MASİF BETON YAPILARDA HASAR İLERLEMESİ .... Uluslararası Deprem Mühendisliği ve Sismoloji Konferansı 11-13 Ekim 2017 – ANADOLU ÜNİVERSİTESİ – ESKİŞEHİR MASİF BETON

4. Uluslararası Deprem Mühendisliği ve Sismoloji Konferansı

11-13 Ekim 2017 – ANADOLU ÜNİVERSİTESİ – ESKİŞEHİR

MASİF BETON YAPILARDA HASAR İLERLEMESİ SİMÜLASYONU,

ÖRTÜŞMELİ KAFES MODELİ VE SONLU ELEMANLAR YAKLAŞIMLARI

KARŞILAŞTIRMASI

B. F. Soysal1, Y. Arıcı2, B. Binici3 and K. Tuncay3

1Araş. Gör., İnşaat Müh. Bölümü, Orta Doğu Teknik Üniversitesi, Ankara 2 Doç. Dr., İnşaat Müh. Bölümü, Orta Doğu Teknik Üniversitesi, Ankara

3 Prof. Dr., İnşaat Müh. Bölümü, Orta Doğu Teknik Üniversitesi, Ankara

Email: [email protected]

ÖZET:

Hesaplama kuvvetinin ciddi derecede artması beton ağırlık barajları gibi masif beton yapılar için performansa

dayalı değerlendirme olanağını ortaya çıkarmıştır. Bu değerlendirmeler genelde geleneksel sonlu eleman

yöntemleri ile yapılmaktadır. Bu gibi çalışmalarda öncelik gövdedeki çatlak ilerlemesi ve açılmasının tahmini olup

sonlu eleman yöntemlerinin devamlılık bazlı matematiksel formülasyonları hesaplamalar açısından çok masraflı

ağ yapısı yenileme yöntemleri kullanılmaması durumunda tartışılabilecek sonuçlara yol açmaktadır. Elde edilen

hasar bölgelerinin gerçek ayrık çatlaklara göre çok yaygın olması ve hasarın ileri aşamalarının simüle edilememesi

sonlu eleman yöntemleri ile çalışan araçların ciddi sınırlamaları olarak ortaya çıkmaktadır. Buna karşın, masif

beton yapıların oluşan ayrık çatlakların modellemesinde blokların yapıdan ayrılabilmesi ve salınımını da

gösterebilen yeni bir yaklaşım olarak örtüşmeli kafes modeli büyük potansiyel içermektedir. Bu makalede sonlu

eleman araçlarının masif beton yapıların davranışlarını yansıtma yeterliliği örtüşmeli kafes modeli yaklaşımı ile

karşılaştırılmaktadır. Bu amaçla laboratuvar koşullarında değişik tip yüklemelerle gerçekleştirilen üç değişik test

iki yöntemle de simüle edilmiştir. Yöntemlerin hasar belirlemede ve çatlak ilerlemesini tahmindeki sınırları ve

yeterlilikleri belirlenmiştir.

ANAHTAR KELİMELER: Örtüşmeli kafes modeli, çatlak ilerlemesi, beton ağırlık barajı, laboratuvar testleri,

denektaşı modelleri

SIMULATION OF DAMAGE PROPAGATION ON MASSIVE CONCRETE

STRUCTURES, THE OVERLAPPING LATTICE MODEL VS. THE FINITE

ELEMENT APPROACH

ABSTRACT:

The increase in the computational power enables the performance based assessment of very large structures like

concrete gravity dams. These assessments are usually carried out with the traditional finite element tools. The

continuum based formulation of these analyses in the absence of costly re-meshing operations cast doubt on the

performance assessment of such massive plain concrete structures given the primary output assessed for these

analyses should be the crack propagation and opening on the dam body. Smearing of the cracking in contrast to

the discrete cracks on these systems, and the failure to simulate advanced stages of damage is a significant

limitation for the finite element methods. On the other hand, a new approach in the form of overlapping lattice

model shows a great potential for modeling of discrete cracking on plain concrete structures including the

separation and rocking of individual components on the body. In this paper, the capabilities of the finite element

tools for simulation of large damage on plain concrete structures are compared to the overlapping lattice model

(OLM) approach. A set of three laboratory tests conducted with different types of loading were simulated using

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both tools. The limitations and capabilities of both approaches in predicting damage in the nature of crack

propagation was established.

KEYWORDS: Overlapping lattice model, crack propagation, concrete gravity dam, laboratory testing,

benchmark models

1. INTRODUCTION

In order to evaluate the older infrastructure for higher design standards and for the design of new dams, the use of

nonlinear tools for the prediction of the performance of concrete structures is quite popular (Guanglun et al., 2000;

Pan et al., 2011; Zhang et al., 2013). The common tool utilized for these analyses is the finite element method.

