In the face of climate change, reinforced concrete (RC) bridges encounter significant risks, indicating the need for effective adaptation measures. This paper explores the co-benefits of climate change adaptation for RC bridges and how sustainability and resilience can be achieved through adaptation measures. It also investigates the integration of climate change adaptation into Eurocode standards. The chosen approach includes mapping and analysing (i) climate change impacts on RC bridges and (ii) the co-benefits of different adaptation measures. Moreover, it includes an examination of the current generation of Eurocodes and an exploration of barriers and proposed actions towards climate change adaptation. The research highlights the complex relationships and compound effects characterising climate change impacts on RC bridges and the co-benefits of several adaptation measures. Moreover, it emphasises gaps in existing Eurocodes that need to be addressed to achieve climate change adaptation. Future actions, such as the economic viability of adaptation measures, their long-term performance, and the trade-offs of the bridge’s life extension, especially for measures non-sustainable at first glance, should be further investigated.

Slow-moving landslides are natural phenomena that shape mountainous landscapes over long time scales. These landslides creep at rates ranging from meters to millimeters per year, often unnoticed by people who build houses on them, unaware of the risks. Although slow-moving landslides rarely cause fatalities, they can be triggered into fast-moving landslides by earthquakes, leading to catastrophic outcomes. Therefore, understanding and monitoring these landslides is crucial to mitigate potential hazards, particularly in seismically active regions.

Traditional methods for identifying and monitoring slow-moving landslides rely on fieldwork and in-situ instruments. While these methods are accurate, they are limited in spatial and temporal coverage. Recent advancements in remote sensing, particularly Interferometric Synthetic Aperture Radar (InSAR), offer extensive, high-resolution monitoring capabilities, enabling detailed observations of ground movements. InSAR studies have used Line Of Sight (LOS) velocities to monitor the be- havior of slow-moving landslides. However, these findings do not provide details on the direction of movement, as LOS velocities are always measured along a single dimension. This limitation makes it impossible to determine the direction and type of movement, which are essential for accurate risk as- sessment and developing early warning systems by identifying deformation patterns that may indicate imminent failure.

This thesis aims to investigate the temporal evolution of a slow-moving landslide subjected to an earthquake, focusing on changes in rate and direction, to identify the type of movements. To achieve this, the Multi-Temporal InSAR (MT-InSAR) technique is used, resulting in Persistent Scatterers (PSs) as measuring points to observe changes in the rate and direction of landslide movements post- earthquake. Sentinel-1 data from both ascending and descending orbital configurations were used to obtain LOS velocity time series at the PSs both before and after the earthquake. By combining LOS velocities from both PS orbital configurations, the method decomposed LOS velocities into vertical and horizontal components, providing both changes in velocities and direction, which together enabled the identification of the type of movement.

To test this method, a slow-moving landslide located in Büyükçekmece, Istanbul, was chosen as a case study. This landslide was impacted by a Mw 5.7 earthquake on 26 September 2019. Within the landslide, an urbanized area was selected to analyze both the uniform and spatially variable re- sponses. The uniform results involved averaging the velocities at the PSs, while the individual PSs were analyzed to identify spatially variable movement patterns.

The uniform results indicated three main phases in landslide behavior after the earthquake: an initial translational movement following the earthquake, a roto-translational phase combining rotation and translation, and a new constant state characterized by horizontal spreading. At an individual point level, the results showed that most points transitioned from moving vertically downward to upward, indicating a significant change in underlying mechanisms, highlighting the landslide’s complexity.

The monitored behavior resembles that of an inverse creeping landslide, where after the initial disturbance, the landslide decelerates to a new constant state. Based on the collected real data, it is possible to construct hypothetical risk scenarios with behavior curves characterized by continuous acceleration, which would pose an immediate threat of catastrophic failure. Although this earthquake did not cause the Büyükçekmece landslide to fail, and the landslide decelerated to a constant state, it is crucial to continue monitoring as there are signs of instability and conditions may change.

The main motive for this research was to study the behaviour of quay walls when there is an uneven pile foundation present. This means that the number of piles varies in the thickness of the quay wall along the length. The inspiration came from the failure of the Grimburgwal (Amsterdam, the Netherlands) that collapsed in 2020, which had a length of 65 meters, according to Korff et al. (2021). Korff et al. (2021) reported that the main failure mechanisms that are considered in the case of the Grimburgwal, is the deformation of the piles due to horizontal bending, in the section where there were only two instead of three rows of piles present in the thickness of the wall.

