Cracks in Arch Dams: An Overview of Documented Instances

Abstract

It is essential to understand how failure mechanisms work in arch dams and, in particular, their most common manifestation: cracking. In this paper, the different types of cracking are explained in terms of their causes and consequences. Then, an exhaustive literature review is carried out that results in a detailed compilation of the characteristics of 38 cracked arch dams from all over the world, including crack characteristics (zone, position, dimensions and probable cause). This review is restricted to only those dams for which information on the position of the cracks or dam displacements is publicly available. As part of the review, a brief summary of key data for each dam is included, as well as a compilation of published crack diagrams. The positions of the cracks of all the dams are classified using diagrams in relation to the type of dam and the origin of the crack. Finally, the distribution of some dam parameters and crack features is analyzed by studying the relationships between them.

1. Introduction

Clean water and renewable energy sources are indispensable, particularly in those areas that have suffered large population increases (resulting in an increase in the demand for resources) or in areas that are undergoing desertification processes. Dams are essential for both of these purposes, and it is therefore necessary to develop policies and research studies focused on the efficient performance of dams. Dams are designed to harness and manage water resources and play a key role in providing essential services critical to human development. They are essential and sensitive infrastructures and perform different important functions by fulfilling a variety of significant economic, environmental, and social benefits, such as flood control, water supply, hydroelectric power, etc.

The safe performance of dam systems is highly relevant, as their deterioration or malfunction can lead to economic costs and loss of human lives. In that way, the benefits of dams are sometimes counterbalanced by the risks they can entail in downstream populations and properties, making dam health studies an integral part of the effort to achieve efficient dam operation. This risk becomes critical for large dams and, according to the International Commission on Large Dams, ICOLD, more than 61,000 large dams have been built around the world [1]. Therefore, it is necessary to pay close attention to the design, performance and maintenance of a dam to ensure its reliability, safety and stability and to minimize the probability of major failure. The American Society of Civil Engineers report classifies dam risks as (i) high (potentially causing human losses), (ii) significant (economic losses), (iii) low and (iv) undetermined. Approximately 17% and 12% of dams fall into each of the first two categories [2], so it is essential to conduct structural health monitoring to protect dam structures.

From the moment of construction and throughout their entire operational life, dams are subject to complex physical and chemical factors. This is especially true in the context of climate change, which alters the maximum and minimum values for temperature oscillations, the main cause of cracking in arch dams. This translates into the fact that, in some dams, aging occurs more rapidly than expected, sometimes reaching at an early stage a critical degree of degradation [3]. This complexity leads to dam engineering problems being among the most challenging in civil engineering [4] not only due to their particular geometry, but also due to the interaction of different material phases (e.g., solid–fluid), the fact that the construction material is continuously changing over time (concrete, asphaltic membranes, permeability of earth dams, etc.) surrounded by a large amount of material that causes a higher degree of heterogeneity and lastly, due to the diverse nature of the loads applied.

Research studies, such as the one presented below, categorize previously recorded events in arch dams, their characterization, evolution and causes. With this objective in mind, this state-of-the-art research is focused on arch dams that have suffered some type of cracking with the particularity of being limited to the dams for which public data about the cracks are available. This restriction greatly reduces the number of cases available, sometimes leading to very limited sources of information on the cracks presented. The following sections of this article are carried out as described below. In Section 2, a detailed compendium of the studied dams is presented, while Section 3 of this study provides a comparative analysis and discussion of the relationships between dam features and crack features. As previously stated, this analysis scale is severely limited by the small number of cases, rendering it therefore difficult to establish conclusions of a global scope.

1.1. Effect of Cracking on Arch Dams

Among the different types of dams, arch dams have emerged as the most cost-effective and safest type of dam over the past few hundred years [5]. Arch dams are continuous monolithic designs in which the structural capacity is conditioned by the conduction of the received loads to its foundation in an undivided bonded system. Any interruption in the continuity or monolithicity of the structure or a weakening of the bedrock causes the dam to adopt a behavior for which it was not intended and can lead to dam failure or even total collapse if the foundation is affected. Globally, arch dams are susceptible to failure as a result of the following [6]:

• Structural failure within the dam body;
• Sliding along the dam–foundation interface;
• Movement of the abutment rock wedges formed by rock discontinuities.

These types of failures normally cause a high tensile stress in a certain area, leading to the formation of cracks. This cracking can be in the form of small surface cracks to severe crack damage. Minor cracks developed as concrete cures should not pose a risk to the reliability, appearance or maintenance of the dam. However, open cracks and cracks that connect different sections of the dam or penetrate deep into the structure can be harmful and should be the subject of attention.

The maximum limit of the load-carrying capacity of an arch dam is determined by the compressive strength of the concrete, unless the dam malfunctions. The presence of cracks will reduce strength and rigidity, impair integrity and impermeability, aggravate concrete deterioration and jeopardize the safe performance of the dam. On this basis, joint opening and excessive and widespread cracking can deplete the concrete’s ability to withstand compression as a result of load redistributions or may result in partial sliding. Causes of arch dam cracking often interact with each other in a non-linear way, so it is usually not possible to consider them separately, yet they can be summarized in the following categories:

• Thermal effects: external temperature variations, freeze–thaw effects, hydration heat during concrete curing, etc. Due to its size and massive cross-section, significant thermal or moisture gradients may occur where parts of the structure are subjected to water, while other parts are in contact with the ambient air. These effects can introduce significant stresses into the structure. Most horizontal cracks in the arch dam are due to summer temperatures when the dam is empty and develop downstream. These cracks, although still required to be studied, are generally not hazardous because they will close once the reservoir is filled. More detailed information can be found in [7,8];
• Chemical effects: expansive chemical reactions, shrinkage, alkali–aggregate reactions (alkali–silica reaction, alkali–carbonate reaction and sulfate attack), etc. More detailed information on chemical reactions in dams can be found in [9];
• External events: these include microseismic, earthquakes, deformation of the foundation, seepage, overtopping flooding, etc.;
• Inadequate design or execution of construction and maintenance: the profile of the arch dam is directly related to the stress distribution in the body of the dam, which can be affected by weak foundations, weak joints, not suitable concrete materials (high-strength concrete has high hydration heat), wrong design affecting its rigidity, gallery weaknesses, etc.