Smeared crack model, which was first proposed by Rashid (1968), is an important constitutive model for engineers

conducting nonlinear analysis for concrete structures. Main advantages are the ease of formulation &

implementation, and the robust convergence behavior (Rots, 1988). The cracked concrete is analyzed as a

continuum in smeared crack models (Rashid, 1968) despite the heterogeneous nature of the concrete. Various

versions of this model were implemented by researchers specifying the post-peak response, reloading-unloading

behavior and the effect of confinement (Rots, 1988; Hordijk, 1991; Selby and Vecchio, 2013). Smeared crack

models were also used to predict the behavior of concrete dams in a number of studies (Guanglun et al., 2000;

Espandar et al., 2003; Hariri-Ardebili et al., 2016). A review of these studies reveals that the model calibration

was usually conducted to match the observed damage in the Koyna Dam or to match the behavior of a specimen

tested in the laboratory. However, the finite element method has significant limitations regarding the use for

simulation of the behavior of such massive unreinforced plain concrete structures given the discrete nature of

cracking violating the continuum assumptions. Moreover, the performance levels for these systems at the extreme

scenarios require separation, rocking or sliding phenomena which is challenging to simulate in the continuum

finite element setting.

The overlapping lattice model (OLM); on the other hand, is a promising alternative for studying the nonlinear

behavior of the concrete gravity dams under dynamic loading. The overlapping lattice approach employs pin

connected bar elements extending over a predefined horizon to discretize the continuum similar to the concept

used in peridynamics and hence can model the separation, opening of the cracks and crack propagation much

better compared to the conventional finite element approach. OLM considers cracking by employing brittle or

elastic-softening force displacement models (Madenci and Oterkus, 2014; Aydın et al., 2016). Hence OLM has

the potential to model crack initiation, opening and propagation naturally.

In this study, the capabilities of the finite element tools for simulation of large damage on plain concrete structures

are compared to the OLM approach. A set of three laboratory tests conducted with different types of loading were

simulated using both tools. The first benchmark study is modeling the experiment on a scaled dam monolith tested

under lateral pushover type loading (Carpinteri et al., 1992). Then, the lateral pushover loading test performed

after a pseudo dynamic testing on a scaled monolith was simulated (Aldemir et al., 2013). The final benchmark

study used is a well-documented shake table testing of a scaled gravity dam model constructed by Tinawi et al.

(2000). The limitations and capabilities of both approaches in predicting damage in the form of crack propagation

was established.

2. MATERIAL MODELS

2.1. Finite Element Model

The material model employed herein follows the rules described by Selby and Vecchio (2013). The behavior of

concrete is described by elastic isotropic stress-strain relationship prior to cracking. Upon cracking, the material

is treated as orthotropic (Rots, 1988). The tensile, ft, and compressive strengths, fc, and the shape of the post-peak

response are the key characteristics of the stress-strain models. Mesh dependence of such models was addressed



by using the fracture energy, Gf, determining the stress-strain response with respect to the characteristic size of the

finite element (h) (Figure 1a). The general purpose finite element program DIANA was used as the simulation tool

in this study (DIANA, 2014).

(a) (b)

Figure 1. Concrete tension softening models (a) FEM (b) OLM

2.2. Overlapping Lattice Model In the overlapping lattice model, in order to take the nonlocal effects into account, each node interacts with points

within a predetermined distance called horizon (δ) (Figure 2a and Figure 2b). For initially uniformly distributed

particles separated by a grid spacing of d in x, y and z directions, δ is commonly taken slightly more than three

times d. Therefore, for problems in a two-dimensional setting, a particle located away from boundaries initially

interacts with 28 neighboring points as presented in Figure 2b.

Figure 2. (a) and (b) OLM

Concrete exhibits tension softening beyond the critical strain; therefore, the elements can transfer further tension

by softening as shown in Figure 1b. Nonlinear tension softening was assumed to be in the form of a stepwise linear

softening function as shown in Figure 2Figure 1b. Force-deformation curves for direct tension tests for a specific

gauge length were employed to calibrate the input force-deformation response of the truss elements (Aydın, 2017).

For elements with different sizes, the length scale was then used to adjust the input force-deformation function

similar to the approach used in the mesh regularization in finite element simulations (Bazant and Oh, 1983) as

shown in Figure 1b. A classical structural analysis approach with explicit time integration was used in the

simulations (Chung and Lee, 1994).