A 2D model with a length of 22.5 meters in the longitudinal direction (along the length of the quay) wall is used in this research, to study the influence of the uneven pile foundation in the thickness of the wall. The quay wall’s out-of-plane behaviour is not considered. The masonry and timber floor are modelled with linear plane stress elements. An interface condition is used to model the interaction between masonry and the timber floor. The longitudinal support beams and kespen are modelled as one element. The piles are modelled as equivalent translational springs that are evenly distributed in the longitudinal direction. In the central area, one spring represents two piles in the cross-section, while the rest of the springs represent three piles. After the application of the deadweight of masonry and timber, a uniform distributed load was used on top of the model to cause settlement of the piles and wall. The dilatation joint was modelled with a nonlinear interface with a high dummy stiffness and no tension, and with a gap of one millimeter.

If the length of the section with two rows of piles is increased, the capacity of the wall reduces. The cracks at the bottom of the masonry, still do not increase significantly if the length of the length of the section with two rows of piles is increased, but it does take less load to generate the same cracks. The boundary conditions also play a large role in the distribution of forces, since it is seen that the piles near the dilatation joint are less critical than the piles near the constrained edge. In the end, this model does give information on how the forces in the piles distribute and how the piles settle, before both brittle and ductile failure of the piles occurs and cracking within the model. However, it should be kept in mind that the model that is considered is a 2D model, whereas the problem of a quay wall is a 3D problem, so the results are not expected to be accurate.

Nowadays, Rijkswaterstaat reassesses many older concrete bridges to guarantee their structural safety under the influence of increased traffic loads and stricter standards. Many of these concrete bridges contain open straight-legged stirrups, which are not allowed to take into account for the calculations of the shear resistance according to current standards. This often results in theoretical insufficient shear capacity and critical damage to structures, but this is not observed in reality. This indicates that the open straight-legged stirrups probably do contribute to the shear resistance, where an accurate assessment of this contribution could prevent unnecessary and costly structural safety measures. However, very few shear tests with relevant cross-sectional dimensions are performed and documented in literature, especially tests containing open straight-legged stirrups.

The application of Nonlinear Finite Element Analysis (NLFEA) is a useful tool to evaluate and understand the behaviour of structures, but provisions for the implementation of open straight-legged stirrups in concrete structures are lacking. Thus, the goal of this research is to provide a finite element modelling strategy that is able to accurately describe the behaviour of concrete beams with open straight-legged stirrups subjected to shear. The research focusses on describing the behaviour of rectangular concrete beams with open and closed straight-legged stirrups with finite element models using DIANA 10.5 [1].

Schramm [2] has performed multiple shear tests on prestressed concrete beams with several no longer permitted stirrups, including open straight-legged stirrups. He found that open straight-legged stirrups can significantly contribute to the transfer of shear forces [2]. The relevance of the rectangular test beams for comparison with box-girders is validated in this thesis, where the stress distributions in a linear elastic rectangular and box-girder cross-section due to axial forces, bending moments, shear forces and torsion are compared.

In the interest of providing a suitable solution strategy, Schramm’s test beams with closed and open straight-legged stirrups are reproduced with 3-dimensional nonlinear finite element models based on the recommendations of the RTD1016-1 [3], where the influence of various modelling considerations is investigated. The concrete is modelled with a smeared total strain-based crack model with the Hordijk tensioning and parabolic compression relations, including confinement and lateral cracking effects. Reinforcements are modelled as embedded truss elements with the Von-Mises plasticity model. To describe the accurate anchorage behaviour of the open straight-legged stirrups, the interaction between the surrounding concrete and the stirrups is described with the Shima bond-slip relation. The finite element model is first calibrated with a beam with closed stirrups, where modelling clamped restraints with supports on both sides of the beam result in a too-stiff response. By allowing a little rotational freedom in the form of boundary springs, the stiffness of the beam is manipulated without changing the overall load-bearing behaviour...