1.2. Detection and Treatment of Cracks

In the behavior or structural response of dams, the detection of any anomaly is essential. The detection of faults or anomalous behavior has always been a critical issue in the maintenance of an arch dam. Over the decades, in addition to visual inspection, different auscultation methods have been used in dams to measure several parameters and detect possible failures. These methods can be ADASs (Automatic Data Acquisition Systems) or can be handled manually, but all of them suffer from limitations of precision inherent to the measuring device and from errors (in measurements or data storage). The parameters that are usually measured in dams are air temperature and relative humidity, concrete temperature, displacement of dam body, displacement of foundation, ice thickness, joint and crack movement, pore pressure, seismic motion, snow and rainfall, stream flow, water leakage, water level and water temperature and, less often, strain in concrete. More information about the instruments used for each of these parameters can be found in [10].

Once a crack is detected in a dam, technical experts must assess whether the crack could lead to a problem in the operation of the dam and, if so, some type of treatment must be applied to avoid serious problems. This treatment is chosen in relation to the causes of the crack. The next table (

Table 1. Treatments against cracking.

Problem	Possible Causes	Treatment
Structural distress	Thermal effects. Chemical effects. External events. Inadequate construction or maintenance.	Structural distress may require reducing the reservoir water level, thus reducing the stresses in the dam. Update risk assessment covering all structural design parameters. Post-stressed tendons.
Foundation and abutment behavior	External events. Inadequate construction or maintenance.	Grouting, drainage, post-stressed tendons, shear keys, shotcrete, dental concrete, re-shaping (benching, flattening slopes), toe blocks, berms.
Shrinkage	Chemical effects. Thermal effects.	Sealing, epoxy grouting.
Thermal distress	Thermal effects.	Cooling, heating, insulation.
Freeze–thaw effects	Thermal effects.	Sealing: upstream membrane, shotcrete, restore original lines and grades via build back, epoxy grouting.
Expansive chemical reactions	Chemical effects.	Slot cuts: post-stressed tendons, water proofing, membranes, grouting, drainage.
Earthquake distress	External events.	Site-specific seismic hazard assessment, pre-stressed tendons, grouting.
Corrosion of rebar and embedded parts	Chemical effects.	Chip, saw-cut surrounding concrete to grit blast steel or remove damaged metal and replace steel (epoxy coated rebar) or embedded part and reconcrete. Corrosion inhibitors can also be included in the concrete mix, such as calcium nitrite.

) summarizes different usual treatments against cracking [11].

1.3. Study of Cracked Arch Dams

For crack control and long-term stability of the dam, knowledge of the cracking phenomenon is essential. There are many methods aimed at analyzing dam cracking, including geomechanical model experiments, data-based numerical models or in situ monitoring and field testing. More detailed information on these methods can be found in [10,12,13].

As mentioned before, numerous studies have been published on dams involving cracked arch dams; the most relevant of them are briefly described in the next paragraphs. It should be noted that, of all the reviews analyzed, only [13] includes dams that provide monitoring data, although it does not take into account whether they are cracked or not.

1.3.1. Previous to 2010

Jansen et al. [14] present a state of the art in dam engineering for the design, construction and repair of dams in which 21 case studies (9 of them arch dams) are examined to outline proven principles and procedures. Sarkaria [15] studies the severe problems that have occurred in seven arch dams, examining the causes and the insights obtained, and also analyzing the evolution of the design of modern arch dams. FERC [16] presents a guide, based on 55 episodes that have occurred in arch dams, on the criteria and procedures applied to determine the reliability and structural stability of current arch dams, in order to establish standards and evaluation methods to serve as a reference for the examination and validation of the analysis and inspection work. Segarra et al. [9] address the expansive reactions in concrete and their effects on dams through information provided by 101 cases of dams affected by AAR (33 of them arch dams) thoroughly reviewed in order to provide specific data on structures in which the reaction has been positively identified.

1.3.2. Between 2011 and 2015

Bisus and Baena [17] analyze the determination of the slenderness coefficient in arch dams based on a state-of-the-art andevaluation of 95 arch dams employing the Lombardi break curve, the Qingwen break curve, the Fanelli–Lombardi break curve and the Tian Bin and Lu Xiaochun break curves. Jonker and Espandar [6] present a report on the existing status of arch dam design standards employed by some international dam organizations based on the review of events and deficiencies of 26 arch dams, as well as contrasted with the criteria established in the updated ANCOLD Guidelines on Design Criteria for Concrete Gravity Dams, in order to lay the groundwork for consistent and unified design standards for arch dams in Australia. Hariri and Seyed-Kolbadi [18] explore seismic cracks in three types of concrete dams and expose an integrative 3D rotating coaxial smeared crack model for crack analysis in large-mass concrete structures. He fits an advanced five-parameter failure criterion for crack initiation and propagation under monotonic and cyclic loads, while establishing the vulnerable area in the three types of concrete dams through the study of 17 dams affected by major earthquakes (6 of them arch dams). Lin et al. [12] give a scientific guide for performing geomechanical model tests to assist in the non-linear design of super-high arch dams based on the test results of 3D geomechanical models and plane models of seven arch dams. They examine displacements, global factors of safety, stress distribution, cracking and failure processes of dam foundations. In addition to the cracking characteristics of the upstream and downstream dam surfaces and induced joints in the dam heel, the rock mass of the dam–foundation interface and abutments are also studied. Salazar et al. [13] provide a review of data-based predictive models derived from statistical and machine learning performed in 53 dam reliability studies (24 of which are arch dams). There are various points to consider in the analysis approach, including the choice of input variables, their distribution in training and validation sets and the analysis of errors.

1.3.3. Between 2016 and 2021

Alonso and Baena [19] study incidents in 37 arch dams to prepare an inventory as complete as possible, based on the available documentation, of cracking and incidents in arch dams, characterizing them and identifying the root cause. Baena [20] obtains the slenderness coefficient for 49 arch dams around the world and proposes an update of the slenderness limit. She also analyzes the cracking effects that some of these dams have had due to slenderness problems. Lin et al. [21] synthesize the variety in cracking modes and effect factors by analyzing 15 arch dams. They also examine the overall stability, the cracking risk and the reinforcement of the abutments of an arch dam through numerical simulations. Salazar et al. [8] study the most relevant characteristics with respect to numerical modeling of the thermomechanical performance of arch dams, focusing on the construction process and the determination of the reference temperature. A detailed bibliographical review is made on 31 arch dams based on the criteria applied in the elaboration of the model, including boundary conditions, computational domain or time integration. The parameters used in the respective case studies are described. Wei et al. [5] examine the aspects that lead to gallery cracks in eight arch dams. The authors explore the strike, width, depth and cause of gallery cracks through a set of field tests and monitoring data. The crack mechanism and crack prevention in the galleries of arch dams are analyzed from a 3D non-linear numerical simulation.