3. COMPARISON OF FINITE ELEMENT METHOD AND OVERLAPPING LATTICE MODEL

3.1. Pushover Loading of a Notched Model Concrete Dam

A 1:40 scale concrete gravity dam was tested by (Carpinteri et al., 1992) under hydrostatic, monotonically

increasing loading conditions. A 30 cm deep notch was cut on the upstream face of the dam at a height of 0.6 m

from the base in order to determine the location of crack initiation on the specimen. The tensile strength, modulus

of elasticity and the fracture energy of the specimen were reported as 3.6 MPa, 35.7 GPa and 184 N/m,



respectively. The load-crack mouth opening displacement (CMOD) curves from the test as well as the propagation

of the crack were used as benchmark values to compare FEM and OLM.

In FEM, displacement controlled analyses were performed using the arc-length control on the crack mouth opening

displacement in order to evaluate the behavior of the specimen. The modulus of elasticity and the fracture energy

was increased by 1.58 and 1.36, respectively in the analytical simulations to overcome initial low stiffness and

capacity of the model. Exponential form of tension softening was used in the simulations. The finite element mesh

constituted in plane stress setting consisted of 1503 elements. For the OLM analyses, the modulus of elasticity

was increased by 1.58 and the tensile strength by 1.38. This model consisted of 17343 elements with horizon

δ=3.01d. The proportional-integral-derivative (PID) control method was employed in the OLM simulation. The

cracking pattern for the two methods are compared in Figure 3a and b together with the experimental result (shown

with the red line). Furthermore, the load-CMOD graph is presented in Figure 3c.

(a) (b) (c)

Figure 3. Comparison of the results (a) FEM cracking pattern (b) OLM cracking pattern (c) load-CMOD graphs

The FEM and OLM simulated the length of the cracking less than the experiment (Figure 3a and b); however, the

orientation of cracking was close to the laboratory observations. The load vs. CMOD behavior of the two models

were also similar. Both models successfully simulated the experimental behavior. However, the load capacity

estimation of OLM was better than the FEM model (Figure 3c).

3.2. Pseudo-Dynamic Earthquake Simulation of a Scaled Gravity Dam

A 1/75 scaled model of the 120 m high Melen Dam was tested by (Aldemir et al., 2015) using three different

scaled ground motions in a pseudo-dynamic setup. After the completion of the earthquake loading, the specimen

was pushed to failure by increasing the lateral load on the system in a static fashion. The special setup of the test

enabled the use of only the bottom half of the dam section, the inertial and hydrodynamic load effects were

simulated using a special loading apparatus. The tensile strength and modulus of elasticity used were 1.0 MPa and

15 GPa, respectively. The flexibility at the base of the specimen was taken into account by using spring elements

at the base for both FEM and OLM models. In the FEM analyses, the performance of the specimen was simulated

by applying a lateral force at the top controlled using the arc-length method. The linear tension softening function

was used in FEM simulations. The model in OLM was constituted with horizon δ=1.5d. For both FEM and OLM,

the simulation was conducted on a damaged system in which the cracking occurring during the transient motions

were reflected by an equivalent reduction in the strength of those members. The simulated load-displacement

behavior together with the cracking pattern for the specimen are compared with the experimental results in Figure

4.



(a) (b)

(c) (d)

Figure 4. Prediction of pushover testing (a) cracking on the specimen (b) FEM simulated cracking pattern (c)

OLM simulated cracking pattern (d) load-displacement behavior

It can be observed from Figure 4b and c that the crack propagation of FEM model was better than the OLM model

as the crack at the body of the dam joined to the downstream side, unlike the OLM model. Given the capacity was

estimated higher by the OLM model (Figure 4d), the crack propagation was less than that of the experiment. The

FEM model exhibited a stiffer behavior than the experiment (Figure 4d). The base shear capacity was estimated

quite close to the laboratory result; however, the displacement capacity was lower than the experiment. The OLM

model, on the other hand, had stiffness that matched the laboratory observation. Although the base shear was

overestimated, the displacement capacity matched with the experiment (Figure 4d).

3.3. Shake Table Testing of a Scaled Gravity Dam

The experimental results of Tinawi et al. (2000) were reproduced in this study in order to determine the effect of

the modeling assumptions for the analytical prediction of the behavior of concrete gravity dams. In this experiment,

a plain concrete gravity dam specimen having a height of 3.4m was tested using a pulse excitation at three different

intensity levels. The pulse was scaled with respect to its first peak acceleration (FPA) to three levels: 0.87, 0.94

and 0.98g. The tests with the FPA of 0.94g and 0.98 are referred as the first and second cracking tests, respectively

(Tinawi et al., 2000), as the first test with the FPA of 0.87 did not lead to any cracking on the specimen. The

specimen had notches both in the upstream and downstream sides. The elasticity modulus, tensile strength and

fracture energy was reported as 18.5 GPa, 3.73 MPa and 105 N/m, respectively. It should be noted that the dynamic

amplification factor for tensile strength and fracture energy was 1.75 (Tinawi et al., 2000). The natural frequency

of the specimen was obtained as 16.4 Hz in the laboratory testing.

