected by ASR: (1) how t...

The process of ice melting during abrasive interactions with concrete is essential in a variety of contact phenomena. In this paper, we refer to abrasive tests for different samples of concrete with roughness in the range of 9–35 μm. The experimental conditions were: 1 MPa ice pressure, ambient temperature −10 °C, average sliding velocity 0–0.16 m/...

This paper proposes a new damage identification method, namely, the probability density field of acoustic emission (AE) events. This new method provides a different perspective to deal with the uncertainties in the source localization process. We treat the source location as a random variable, and estimate its probability density field based on a p...

When the shear resistance of prestressed beams with stirrups is determined with the current Eurocode, no distinction is made between regions with and without flexural cracks. This while it may be expected that a region without flexural cracks will have a higher shear resistance. This is due to the lower longitudinal strains and the narrow crack wid...

Acoustic emission (AE) signal parameters can be used to classify the source type in concrete structures. However, signal parameters are influenced by the wave propagation from the source to the receiver, leading to wrong source classification results, especially for monitoring large concrete structures. This paper experimentally evaluates the influ...

Significant infill wall damage in reinforced concrete frame buildings was observed in the past earthquakes. A vast number of numerical approaches have been proposed to estimate the non-linear behavior of infilled frames at different scales. Mesoscale lattice models were successfully used in the past to simulate the behavior of reinforced concrete m...

Nineteen nonlinear finite element analysis (NLFEA) solution strategies were benchmarked against a wide variety of 101 experiments on reinforced concrete beams. The relatively high number of solution strategies was motivated by the conviction that choices for the constitutive models, the finite element kinematics and equilibrium settings will intera...

Material modelling, from the micro to the macro level, of concrete affected by alkali–silica reaction (ASR) has been devoted a lot of research. However, the application of the material models in structural analyses of reinforced concrete (RC) structures, showing the structural implications/consequences of ASR, has got little attention in the litera...

When non‐linear finite element analyses are used in design of new or assessment of existing concrete structures, one should account for the modelling uncertainty before conclusions are drawn based on the results. The present article describes the basis for how this topic is treated in the draft of fib Model Code 2020. There are two components of th...

In Europe, design for the durability of new reinforced concrete structures is currently based on a prescriptive approach. The design, execution (construction) and planned maintenance of a concrete structure have to lead to the intended level of safety and serviceability throughout its entire service life. This requires numeric models based on a sou...

In the finite element modelling of masonry structures, the micro-modelling technique of differentiating the continuum into a linear elastic bulk, and interfaces representing non-linear joints is common. However, this approach of simulating cracking-crushing-shearing failure possibilities in interfaces, typical of damage in masonry, also poses numer...

In the Netherlands, existing bridges are being assessed to investigate whether they are capable to resist the current traffic loads, which have increased since the bridges were designed. A substantial part of these bridges consists of prestressed concrete girders with a thin web and a low amount of shear reinforcement. Preliminary assessments show...

This paper presents a contest on modelling shear behaviour of deep concrete slab strips using nonlinear FEM. In the contest, participants were asked to predict two configurations representing three shear tests. The shear tests were selected because of their exceptionally configurations, namely, large dimensions, lower longitudinal reinforcement, no...

Reinforced concrete (RC) submerged floating tunnels (SFTs) represent a possible solution for crossing wide, deep fjords, and is considered for the E39 highway route along the Norwegian west coast. With regard to SFTs, the specific accidental scenario that is under investigation is the combined action of fire and subsequent internal explosion, as th...

Underground construction activities, such as tunnelling, cause local ground movements to occur. Nearby surface structures interact with the moving ground, potentially leading to building damage. Although it is understood that the severity of building damage is influenced by the façade opening ratio (OpR) and the stiffness of the floors, experimenta...

p>Diagonal tension cracking is the governing failure mode for bridge girders with a thin web that are highly prestressed and contain little shear reinforcement. When assessing existing bridge girders using the Eurocode 2 [1], it often turns out that it is not possible to demonstrate sufficient resistance to diagonal tension cracking. This paper eva...

p>The Dutch Directorate-General for Public Works and Water Management (Rijkswaterstaat) is assessing its bridges as a part of the major renovation and replacement task of bridge-structures in the Netherlands. For assessments it appears that calculations show that an increasing number of existing bridges no longer comply with current assessment stan...