2. Observational Data/Material: Summary of Case Studies

As the core section of the current state of the art, a literature search for cracked arch dams that have published records of the displacements or location of the cracks was carried out. This search resulted in the compilation of publications based on 42 dams, although 4 of them (named Dam A, Dam G, Dam H and Dam I) were not analyzed independently in Section 3 and Section 4 because they were assumed to be the same dam as another of the analyzed dams. Below is presented a table with the main characteristics of the dams analyzed in this study (

Table 2. Characteristics of the dams.

	Dam	Type	Height (m)	Slenderness	Lombardi Coefficient	Nearby City	Base Elevation (m)	Thermal Amplitude (°C)	Publications
1	Baishan	Single-curvature gravity-arch dam	149.5	7.0	20.1	Baishan Town, Jilin, China	274.0	45	[22]
2	Cabril	Double-curvature arch dam	132	18.2	22.7	Pedrógao Grande, Portugal	165.0	28	[23,24,25,26,27,28,29]
3	Castro de las Cogotas	Double-curvature arch dam	67.0	39.2	44.8	Mingorría, Avila, Castille and León, Spain	987.5	30	[17,20,30,31]
4	Chencun	Single-curvature gravity-arch dam	76.3	11.2	39.3	Pinghu, Anhui, China	50.0	30	[32,33,34,35]
5	Copper Basin	Single-curvature thin dam	57.0	-	52.6	Cienega Springs, Arizona, USA	257.0	36	[9,16,36]
6	Dagangshan	Double-curvature arch dam	210.0	18.9	14.3	Shirong, Yaan, Sichuan, China	925.0	24	[5,12,37]
7	Daniel-Johnson	Multiple-arch buttress dam	214.0	63.2	14.0	Port-Cartier Côte-Nord, Quebec, Canada	130.0	38	[21,38,39,40,41,42]
-	Dam A	Single-curvature gravity-arch dam	76.3	-	39.3	-	50.0	-	[43,44,45,46,47,48,49]
8	Dam B	Single-curvature, single-radius thin dam	40.0	-	75.0	Northern Sweden	-	-	[50,51,52,53,54,55]
9	Dam C	Double-curvature arch dam	289.0	15.4	10.4	Pisha, Sichuan, China	545.0	27	[56]
10	Dam D	Single-curvature gravity-arch dam	178.0	3.6	16.9	Longyangxia, Qinghai, China	2432.0	37	[57]
11	Dam E	Single-curvature gravity-arch dam	100.5	-	29.9	Muang Kasi, Vientiane, Laos	1002.5	18	[58]
12	Dam F	Single-curvature gravity-arch dam	110.0	-	27.3	Bama, Guangxi, China	123.0	25	[59]
-	Dam G	Parabolic double-curvature arch dam	240.0	-	12.5	-	965.0	-	[60]
-	Dam H	Single-curvature gravity-arch dam	45.0	8.7	66.7	-	-	-	[5,61]
-	Dam I	-	294.5	-	10.2	-	-	-	[62]
13	Dam J	Double-curvature compound-arch dam	270.0	3.9	11.1	Laojiezi, Malutangxiang, Yunnan, China	718.0	27	[5]
14	Dam K	Double-curvature arch dam	45.0	-	66.7	South of France	2000.0	-	[63]
15	El Atazar	Double-curvature arch dam	141.4	11.9	21.2	Cervera de Buitrago, Madrid, Spain	720.0	29	[7,14,17,19,20,30,64]
16	Ertan	Parabolic double-curvature arch dam	240.0	13.3	12.5	Panlian, Sichuan, China	965.0	27	[17,21,65]
17	Gene Wash	Single-curvature thin dam	40.0	-	75.0	Cienega Springs, Arizona, USA	185.0	36	[9,16,30,36]
18	Huaguangtan	Double-curvature arch dam	103.9	-	28.9	Yutiao, Zhejiang, China	345.0	31	[66]
19	Isola	Single-curvature gravity-arch dam	45.0	8.7	66.7	Braggio, Switzerland	1550.0	27	[67]
20	Kariba	Double-curvature arch dam	128.0	23.6	23.4	Kariba, Mashonaland West, Zimbabue	593.0	21	[14,19,68,69]
21	Karun IV	Double-curvature arch dam	230.0	9.7	13.0	Lordegān, Chaharmahal and Bakhtiari, Iran	680.0	38	[20,70]
22	Kolnbrein	Double-curvature arch dam	200.0	17.7	15.0	Mauterndorf, Austria	1702.0	29	[6,14,15,17,19,21,30,71,72,73,74,75,76,77,78]
23	Kromme-Churchill	Multiple-arch dam	39.5	-	75.9	Kareedouw, Sudáfrica	120.0	18	[9]
24	La Tajera	Double-curvature arch dam	62.0	16.1	48.4	Masegoso de Tajuña, Guadalajara, Spain	920.0	31	[17,19,30,79,80,81]
25	Matka	Double-curvature arch dam	30.0	38.1	100.0	Bukovikj, Macedonia	289.4	33	[82]
26	Nuraghe Arrubiu-Flumendosa	Double-curvature arch dam	115.0	9.5	26.1	Escalaplano, Provincia di Cagliari, Italy	155.0	27	[19,30,71,76,83,84]
27	Pacoima	Double-curvature arch dam	112.0	-	26.8	San Fernando, Los Ángeles, California, USA	1990.0	25	[3,6,15,16,19,30,85,86,87]
28	Punt dal Gall	Double-curvature arch dam	130.0	15.8	23.1	Aprica, Provincia di Sondrio, Italy	1675.6	25	[5,88]
29	Quiebrajano	Double-curvature arch dam	71.5	10.6	42.0	La Guardia de Jaén, Spain	720.0	35	[7,17,19,30]
30	Sayano-Shushenskaya	Single-curvature gravity-arch dam	242.0	-	12.4	Mayna, Jakasia, Rusia	270.0	45	[21,77,89]
31	Shuanghe	Hyperbolic double-curvature dam	65.0	8.7	46.2	Laitan, Chongqing, China	487.3	26	[21,90,91,92]
32	Spitallamm	Single-curvature gravity-arch dam	113.0	10.1	26.5	Sarnen, Obwalden, Suiza	1800.0	26	[93,94]
33	Susqueda	Double-curvature arch dam	135.0	19.0	22.2	La Cellera de Ter, Girona, Catalonia, Spain	222.0	29	[17,19,30,95,96]
34	Tolla	Single-curvature thin-arch dam	90.0	50.0	33.3	Peri, Corsica, France	490.0	24	[6,14,15,19,30,85]
35	Xiaowan	Double-curvature arch dam	294.5	13.4	10.2	Fengshan Village, Yunnan, China	950.5	24	[5,12,17,21,97,98]
36	Xiluodu	Double-curvature arch dam	285.5	11.7	10.5	Xiluodu, Zhaotong, Yunnan, China	324.5	28	[5,12,17,92,99,100,101,102,103]
37	Zeuzier	Double-curvature arch dam	156.0	-	19.2	Montana, Sierre District, Valais, Switzerland	1623.0	26	[5,14,15,19,20,30,67,71,76,85,104,105]
38	Zillergrundl	Double-curvature arch dam	186.0	14.3	16.1	Rohrberg, Politischer Bezirk Schwaz, Tyrol, Austria	1650.0	27	[17,19,21,30,71,77,78,106]