The FEM simulations were conducted with element size of 10 cm. The elasticity modulus and tensile strength was

assumed as 18.5 GPa and 3.78 MPa, respectively and linear tension softening was used. The fracture energy was

55 N/m, i.e. no dynamic amplification factor was employed. The natural frequency of the FEM model matched

with the experimental result. Similar to the analytical model named as M2 by Tinawi et al. (2000), the FEM and

OLM models had springs at the base. The material properties used in the OLM model was 18.5 GPa, 3.0 MPa and

54 N/m for the elasticity modulus, tensile strength and fracture energy, respectively. The model was constituted

with horizon δ=1.5d. The first frequency was slightly higher than the experiment: a natural frequency of 18.3 Hz

was obtained. For both FEM and OLM models, the notch was simulated by removing the elements at the notch

locations. For the first and second cracking tests, the cracking schemes for FEM and OLM methods are given in



Figure 5b and c. Furthermore, the CMOD time history for the second cracking test was compared with the

experimental results in the same figure (Figure 5d).

First Cracking Test

Second Cracking Test

(a) (b) (c) (d)

Figure 5. Analysis results (a) Experimental result (Tinawi et al., 2000) (b) FEM cracking scheme (c) OLM

cracking scheme (d) CMOD time history

As shown in Figure 5a, in the first cracking experiment, a partial crack with a length of approximately 350 mm

with an initial angle of about 300 downward was observed at the downstream notch. In the second cracking

experiment the crack at the downstream notch joined to the upstream notch (Tinawi et al., 2000). In the FEM

model, the inclination of cracking in the first test could not be simulated correctly; moreover, the obtained crack

length was higher than that of the experiment (Figure 5b). The OLM model, on the other hand, was successful in

simulating the direction and length of the cracking in the first test (Figure 5c). In the second test, in both models

the downstream crack propagated towards and joined to the upstream notch. The CMOD time histories for the

downstream notch opening were compared in Figure 5d for both models. In the FEM model, the cracking initiated

earlier than the experiment; the peak value was obtained as 3 mm, a little lower than the peak CMOD observed in

the test (3.5 mm). The CMOD behavior was simulated better with the OLM model. Both the timing of the cracking

and the maximum value of CMOD matched the experimental results.

4. SUMMARY AND CONCLUSIONS

In this study, the capabilities of the finite element tools for the simulation of extensive damage on plain concrete

structures are compared with the capabilities of the Overlapping Lattice Models (OLM). Three laboratory tests

conducted with different types of loading were simulated using both tools and the following conclusions were

drawn:

The first benchmark study was modeling the experiment on a scaled dam monolith tested under lateral

pushover type loading (Carpinteri et al., 1992). The FEM and OLM simulations yielded similar results in

propagation of cracking and the load-crack mode opening behavior. The load capacity estimation of OLM,

however, was slightly better than the FEM model.

The lateral pushover loading test performed after a pseudo dynamic testing on a scaled monolith was

simulated (Aldemir et al., 2013). The base shear capacity was estimated quite close to the laboratory result

with the FEM model; however, the displacement capacity was lower than the experiment. The OLM

model, on the other hand, had stiffness that matched the laboratory observation. Although the base shear

was overestimated, the displacement capacity matched the experiment. Since the base shear was estimated

higher, the crack propagation was less in the OLM method. On the other hand, for this experiment, the

FEM model could simulate the crack propagation correctly.

The final benchmark study used was the shake table testing of a scaled gravity dam model constructed by

Tinawi et al. (2000). In the first cracking test, the inclination and propagation of the cracking could not be

exactly matched with the FEM model. Conversely, the OLM model was successful in simulation of this



test. In the second cracking test, in both FEM and OLM models, the crack propagation matched with the

laboratory observation. The CMOD behavior was simulated nearly perfectly by the OLM model and

satisfactorily with the FEM counterpart. The timing of cracking and the maximum value of CMOD

matched the experimental results very well using OLM.

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Documents

MASİF BETON YAPILARDA HASAR İLERLEMESİ .... Uluslararası Deprem Mühendisliği ve Sismoloji Konferansı 11-13 Ekim 2017 – ANADOLU ÜNİVERSİTESİ – ESKİŞEHİR MASİF BETON