The Oscillating Water Column (OWC) device is a relatively young and underdeveloped technology for generating electricity from wave energy. Compared to other common renewable sources such as solar and wind energy, the costs for bottom-standing OWC’s are too high for the technology to be economically competitive. A first step in lowering the cost was...

Strut-and-Tie modelling (STM) is a well-known approach to design D-regions in reinforced concrete structures. Because the STM method is based on lower-bound analysis, finding a suitable truss-analogy model is the most important aspect to guarantee good structural and economic performance of a resulting design. Continuum topology optimization (TO) m...

The most common methods for detecting chloride-induced corrosion in concrete bridges are half-cell potential (HCP) mapping, electrical resistivity (ER) measurements, and chloride concentration testing, combined with visual inspection and cover measurements. However, studies on corrosion detection in pretensioned structures are rare. To investigate...

Strut‐and‐tie modelling (STM) is an effective and widely used method to design disturbed regions (D‐regions) of reinforced concrete structures. Among the various steps of STM, finding a suitable truss‐analogy model is the most challenging part. Even for experienced engineers it is difficult to find representative models for complex D‐regions, and t...

An editorial commenting on the impact and prestige of the Computer-Aided Civil and Infrastructure Engineering (CACAIE) journal and its editor.

Sequentially linear solution procedures provide a robust alternative to their traditional incremental-iterative counterparts for finite element simulation of quasi-brittle materials. Sequentially linear analysis (SLA), one such non-incremental (total) approach, has been extended to non-proportional loading situations in the past few years. Although...

The alkali silica reaction (ASR) in concrete causes internal localized swelling and micro cracking, which result in expansion and correlated deterioration of the concrete material. The stress state of the concrete is known to affect expansion due to ASR, with an anisotropic stress state giving rise to anisotropic expansion. Similarly, the orientati...

Defining a suitable truss model is one of the most important steps of applying the strut‐and‐tie modeling (STM) method to design D‐regions in reinforced concrete (RC) structures. The truss model is a discrete representation of the stress field developed within a region of a concrete element. Topology optimization (TO) methods have been investigated...

Sequentially Linear Analysis (SLA), an event-by-event procedure for finite element (FE) simulation of quasi-brittle materials, is based on sequentially identifying a critical integration point in the FE model, to reduce its strength and stiffness, and the corresponding critical load multiplier (λcrit ), to scale the linear analysis results. In this...

This paper formulates an analytical calculation model for predicting the cracking behavior of reinforced concrete ties to provide more consistent crack width calculation methods for large-scale concrete structures in which large bar diameters and covers are used. The calculation model was derived based on the physical behavior of reinforced concret...

In order to make non-linear finite element analyses applicable during assessments of the ultimate load capacity or the structural reliability of large reinforced concrete structures, there is need for an efficient solution strategy with a low modelling uncertainty. A solution strategy comprises choices regarding force equilibrium, kinematic compati...

Sequentially linear analysis (SLA), a non‐incremental‐iterative approach towards finite element simulation of quasi‐brittle materials, is based on sequentially identifying a critical integration point in the model, to reduce its strength and stiffness, and the associated critical load multiplier (λcrit), to scale the linear analysis results. In thi...

This study was based on findings from the Norwegian Public Roads Administration's Bridge Management System and field investigations on corrosion damage in pretensioned Norwegian standard I‐beam (NIB) girders in 227 coastal climate bridges. The main durability design parameters are summarized and related to regulations over the last 80 years. Enviro...

The modified cracked membrane model (MCMM) presented in this paper was formulated to facilitate a mechanical calculation model that predicts crack widths in reinforced concrete (RC) structures subjected to in-plane loading for all cracking stages. It was formulated using the basic concepts of the existing cracked membrane model (CMM). Furthermore,...

With the recent developments in modelling the shear behaviour of reinforcement concrete (RC) members without transverse reinforcement, the contribution of aggregate interlock has been more and more recognized as one of the critical components in the shear resistance of RC members. This paper presents a study on the aggregate interlock action utiliz...