). These characteristics include the following:

• Type: Double curvature (curve both in layout and vertical section), single curvature thin (curved only in layout), single-curvature gravity arch (a single-curvature arch dam thicker than usual but thinner than a gravity dam), or multiple arches;
• Lombardi coefficient: Slenderness maximum value according to Lombardi’s formula. More accurate parameters (such as those discussed in [20]) were not used because there was not enough information available to determine their value for most of the dams;
• Nearby city: Closest city where temperature records are available;
• Thermal amplitude: Difference between the average temperatures of the warmest and coldest month in the nearby city.

Further information on the cracks and records of the dams is shown in

Table 3. Crack features and dam monitoring records.

	Dam	Main Causes of Cracking	Cracked Zone	Location of Cracks	Crack Dimensions	Published Records
1	Baishan	-	Downstream surface	Along the entire surface.	Max. width: 3.5 mm.	Evolution of crack opening of 24 cracks.
2	Cabril	Inadequate design or execution of the construction. The change in the project during the construction phase lead to a more rigid crest.	Upstream surface.	Horizontal at the top. At 112–122 m above the dam base.	-	Precise placement of the cracks. Displacements on the central cantilever.
3	Castro de las Cogotas	Thermal effects. Shrinkage coupled with thermal gradients.	Internal.	Between the downstream face and the perimeter gallery.	Max. width: 1.3 mm.	Crack opening evolution.
4	Chencun	Thermal effects. Combination of high air temperature and low reservoir level. Short pouring interval, so the shrinkage deformation of the second phase concrete is under strong constraint.	Downstream surface.	Horizontal at the top.	Max. width: 4 mm. Max. length: 300 m. Max. depth: 5 m.	Evolution of crack opening. Precise placement of the cracks. Radial displacements (in the dam blocks and foundations).
5	Copper Basin	Chemical effects. Wetting–drying cycles connected with the expansion of the dam mass. Reaction: Alkali–silica.	Downstream surface.	Horizontal and oblique. Center and abutments.	-	Precise placement of the cracks.
6	Dagangshan	Seismic events. Microseismic. Dam weight and overhang.	Internal.	At 15 m and 45 m above the dam base.	Max. length: 5 m. Max. width: 0.15 mm. Max. depth: 3.7 m.	Crack opening evolution.
7	Daniel- Johnson	Thermal effects. Inadequate design or execution of the construction. Seasonal temperature. Geometric discontinuities.	Downstream and upstream surfaces.	Upstream at the heel. Downstream at the center.	-	Displacements (measured by pendulum).
-	Dam A	The pouring interval is short, so the shrinkage deformation of the second phase concrete is under a strong constraint.	Downstream surface.	Horizontal at the top.	Max. width: 4 mm. Max. length: 300 m. Max. depth: 5 m.	Evolution of crack opening. Radial displacements (in the dam blocks and foundations).
8	Dam B	Thermal effects. Seasonal temperature variations.	Downstream surface.	Oblique. Lower and central area.	-	Precise placement of the cracks. Displacements (on the crest and in the center of the dam).
9	Dam C	Soil displacements. Grouting or uneven deformation of the foundation.	Internal.	Bottom gallery.	Max. width: 0.19 mm. Max. depth: 0.08 m.	Crack opening evolution. Precise placement of the cracks. Displacements.
10	Dam D	-	Downstream and upstream surfaces.	At 78–138 m above the dam base.	-	Evolution of crack opening.
11	Dam E	Thermal effects. The temperature of the dam dropped during the flood period.	Upstream surface.	Seven cracks at the center 41,9 m above the dam base.	Max. width: 2.5 mm. Max. depth: 15 m.	Radial displacements.
12	Dam F	-	-	-	Max. width: 0.7 mm.	Crack opening evolution.
-	Dam G	Thermal stress.	Downstream surface.	-	-	Radial displacements.
-	Dam H	Chemical effects. Alkali–aggregate reaction.	Internal.	Gallery.	Max. length: 246 m. Max. width: 2.4 mm.	Evolution of crack opening. Radial displacement (dam crest).
-	Dam I	-	Internal.	Gallery.	-	-
13	Dam J	Inadequate design or execution of the construction. Grout splitting of the interlaminar bonding surfaces, which caused the grouting uplift.	Internal.	Gallery at 15 m above the dam base.	Max. length: 23 m. Max. depth: 0.51 m. Max. width: 0.3 mm.	Crack opening evolution. Precise placement of the cracks.
14	Dam K	-	Upstream surface.	Rock–concrete interface.	Max. width: 2.5 mm.	Measurements of pendulums in the central block. Crack opening displacements.
15	El Atazar	Thermal effects. Soil displacements. The deformational asymmetry of the foundation leads to tensile stresses on weak joints.	Downstream, upstream and internal.	Horizontal. Principal internal at 25 m above the dam base. Downstream at the base. Others between 55 and 100 m.	Max. length: 160 m. Max. depth: 19 m.	Displacements (measured by 8 pendulums). Precise placement of the cracks.
16	Ertan	Thermal effects. Non-uniform temperature distribution on the downstream surface.	Downstream surface.	Upper-right side.	-	Radial displacements (in 4 central points).
17	Gene Wash	Chemical effects. Wetting–drying cycles connected with the expansion of the dam mass. Reaction: Alkali–silica.	Downstream surface.	Horizontal and oblique. Abutments.	-	Precise placement of the cracks.
18	Huaguangtan	Thermal effects. Low temperature and high water level.	Downstream and upstream surfaces.	Dam–foundation interface.	Max. width: 20 mm.	Horizontal displacements (central cantilever). Vertical displacements (monoliths). Displacement (abutment).
19	Isola	Chemical effects. Alkali–aggregate reaction.	Internal.	Horizontal. Gallery at 31 m above the dam base.	Max. length: 246 m. Max. width: 2.4 mm.	Evolution of crack opening. Precise placement of the cracks. Radial displacement (dam crest). Displacements (measured with a pendulum in the central part of the dam).
20	Kariba	Chemical effects. Alkali–aggregate reaction.	Downstream surface.	Horizontal. On the heel of the dam and the dam–foundation interface.	-	Vertical displacements. Radial displacements (on the crest).
21	Karun IV	Inadequate design or execution of the construction. The absence of a drainage system together with the presence of an impervious clayey layer in the foundation and incomplete vertical joints grouting of the upper half of the dam body.	Upstream and internal.	Horizontal and vertical. Dam heel and mid-arches close to the left abutment.	Max. width: 6 mm.	Precise placement of the cracks.