Tensioned membrane structures are increasingly in demand, because of their ability to cover large spaces with minimum use of material. The material’s mechanical properties play a key role in the design of such structures. The shear behaviour is one of the main influential properties of woven textiles during complex deformations, such as the ones in doubly curved structures where the change in curvature challenges the shear-bearing capacity of the textile during its service life.
This study provides a methodology to characterise a novel uncoated woven solar cell integrated textile for tensile structure application. It consists of investigating the limit angle, that avoids damage to the inserted solar strips, and the determination of the shear stiffness of the material. To evaluate the applicability of the material, different mechanical properties are assessed. Mono-axial, picture frame and bi-axial tests were used to determine the strength, elasticity and shear modulus. All results have been validated by comparison with existing experimental data of similar architectural textiles.
This research introduces a method of investigation of shear properties of uncoated textiles that can be followed to evaluate other uncoated textiles. In addition, it is now possible to start a preliminary design of a tensile structure with the newly developed material. It is the first step in the introduction ofthe new building material.

Discontinuities have an important influence on the bulk behaviour of geomaterials. Discontinuities can be physical openings like fractures and joints, interfaces between different material types, or zones with different material behaviour like mortar or reinforcement material. Bulk material behaviour is often determined by the behaviour of the discontinuities by providing preferential pathways for flow or by acting as failure planes.
FEM simulations with continuum elements are typically not suitable for modelling discontinuities with no width, due to the inability to model discontinuous fields. One solution is to represent discontinuities using zero-thickness interface elements. Inserting zero-thickness interface elements allows for discretely modelling discontinuous behaviour between neighbouring continuum elements. The continuum elements are then used to represent the bulk behaviour and the zero-thickness interface elements discretely model the discontinuity.
A new constitutive law for zero-thickness interface elements that expands the cohesive zone model with friction is formulated in this thesis. The tangential stress response of the interface elements consists of a cohesive and frictional contribution. The cohesive component of the constitutive law is based on the Crisfield’s cohesive elasto-damage model, which is characterised by a linear elastic response to increased relative displacement, followed by degradation of the cohesive strength and stiffness. The elasto-plastic frictional component is based on the Dahl friction model and implemented in parallel to the cohesive component.
The implemented new constitutive law is verified in a large variety of loading conditions, including tangential loading, tangential loading with a reversion of loading direction and combinations of mixed-mode loading. The constitutive laws are validated based on shear box experiments performed on London clay where interface elements are used to model a predefined shearing plane.
The cohesive and frictional constitutive law can represent confinement-dependent tangential stress and residual stress at large relative displacements. These features, observed in the shear box experiments, could not be reproduced by the purely cohesive constitutive law. This new constitutive law can be used to better model discontinuities in geomaterials represented by zero-thickness interface elements.

The extraction of natural gas in the northern part of the Netherlands, from the region of Groningen, has been causing human-induced seismic activities for the past several decades. This is a problem since the existing building stock in this region, which consists of mainly unreinforced masonry buildings and historical structures, are not designed to withstand seismic events due to the lack of empirical earthquake-resistant design features. Further, the combination of a soft topsoil and the gas extraction, is responsible for ground settlements which may compromise the capacity of the existing buildings.

The bed-joint reinforcement technique is a strengthening method which consists of cutting a slot in the bed-joints and installing steel bars embedded in a high-strength repair mortar. Although this strengthening method is commonly applied in the Netherlands to counteract settlement damage, limited investigations on the performance against seismic loading are available in the literature. Therefore, an experimental campaign (Licciardello et al., 2021) was conducted at Delft University of Technology in which a quasi-static cyclic in-plane test on a full scale wall was performed to characterize the performance of the bed-joint reinforcement technique. The wall featured artificially introduced cracks (pre-damage), achieved by the inclusion of plastic sheets between bricks and mortar, to account for the settlement-induced damage. Compared to the un-strengthened walls, tested in a previous experimental campaign (Korswagen et al., 2019) under similar conditions, it is observed that the bed-joint reinforcement technique can provide a significant increment in terms of displacement capacity and ductility of the wall but not in terms of the force capacity.

In this thesis, numerical simulations of both un-strengthened and strengthened walls from the experiments were performed using 2D-models and the nonlinear static analyses (monotonic and cyclic) were carried out in the finite element software DIANA. The objective of this research was to compare different numerical modeling approaches and material models to find the best suited one for simulating the in-plane seismic response of both un-strengthened and strengthened masonry walls. Moreover, the objective was also to extrapolate the experimental results to other wall configurations, which are not experimentally tested, to investigate the combined effect of the bed-joint reinforcement technique and the change in size and location of the window opening on the in-plane response of the wall (parametric study).