Topography studies of concrete-ice abrasion were made to proceed in our understanding of the mechanisms of concrete wear by ice on Arctic offshore structures. The effects on various initial surfaces of a B75 normal-weight concrete (smooth, rough, sawn) and on the sawn surface of a LB60 lightweight concrete were studied during concrete-ice abrasion...

p>The Dutch Ministry of Infrastructure and the Environment is concerned with the safety of existing infrastructure and expected re-analysis of a large number of bridges and viaducts. Nonlinear finite element analysis can provide a tool to assess safety; a more realistic estimation of the existing safety can be obtained.
Dutch Guidelines, based on...

The cracking behaviours of reinforced-concrete (RC) ties are investigated by conducting virtual experiments using non-linear finite-element analysis. The assumptions in the model are verified by benchmarking the classical experiments of B. Bresler and V. V. Bertero as conducted in 1968 and P. J. Yannopoulos, conducted in 1989, which shows good agre...

The strain profile over the cover in reinforced concrete ties subjected to tension is investigated in this paper. This is normally neglected in the crack width calculation methods recommended by Eurocode 2 and fib Model Code 2010, meaning that it is assumed uniformly distributed over the cover. However, this assumption is questionable in the case o...

Concrete structures in the Arctic offshore are often exposed to drifting ice causing abrasion of concrete surfaces. This paper presents the results of a laboratory study of concrete-ice abrasion. The sawn concrete surfaces (two high-performance concrete mixes and one light weight mix of concrete) were exposed to sliding fresh-water ice under 1 MPa...

This paper theoretically and experimentally investigates the semi-empirical formulas
recommended by Eurocode 2 (EC2), fib Model Code 2010 (MC2010), and
Eurocode 2 with the German National Annex (DIN) for calculating crack widths in
reinforced concrete. It is shown that the formulas can be derived from the principles
for the idealized behavior of RC...

A hierarchical model for the variability of material properties in ready-mixed concrete is formulated. The model distinguishes between variation on the batch, recipe, plant, producer, durability class, strength class, and regional standard level. By considering Bayesian inference and maximum likelihood estimators, the contributions from the differe...

The current article presents a case study of the settlement response of the historic Hoca Pasha Mosque that involves uncertainties arising from the complex excavation activities, soil properties, building materials, and geometry and the presence of pre-existing cracks in the mosque’s walls. The objective is to demonstrate the added value of a two-s...

Motivated by the establishment of a Ferry-Free E39 coastal highway route, crack width calculation methods for design of large-scale concrete structures are discussed. It is argued that the current semi-empirical formulas recommended by Eurocode 2 is inconsistent and overly conservative for cross sections with large bar diameters and covers. A sugge...

This article presents a new non-proportional loading strategy for Sequentially Linear Analysis (SLA), which is a robust secant stiffness based procedure for nonlinear finite element analysis of quasi-brittle materials, like concrete and masonry. The strategy is based on finding the principal planes for a total strain based fixed cracking model, by...

The use of non-linear finite element analyses for reliability assessments of reinforced concrete structures has gained much attention during the last decade, particularly with the introduction of semi-probabilistic methods in fib Model Code 2010. In a recent PhD project, the topic has been elaborated on with a special focus on the applicability to...

The current crack width calculation methods according to Eurocode 2 and fib Model Code 2010 have been evaluated. The physical nature of the equations is found to be inconsistent, which limits the generalization of the formulas. An improvement of the formulas is suggested by looking to more physical realistic assumptions in a reinforced concrete tie...

The current crack width calculation methods according to Eurocode 2 and fib Model Code 2010 have been evaluated. The physical nature of the equations is found to be inconsistent, which limits the generalization of the formulas. One of the inconsistencies is related to the cover term, which is currently being investigated in an experimental study of...

In this paper, limiting tensile strain method (LTSM) is reviewed, and advantages and disadvantages resulted from the simplicity of this method are examined in the light of the findings of the existing experimental and numerical studies. Using the viewpoint of the transfer functions for the LTSM, a more independent sight for the interpretation of th...

The assessment of concrete structures affected by alkali–silica reaction (ASR) is a complex problem due to the multiscale nature of this long-term phenomenon. The reaction starts within the concrete constituents and developed at aggregate level by inducing swelling and deterioration of concrete material, which eventually affect the capacity of the...

The background theory for the crack width calculation methods according to Eurocode 2 and fib Model Code 2010 is discussed to evaluate the applicability for the more general case of relatively thick beams, slabs and shells. Essentially, the formulas originate from the maximum transfer length and the difference in steel and concrete strains over thi...