22	Kolnbrein	Inadequate design or execution of the construction. Weak foundations, inadequate injection of joints, and slenderness of the dam.	Downstream and upstream surfaces.	On the base of the dam. Upstream up to the inner gallery.	Max. width: 3 mm.	Precise placement of the cracks. Radial displacements (crest and base).
23	Kromme-Churchill	Thermal effects. Chemical effects. Alkali–acid reaction. Volume changes due to shrinkage and thermal effects.	Downstream, upstream and internal.	Horizontal and oblique. On the base. Upstream and internal in the center.	Max. width: 10 mm. Max. length: 0.45 m. Max. depth: 0.25 m.	Precise placement of the cracks.
24	La Tajera	Thermal effects. Inadequate design or execution of the construction. Reservoir empty at high temperatures, galleries without the necessary concrete overlay.	Downstream surface.	Oblique. Along the transition between vault and base.	Max. width: 0.5 mm.	Horizontal and vertical displacements (crest and cantilevers). Precise placement of the cracks.
25	Matka	Thermal effects. High temperature stresses.	Downstream surface.	Oblique. In the immediate vicinity of the right abutment.	Max. width: 2 mm. Max. length: 3 m.	Precise placement of the cracks. Displacements (at 24 points before and after cracking).
26	Nuraghe Arrubiu-Flumendosa	Thermal effects. Cooling of the concrete.	Upstream surface.	Horizontal. From 65 m above the dam base until the crest.	Max. length: 4.7 m.	Precise placement of the cracks.
27	Pacoima	Seismic events. Earthquakes.	Downstream and upstream surfaces.	Vertical. Between the arch dam and the thrust block on the left abutment.	Max. width: 50.8 mm. Max. length: 18 m.	Precise placement of the cracks.
28	Punt dal Gall	Thermal effects. Chemical effects. Efflorescence.	Internal.	Gallery at 68.4 and 122.4 m above the dam base.	Max. width: 2 mm.	Crack opening evolution. Uplift pressure measurements. Displacements (measured by inverted pendulums).
29	Quiebrajano	Thermal effects.	Downstream surface.	Horizontal and oblique cracks at the intersection with the basement of both abutments (first on the right side and then on the left side).	-	Precise placement of the cracks.
30	Sayano-Shushenskaya	Thermal effects. Concrete hydration heat and temperature. Changes in the stress state in the dam foundation.	Downstream and internal.	Internal at elevation 24.5 and 129 m above the dam base. Joints opening downstream at elevations 114 and 192 m.	Max. depth: 3 m. Max. width: 3.8 mm.	Displacements (crest).
31	Shuanghe	Inadequate design or execution of the construction. Self-weight and weak foundation.	Downstream surface.	Vertical. Along the entire surface.	Max. length: 3 m. Max. width: 8 mm.	Precise placement of the cracks.
32	Spitallamm	Inadequate design or execution of the construction. Pressure grouting.	Downstream surface.	Horizontal. At elevation 103 m above the dam base.	Max. length: 50 m.	Evolution of crack opening. Precise placement of the cracks. Displacements (measured by the pendulum on the crest). Upstream–downstream displacements (crest below crack level and near dam crest).
33	Susqueda	Thermal effects.	Upstream and internal.	Horizontal. Upper and left areas.	Max. width: 0.92 mm.	Crack opening evolution. Precise placement of the cracks. Displacements (crest).
34	Tolla	Thermal effects. Inadequate design or execution of the construction. High rigid foundations, high ambient temperature and the dam was too thin.	Downstream and upstream surfaces.	Oblique. In the immediate vicinity of both abutments.	-	Precise placement of the cracks.
35	Xiaowan	Thermal effects. Tensile stress caused by the temperature drop during the second stage post-cooling process before joint grouting.	Internal.	Vertical. Gallery at 40 and 107 m above the dam base.	Max. length: 3.5 m. Max. width: 1 mm.	Evolution of crack opening. Precise placement of the cracks. Displacements. Evolution of stresses.
36	Xiluodu	Inadequate design or execution of the construction. Dam weight, overhang and foundation constraint.	Internal.	Gallery at 15 m above the dam base.	Max. length: 3.5 m.	Crack opening evolution. Longitudinal and tangential displacements.
37	Zeuzier	Soil displacements. Abutment movement and settlement of the foundations. Change in ground phreatic conditions.	Downstream, upstream and internal.	Oblique. Galleries from 69 to 156 m above the dam base. Vertical joints open at central part on the upstream face. Peripheral joints on the downstream face parallel to both abutments.	Max. width: 15 mm. Max. length: 2 m.	Precise placement of the cracks. Radial displacements.
38	Zillergrundl	Thermal effects. Concrete hydration heat. Water infiltration in joints.	Upstream and internal.	Horizontal cracks in the heel. Vertical cracks in the elevator shaft.	Max. width: 1.9 mm.	Displacements. Precise placement of the cracks.

. This information includes the main cause of cracking in each dam according to the classification explained in Section 1.1, the position and dimensions of the cracks and the type of dam auscultation records that are available. To be able to perform a comparative analysis, only the most relevant causes of cracking are taken into account, although it is acknowledged that there may be dams with some cracks due to a cause other than the main causes.

The next sections present a brief background on each of the dams analyzed, adding information on the dam that has not been included in the tables presented before. This information presents a non-uniform structure due to the very different characteristics of the dams and the limited available data. To facilitate readability, the summary does not include again the information already specified in Table 1 and Table 2.

2.1. Double Curvature Dams

Cabril dam (1954): It is a high concrete arch dam that presents, since the first filling of the reservoir, some horizontal cracks in the central upper zone. Some concrete swelling phenomena due to alkali–aggregate reactions were detected in the 1990s.

Castro de las Cogotas dam (1993): The injection of joints was carried out in 1991. In 1992, some cracking was detected in the body of the dam along two trajectories. The first one was almost parallel to the intersection line, between the base and the downstream face and approximately 5 m above it. The second one was following horizontally the joints between sections. Cracking developed during the summer after joint injection (1991). In 1993, the cracks were injected with a mixture of epoxy resins. In 2021, consolidation and drainage works were carried out on the foundation and the body of the dam.