In the scope of this thesis, three numerical modeling approaches were investigated (Figure i). The bricks and mortar joints are modeled as one homogeneous continuum in the macro-model. On the other hand, the bricks and mortar joints are modeled separately for the continuous and detailed micro-model where interface elements are included at the brick-mortar bonds for the latter one. The discrete (simplified) micro-model was not investigated because the reinforcement bars cannot be connected to the mortar joints since they are substituted by zero-thickness interface elements. Moreover, the Discrete modeling approach of the reinforcement was used in order to simulate the pull out behavior of the bars. Cracks were modeled using the discrete cracking approach and the smeared cracking approach where the former one was used at the brick-mortar interfaces and the latter one was used for cracking in the mortar joints (micro-models) and in the masonry composite (macro-model)…

The goal of the thesis is to investigate two main questions for the purpose of modelling fractures in timber with a finite element method. The first question is to evaluate the use of digital image correlation during a three point bending test to obtain mean values for tensile strength and fracture energy, and the follow up question is if it is possible to replicate the tests with these mean values. The final result should be a guide to help modelling fractures in timber and how to obtain the necessary data.

The demand to build with wood and other bio-based materials has increased rapidly the last decade, due to the ambition to build more with sustainable building materials. One of the major challenges in building with wood, is to account for the lower strength and stiffness perpendicular to the grain. Wood is an anisotropic material, meaning the material has different properties in different directions. Loading in the perpendicular to the grain direction is sometimes unavoidable and fracture often occurs in a brittle manner. Unfortunately, our understanding and knowledge of the perpendicular to the grain fracture is limited. This is especially the case for hardwoods, for which the material properties and the parameters important for the fracture process are often unknown.

The goal of this thesis is to reduce this knowledge gap on the material properties and the relevant parameters in mode-I (pure tension) fracture process of (tropical) hardwood. The knowledge gained in this research provides the answer to the main research question of this thesis: Which parameters should be considered when describing the constitutive model of a (tropical) hardwood in mode-I tension?

A single-end notch three-point bending (SEN-TPB) test demonstrated a strong influence of the orientation of the growth rings on the perpendicular to the grain fracture process of azobé. The value for the peak load and post-peak behaviour change significantly depending on the orientation in which the sample is placed. Furthermore, visual observations and results from a profilometer revealed that there is an inconsistency in the roughness of the cracked surface area between the different series. From the microscopic analysis is concluded that this inconsistency in general mechanical behaviour and the roughness of the cracked surface area is linked to the composition of ray and parenchyma cells. Moreover, the direction of the ray and parenchyma cells with respect to the fracture plane is different depending on the orientation of the sample. When the ray cells are orientated perpendicular to the crack plane, a higher strength is obtained. The thin-walled parenchyma cells significantly reduce the post-elastic stiffness if these cells are orientated perpendicular to the crack plane. The influence of the composition and orientation of both cells is reflected in the numerical value for the modulus of elasticity, the tensile strength and the fracture energy. This research showed that the composition of the cells in a wood specie and the orientation in which the growth rings are placed significantly influence the mode-I fracture process of a hardwood. This influence is reflected in the modulus of elasticity, the tensile strength, the fracture energy and the shape of the tension softening curve perpendicular to the grain. The results of this research provide new insight into the fracture modelling of hardwood. Both in numerical modelling and design considerations the variation in the material properties because of the orientation of the growth rings, should not be neglected.