Dagangshan dam (2008): Due to its position in a region of extremely high seismic intensity, the strengthening criteria for its design were the most stringent among similar projects worldwide. Even before the reservoir was operational, continuous and deep transverse cracks in the low galleries of the arch dam could be observed.

Dam C (2021): During 2017, cracks were detected on the surface of the upper arch of the intersection between the drainage gallery and the traffic gallery and in the dome of the drainage gallery at the 19# dam monolith. The depth was measured with core drillings. By 2019, a total of 10 cracks existed in the dome of the dam foundation galleries, six cracks existed in the dome of the horizontal galleries at elevation 55 m above the dam base and four cracks existed in the dome of the horizontal galleries at elevation 111 m above the dam base.

Dam J (2020): A large crack was detected along the gallery dome axis of the 7# dam monolith in 2018. Subsequently, a water pressure test was performed for the orifice prior to grouting. Slurry interconnection occurred between the injection holes during grouting in the holes. Furthermore, the intersection of the access gallery with the foundation gallery cracked, resulting in a grout leak. As a result, borehole coring, water pressure testing, borehole imaging, ultrasonic wave testing and in situ monitoring of temperature and displacement were performed.

Dam K (1960): During the construction phase, a complete monitoring system was integrated, consisting of 10 pendulums, piezometers, crack opening displacement sensors and infiltration measurements.

El Atazar dam (1972): In 1978, there was a sudden increase in flow that flooded the galleries at the same time that the reservoir reached its historical maximum. As a result, a large crack appeared, which continued to grow for 8 days. The causes that led to the appearance of the crack were both thermal stress (microcracking due to the strong thermal gradients caused by the change in the cooling system during construction) and constructive asymmetry (difference in structural stiffness of the dam body due to the construction of the basement on the right slope, the main cause of the displacement asymmetry). Subsequently, this crack was treated with epoxy resin injections.

Ertan dam (1999): The dam was thoroughly instrumented with monitoring systems; there are up to 138 joint meters and three rows of uplift pressure gauges embedded to supervise transceiver joint opening variations and seepage in real time. Twenty-four thermometers were also installed in the dam.

Huaguangtan dam (2005): Several borehole video tests were carried out on the dam and its foundations. These video images inside the drainage holes revealed some cracks at the interface. Two additional borehole videos were taken to check the morphology of these cracks. As a result, small cracks were detected on the upstream and downstream surfaces, while the bedrock of the dam abutment remained stable.

Kariba dam (1959): From the beginning of its exploitation, the structure showed some swelling. In 1963, localized cracks appeared to be forming. The right abutment was found to be insufficient to resist the load of the structure, so a large concrete block was added to the downstream face anchored by tendons, making the last four arch monoliths part of the original thrust block. In addition, the abutment was upgraded with grouting and underground buttresses. Since 2012 and due to the appearance of cracks on the right foundation, the dam has been at risk of collapse. Therefore, in 2018, work was started to repair the cracks.

Karun IV dam (2010). In 2011, cracks emerged in blocks 7 and 9 on the left bank, which led to the entry of water into a control gallery. In 2014, extensive analysis work was carried out, involving the processing of detected cracks with specific resins. This inspection exercise led to the detection of other cracks in the heel of the dam. These cracks are oriented downstream, while they are sub-horizontal on the upstream face of the dam. Additionally, these cracks lean toward the foundations near the mid-thickness of the dam.

Kolnbrein dam (1977): Cracks developed in the upstream heel of the dam at the first impounding in both the foundations and the concrete of the dam, which enabled water to reach the central third of the base of the dam. Various interventions were adopted: reinforcement of the grout curtain with cement grout to reduce the uplift in 1979; injection of polyurethane resin, freezing of the central part of the bottom of the dam during the imposition in 1980–81; placement of a concrete blanket covered by plastic sheets at the bottom of the valley in 1981–83; repair and extension of the plastic sheets and grouting of the grout curtain in 1984–85.

La Tajera dam (1994): A crack was identified along the connection between the vault and the base before starting to apply the load; that crack reached the core of the perimeter gallery. Various interventions were carried out between 1999 and 2002: solidification of the galleries, crack anchoring, injection of cracks, installation of irrigation in the walls and placement of reinforced concrete strips at the crest.

Matka dam (1938): In 2012, visual evidence was found of two cracks parallel to the slope at the top of the dam, but after considering the accumulation of limescale and moss, it was concluded that the cracks must have been older. In 2016, the cracks were repaired by grouting.

Nuraghe Arrubiu dam (1957): It was necessary to gradually inject the contraction joints during the pouring of the concrete (before the heat of hydration could dissipate and the concrete had cooled down). As a result, immediately after the end of the construction phase, numerous horizontal cracks appeared in the upper part of the upstream face, mainly in the horizontal construction joints. New cracks continued to develop until 1971, at which point a certain equilibrium seems to have been reached. In total, 176 cracks were identified. In 1995, epoxy resin injections were used to restore the continuity of the structure.

Pacoima dam (1928): As a consequence of the 1971 San Fernando earthquake, some instances of contraction joint opened near the thrust block. During the 1994 Northridge earthquake, the contraction joint between the dam and the thrust block at the left abutment opened at the crest level. This opening was tied to a crack that ran diagonally across the bottom of the thrust block until it reached the abutment rock. The diagonal crack in the lower part of the thrust block corresponded to the enlargement of a slip plane below the rock masses. As a result, the left abutment was strengthened with 35 post-tensioned anchors.

Punt dal Gall dam (1969): Several cracks formed along the length of the dam, especially in the upper control gallery. In this respect, 57 joint meters were deployed and cracks in the crest gallery were supervised with crack meters. These cracks opened in winter and closed in summer when the concrete temperature was at its highest in the crest area of the dam. Additionally, some efflorescence was observed on the downstream face, especially near the concrete lifts at the top of the dam that were exposed to seasonal wetting and drying.

Quiebrajano dam (1978): The dam suddenly developed horizontal cracks in its connection to the base. During the revision performed in 1996, deformations and deterioration in the concrete were also visible near these cracks, as well as various cracks on the crest of the dam that were separated by a few meters from the joints.

Shuanghe dam (1992): While the reservoir was not yet in service, six vertical perforative cracks originated on the downstream face. These cracks formed in the central area of the dam height. Eventually, two of the cracks extended along the crest of the dam, and four of them spread toward the foundation.

Susqueda dam (1968): After construction, it was not possible to perform the grouting of the joints under optimal conditions, resulting in the filling of enclosures in which hydration heat still remained to be dissipated. As a result, posterior openings of the vertical joints occurred as temperatures reached their cyclic equilibrium process. These openings had a greater impact on the levels of galleries 1, 2 and 3, which were concreted later. In 1988, thin, mostly horizontal cracking was observed, ranging from the upstream face to the gable of the upper gallery. As a consequence, the vertical joints were re-injected with epoxy resins.

Xiaowan dam (2010): During construction, numerous cracks originated in the dam structure. To monitor the behavior of the cracks and the concrete, joint gauges and extensometers were placed perpendicular to the plane of the cracks at different depths. The first crack was found after two years, almost parallel to the dam axis, in the 110.5 m inspection gallery. Subsequently, similar large cracks with an average opening of 1 mm were detected by probing. One or two cracks were found in nearly all sections of the dam, mostly located between 29.5 and 139.5 m elevation.

Xiluodu dam (2013): During the construction phase at height 245 m above the dam base, the cracks first started to emerge. For that reason, four real-time location systems were implemented at the corners of the 29 monolith 18 pouring block.

Zeuzier dam (1957): Since 1978, the dam deflects upstream. In 1979, severe cracks developed across the downstream foundation line at the same time as the contraction joints on the upstream face opened up, and cracks appeared in the corridors, shafts and crest of the dam. In 1982 and 1983, the dam was intervened by injecting epoxy resin into the cracks and contraction joints.

Zillergrundl dam (1986): During the first filling to a height of 175 m above the dam base, the elevator shaft was flooded, causing water to seep into the gallery area. Additionally, given the anisotropic permeability of the concrete, the downward-oriented hydraulic forces combined with the weight of the concrete generated a large crack in one of the dam blocks. To correct this, the crack was filled with epoxy resin and, subsequently, the load distributions were adapted to reintroduce a partial uplift pressure into the foundation joint. However, due to excessively high injection pressures, secondary cracks were created.

2.2. Single-Curvature Thin Dams

Copper Basin dam (1938): From the very beginning, there were horizontal movements in the crest, which showed that the dam was moving upward rather than downward. In 1945, cracks were discovered, and the most important ones were related to discontinuities in the abutment rock. Between 1942 and 1955, the cumulative upstream displacement was 110 mm, but between 1955 and 1975, it was only 11 mm and stopped. Meanwhile, between 1942 and 1955, vertical displacements averaged about 90 mm (120 μm/year) and between 1955 and 1995, they increased to 21 mm (10 μm/year).

Dam B: Only a few years after its operation start, cracks were detected. In the following years, such cracks continued to grow, so the dam operation was kept under constant surveillance with monitoring systems. After the implementation, the displacement along the crest was mostly enlarged, but over the years the displacement in the crest decreased, and the displacements turned more curved, reaching the maximum at about 20 m above the ground. Meanwhile, on the downstream side, the horizontal cracks arched toward the left and right sides of the dam.

Gene Wash dam (1937): During the initial years of the dam’s operation, deformations developed at a fast rate. Between 1945 and 1964, horizontal movement stopped and only seasonal displacements were recorded; the total displacement amounted to 106 mm. Between 1942 and 1965, vertical movements of 90 mm were recorded, while between 1965 and 1995, only 8 mm of movement was observed. However, the main cracks were related to discontinuities in the abutment rock.

Tolla dam (1961): It was designed to be extremely thin to provide a full-scale check of the validity of theoretical analyses when applied to dams approaching the ultimate degree of slenderness. Severe cracks developed during the first filling of the reservoir. Over the next eight years, these cracks continued to grow, which led to the building of a new arch downstream and the construction of buttresses to reinforce the original arch.

2.3. Single-Curvature Gravity-Arch Dams

Baishan dam (1984): The base concrete was poured over the summer, resulting in a large difference between the maximum temperature rise and the stabilized concrete temperature, which exceeded 40 °C. Despite this, no relevant cracking was observed in the dam concrete, even when it was subsequently subjected to severe cold temperatures. The main and solely feasible reason for cracking was that the MgO content in the cement used was large (up to 4.5%), and the combustion temperature of the cement was relatively low, resulting in a compensatory shrinkage effect of the MgO-containing concrete.

Chencun dam (1971): After detecting cracks in 1972, the reservoir level experienced an obvious increase in the decade of the 1980s, and the crack mouth opening displacement (CMOD) decreased from the rapid growth. In contrast, in 1987, the CMOD records rose rapidly as a result of epoxy grouting. The reason for this was that the grout limited the free crack closure in high-temperature situations and impacted the minimum CMOD, so the minimum CMOD readings of most of the segments climbed.

Dam D (1992): Along this dam, 135 cracks were identified, mostly in Section 9 of the dam. In order to properly monitor the cracks, a total of 134 joint meters were installed in the dam, 74 of them located in Section 9 of the dam.

Dam E (2012): In 2010, the first four cracks were detected on the surface. The expanding state of the cracks worsened when water was allowed to pass over the surface. The cracks became deeper and wider, and two of them even extended from the surface upstream to the surface downstream.

Isola dam (1960): The dam began to deform upstream after about 5 years. Initially, the central area of the crest moved an average of 0.3 mm/year, a rate that increased from 1985 to about 1 mm/year. One crack was clearly detected in the early 1980s, although it was presumed to have originated during construction. This crack was monitored and its width was growing at a rate of 0.15 mm/year.

Sayano-Shushenskaya dam (1978): Between 1988 and 1989, a horizontal construction joint or crack opened close to the upstream face at 87.5 m above the dam base. In 1990, horizontal block joints and cracks were found to have opened in an area 50 m from soil contact. In 1991, the opening of block joints and cracks was detected at 192 m above the base of the dam. Furthermore, it was found that radial section joints on the downstream face penetrated to a depth of up to 3 m with an opening of 1.6–3.8 mm.

Spitallamm dam (1932): After pressure grouting, a crack developed which caused a disconnection between the face concrete and an intermediate tanking concrete zone. The geometrical structure of this crack consisted of a nearly horizontal progression from downstream to upstream along the construction joints; a lateral extension across eight blocks; a vertical detachment at the interface between the face concrete and the tanking concrete located over an elevation of 101.86 m to 31.86 m above the dam base. As a result of the above, the substitution of the original dam with a new dam was initiated in 2019.

2.4. Multiple-Arches Dams

Daniel-Johnson dam (1970): During its construction in 1969, several types of cracks appeared in almost all the arches of this dam. The dam developed oblique cracks on the downstream surface and plunge cracks in the upstream heel. For this case, epoxy resin injections were performed; however, water infiltration continued despite the treatment.