In the last decade, maintenance and adaptive reuse, of the existing building stock, have gained ground in the construction sector. For the adaptive reuse of a building, it is required to analyze, meticulously, the existing structure. Unreinforced masonry structures are indicative of the Dutch built environment. For the assessment of their structural capacity, the European Standard EN 1996 is, currently, applied. Masonry walls of high slenderness, often, comprise the structure of existing buildings, in the Netherlands. It has been noticed that the EN 1996 norm underestimates the vertical resistance of slender walls. This study attempts to extend the applicability of the EN 1996 norm to slender masonry walls, since the norm serves for the assessment of existing structures. Particularly, the research objective is to find an appropriate verification method for existing slender masonry walls, in one-way bending. Literature research is, initially, conducted, with respect to alternative formulas for the calculation of the vertical resistance of slender masonry walls. The formula in the EN 1996 norm and the alternative formulas are reviewed, considering a case study. The case study is one of the slenderest interior masonry walls, that form the structure of a relevant existing building block in Amsterdam. The latter was constructed in the late 19th – early 20th century. The engineering firm STRACKEE BV Bouwadviesbureau provided the technical drawings of the building block. Reference values for the vertical resistance, of existing slender masonry walls, are necessary to develop an appropriate formula for their verification. Therefore, the next step of the research is the numerical analysis. The response of slender masonry walls, subjected to combined vertical and lateral loading, is estimated according to the results of FE analysis. The case study is the reference for the geometry of the FE model. Indicative, for the construction period, properties of masonry are the input for the initial material model. Further, models of slender masonry walls with different geometrical and material properties are analyzed. Specifically, a parametric study is done, to define the influence of geometrical and material properties on the vertical resistance. Based on the FE analysis results, a new formula is proposed. The formula estimates the vertical resistance of existing slender masonry walls, subjected to combined vertical and lateral loading.

Starting from the late eighties induced seismic activity is present in the Northern part of the Netherlands. Cause of these earthquakes is the extraction of natural gas. In this region, most of the building stock comprises out of unreinforced masonry (URM) buildings. Multiple experimental campaigns are performed since 2014 to investigate the structural integrity of these type of structures. Both static and dynamic, full-scale and smallscale, experiments are executed to identify both in-plane and out-of-plane failure mechanisms. Strengthening, or retrofitting, of these already existing structures, is of interest and different researchers propose multiple techniques. From the literature, it is found that the application of strain hardening cementitious composites (SHCC) results in the required improved structural performance of the retrofitted masonry. The SHCC material is characterised by high ductility in the range of 3-7%, tight crack widths of around 60 μm and a relatively low fibre content equal to 2% (maximum by volume). In this experimental campaign small-scale, both inplane and out-of-plane (i.e. shear strength and flexural strength, respectively), experiments are performed on masonry samples retrofitted using a single-sided applied SHCC overlay. Different thicknesses of this overlay, masonry surface preparations, and overlay curing conditions are considered. With the help of these experiments the material properties of retrofitted masonry are investigated. From the initial shear strength experiments, it is concluded that the retrofitting approach did not work as intended. Results of all the different specimen examined shows similar capacities to the non-retrofitted masonry triplets. With the help of digital image correlation, it is shown that for all of the retrofitted specimen, the overlay material is not activated during the tests. Additional experiments and numerical simulations are performed to investigate the several parameters possibly influencing these experiments. The bond strength of the interface between the SHCC and the masonry substrate is determined to be too low. This is one of the main factors resulting in the absence of cracks in the retrofitting overlay. Additionally, the high cracking strength of the SHCC mixture considered, and the applied pre-compression, have influenced the cracking behaviour of the retrofitting overlay. Besides the shear strength of the retrofitted masonry material also the flexural strength is investigated with multiple out-of-plane four-point bending tests. Retrofitted masonry beams are used for these experiments. The plain masonry beams are not able to carry their self-weight, therefore all of the additional capacity is accommodated to the applied overlay. The experimental results are governed by shear failure. For eight out of ten specimens debonding of the masonry units is prevalent. Two of the retrofitted masonry beams showed flexural failure. A thicker overlay will result in higher flexural strength. Again, the bond strength between the overlay and the masonry substrate seems to be governing. No numerical analyses are performed to analyse these experiments in more detail. From this research, it is concluded that a single-sided SHCC overlay can be a very attractive method for retrofitting unreinforced masonry. However, both the interfacial bond strength and the material properties of the SHCC material must be taken into account. The bond strength must be sufficiently high, and the cracking strength of the overlay material sufficiently low, for the overlay to be activated. With the help of numerical simplified micro-models, the requirements of both parameters can be estimated.