Kromme-Churchill dam (1943): In 1957, wide horizontal cracks were detected in the buttresses and arches, some of which extended to the upward face. Between 1987 and 1990, a total of 20 concrete samples were collected. In 1963, reinforced concrete extensions were attached to the downstream face to strengthen the buttresses. In addition, upstream cracks were treated with mortar injections.

3. Results and Discussion: Comparative Analyses of Cracking

The effect of cracks on the displacements of the dam is relevant for the analyses of the structural behavior. Among the 38 different dams reviewed, 24 have published displacement data. Among them, it is unknown when the cracking occurred for six of them, and there has been cracking since the dam was put into operation for 13 dams. From the remaining five dams, displacement data prior to cracking are available for only two of them.

The first of these cases is the Zeuzier dam, where the cracks were caused by an abrupt change in the geology surrounding the dam as a result of the excavation of a tunnel; therefore, it is not possible to determine the influence of the cracks on the change in the displacements of the dam (Figure 1). The other case is the Kariba dam, where the cracks emerged four years after the dam became operational, resulting in the availability of a single displacement measurement prior to the cracking (Figure 2). It should be noted that, although there is a displacement record before and after cracking, it should not be assumed that cracking is the sole cause of the variations in those displacement records.

3.1. Location of the Cracks

Figure 3 and Figure 4 present a compilation of diagrams found in the corresponding literature showing the location of the most important cracks. It should be noted that the location of cracks in multiple arch dams is mainly influenced by its own design. Being a non-symmetrical design, the loads will be distributed quite unevenly in each part of the dam.

Figure 5 shows, on a generic arch dam, the areas where cracks were found for each of the dams studied. In addition, the type of dam corresponding to each one of them is indicated by a color code. It can be seen in this figure that a simple pattern cannot be found. However, some general trends can be observed:

• Cracking happens more often in the downstream face than in the upstream face, and internal cracks are not unusual;
• Internal cracks can be found all along the height of the dam section;
• There is no specific area wherein the cracking concentrates on the downstream face, although it is more common in the abutment zones;
• However, cracking occurs more often at the toe and central areas and rarely in the abutments and crest area in the upstream face;
• Double-curvature dams tend to crack upstream in the crest zone and heel, while downstream on the sides and near the toe;
• Single-curvature thin dams do not usually have internal cracks or external cracks near the base of the dam. Cracking is mainly on the abutments, central and crest zones of the downstream face. When cracking occurs upstream, the cracks are located on the abutments;
• Gravity-arch dams tend to crack in the central zone of the dam upstream and in the central or crest zone of the downstream face.

Regarding the cause of the cracking, it can be observed (Figure 6) that cracks due to chemical reactions generally occur on the downstream face or inside the dam body. Internal cracks are more often in the central part of the dam body than near the base or the crest, while cracks at the downstream face are evenly distributed among the different areas. No cases were found in which cracks were located in the abutments or crest area of the upstream face.

Cracks due to inadequate design or execution of the construction and maintenance (Figure 7) are uniformly distributed throughout the different areas of the downstream face. It can be observed that internal cracks and those located on the upstream face are predominantly near the base of the dam. Considering the whole set of cracks with this type of origin, the location near the base is still predominant.

Figure 8 shows that most of the internal cracks and cracks located on the upstream face are due to the thermal effect, and also that most of the cracks are located near the dam toe on the downstream face. There are only a few cases in which cracks are located on the downstream face, far from the dam toe. It should be noted that cracks caused by thermal effect are predominant in arch dams as a whole.

There are not many cases of cracked dams due to external events, and they are not concentrated in any particular location of the dam faces or body (Figure 9).

3.2. Factors Related to Arch Dam Cracking

In this section, an analysis is performed on the effect of the factors involved in the cracking of the presented arch dams (Table 1 and Table 2), although it should be taken into account that the number of available cases is not enough for the empirical observations to have strong statistical validity and generality.

Firstly, some general facts can be pointed out from the data:

• Regarding the cracked gravity-arch dams, none of them experienced cracks due to external events. Of course, all of them have low slenderness and comply with the Lombardi slenderness limit;
• All the low-height cracked dams comply with the Lombardi slenderness limit;
• Most of the dams (80%) cracked due to external events suffered internal cracks;
• None of the single-curvature thin dams developed internal cracks, and all of them developed cracks on the downstream face. All of them are of low-to-medium height.

Figure 10 shows the distribution of the 38 dams according to every factor considered. The ranges of medium height and slenderness are considered to be <63–131 m> and <12–17.2>, respectively. These values were calculated based on data of 95 dams published in [17]. The mean range of thermal amplitude <20–25 °C> was estimated from the global mean value discounting oceans and using the interpolation of ground-level weather station data by Berkeley Earth Surface Air Temperature [107], where the difference ranges <0–60 °C>.

Figure 11 shows the three main parameters for 25 dams (all double-curvature and single-curvature dams for which slenderness values are available). It can be noticed that most of the cracked dams have a thermal amplitude higher than 23°. In particular, cracked gravity-arch dams have slenderness values under 11 and thermal amplitudes higher than 26°. On the other hand, low-height dams have a slight tendency to crack with higher thermal amplitudes than high dams, as a mean, although this pattern is not strictly consistent.

The parameter known as the slenderness safety factor can be defined as the ratio of Lombardi limit to the slenderness coefficient (the safer the dam, the higher the safety factor). As expected, most of the available cracked-arch dams have a slenderness safety factor lower than 3, and those with a slenderness safety factor greater than 3 have a height below 80 m (Figure 12). However, there are considerably more dams under 80 m than over that value, which offers a possible explanation.

4. Conclusions

In this work, a literature review was conducted, resulting in a detailed compilation of the characteristics of cracked arch dams. Unlike previous similar studies, it was restricted to those dams for which the position of the cracks or dam deformations is publicly available, which, to the best of the authors’ knowledge, had not been documented before. Following a compilation of published crack diagrams (covering 22 of the dams), the crack positions of the 38 dams and their relationship to dam type and crack origin were assembled into a diagram.

The distribution of dam parameters and crack features and the relationships between them were analyzed. Patterns are not clear, and the number of available cases is limited. However, some apparent trends were outlined, most notably among them are the following:

• Most of the cracked dams have a thermal amplitude higher than 23°;
• Cracks due to chemical reactions generally occur at the downstream face or inside the dam body;
• Single-curvature thin dams do not usually have internal cracks;
• Gravity-arch dams tend to crack in the central zone of the dam upstream and in the central or crest zone of the downstream face.