In the past decades, gas productions in the province of Groningen in The Netherlands have caused a significant amount of shallow human-induced earthquakes. Its building stock has shown to be highly vulnerable to these unexpected events. Among various building typologies, damage has been reported for approximately 12.9% of the churches in Groningen. From the perspective of conservation and prevention of loss of our historical and cultural heritage, the assessment of churches is of importance. As a majority of historical structures have undergone restoration works, that can be favourable for their seismic performance, it is worth noticing that for historical structures strengthening may not be necessary. Consequently, the question arises whether structural modifications during the lifespan of historical unreinforced masonry churches, positively influences their seismic performance. This thesis researches the seismic performance of the historical unreinforced masonry Dutch church Zandeweer, prior and post structural modifications, in the earthquake prone area Groningen. The church, built by the Moncks of Abdij van Aduard in the year 1230, underwent major renovation works in 1931. Its structure is composed of masonry walls, masonry ribbed cross vaults and a timber roof with timber cladding. During the restoration works in 1931 steel columns were integrated in the piers of one of the façade in the longitudinal direction, window openings in the curved façade were closed and concrete beams were added on top of the main walls. Its seismic performance was investigating in the positive longitudinal direction by studying its global nonlinear response and structural elemental behaviour and by indicating uncertainties and damage. A Nonlinear Pushover Analysis (NLPO) and the Simplified Lateral Mechanism Analysis method (SLaMA) were employed to capture the influence on the seismic performance of the church models. Although, the acquired results for the church models showed to a certain extend an insight in the influence of the structural modifications, an insight in the ductility behaviour of the structure was not acquired. Additionally, from the eigenvalue it was concluded that adopted single-mode analysis methods (SLaMA and NLPO) were not suitable, as the structural response of the church is governed by multi-modes. Moreover, with the highly unpredictable behaviour of the vaults in the structure the presented results were greatly influence by physical and numerical instabilities. For future studies is recommended to dedicate a detailed study to the numerical modelling and analysis of masonry ribbed cross vault structures. Furthermore, to conduct a detailed study on the church walls, for which subsequently various analysis methods can be employed and the influence of orthotropy of walls on the global response can be studied. Lastly, the analysis method can be changed by using methods that consider multi-modes simultaneously and that are known for less numerical instability problems than static analysis methods.

A lot of concrete structuressufferingfrom ASR show a decrease in material properties. However, it is not clear what might be the influence of ASR on structural behavior. Influence of restraint is often ignored in material property measurement, while reinforcement is present as a restraint of ASR expansion in most structures.Thisresults in so called chemical prestresseffect, whichshould not be neglected. In the presented study,the result indicatesthat neglecting the chemical prestresswould miss the failure mechanism transition and lead to a lowerbeam stiffness. Therefore, a newway to model ASR-affected structures is proposed, called the ASR-layered model.The numerical analysis is done with ATENA.Depending on the reinforcement arrangementand amount, with longitudinal reinforcement acting as a restraint, expansion to the greatest extend occurs in the direction of least confinement and the cracks become parallel to reinforcement. Considering the potential to connect with each other and form long horizontal cracks, the ASR crackingin restrained structuresare modelled as horizontal layers with reduced material properties. The propertyreduction is concentrated in ASR layers only, this local reduction is more realistic than the traditional method done by (Ferche, Sheikh, & Vecchio, 2017)in which a global reductionon material propertiesis applied. For chemical prestress, it is difficult to separate the influence of prestressin experiments,so experimentalresult is always affected both by the reduction of properties and prestress and probably some other phenomena that exist. The chemical prestress effect is modelledherein the way of physical prestress, but the expansion of ASR gel in chemical prestress would possibly influence the bond strength between concrete and reinforcement, so bond model is also considered.Some conclusions can be drawn on this study. The material reduction caused by ASR would only result in a decrease of load capacity. While in combination with prestress, the load capacity of ASR affected beam may be increased to be even higher than the unaffected beam. The application of prestress could also lead to the possible change of failure mechanism from shear to bending failure, whichis also observed in experiments. Including the bond-slip effect in prestressed ASR-layered model provides a better fitting with experimental results,but the influence of ASR on bond strength remains unclear. With parameter study, no obvious influence on ASR-affected structures could be linked to a/d ratio and reinforcement ratio. 1 or 2 ASR layers will only influence slightly on the ultimate load. The limitations of this model exist, the expansion caused by ASR is not directly modelled. Information on ASR layer property is quite limited, it would be difficult to measure the cracking part of ASR affected structures alone. In addition, the chemical prestress and possible cracking depend on the amount of ASR expansion as well as the reinforcement arrangement and amount, but they are not considered to correlate with each other in this model.