No. *
* The same serial number multiple times indicates that the UEEWS generated more than one report for that earthquake.
Information about the earthquakes is from the National Center for Seismology (NCS), Ministry of Earth Sciences, Government of India, which determines and reports source parameters of the earthquakes in this region.
Event No. | dd/mm/yyyy | Origin Time (UTC) | Location (Lat, Long) | Depth (km) | Magnitude ( ) | Region |
---|---|---|---|---|---|---|
1 | 29/11/2015 | 02:47:38 | 30.6, 79.6 | 10 | 4 | Chamoli |
2 | 06/12/2017 | 15:19:54 | 30.4, 79.1 | 30 | 5.5 | Rudraprayag |
3 | 17/05/2019 | 19:38:44 | 30.5, 79.3 | 10 | 3.8 | Chamoli |
4 | 08/02/2020 | 01:01:49 | 30.3, 79.86 | 48.2 | 4.7 | Pithoragarh |
5 | 23/05/2021 | 19:01:45 | 30.9, 79.44 | 22 | 4.3 | Chamoli |
6 | 28/06/2021 | 06:48:05 | 30.08, 80.26 | 10 | 3.7 | Pithoragarh |
7 | 11/09/2021 | 00:28:33 | 30.37, 79.13 | 5 | 4.7 | Chamoli |
8 | 04/12/2021 | 20:32:47 | 30.61, 78.82 | 10 | 3.8 | Tehri |
9 | 29/12/2021 | 19:08:21 | 29.75, 80.33 | 10 | 4.1 | Pithoragarh |
10 | 24/01/2022 | 19:39:00 | 29.79, 80.35 | 10 | 4.3 | Pithoragarh |
11 | 11/02/2022 | 23:33:34 | 30.72, 78.85 | 28 | 4.1 | Tehri |
12 | 09/04/2022 | 11:22:36 | 30.92, 78.21 | 10 | 4.1 | Uttarkashi |
13 | 11/05/2022 | 04:33:09 | 29.73, 80.34 | 5 | 4.6 | Pithoragarh |
14 | 06/11/2022 | 3:03:03 | 30.67, 78.6 | 5 | 4.5 | Tehri Garhwal |
15 | 08/11/2022 | 20:27:24 | 29.24, 81.06 | 10 | 5.8 | Dipayal, Nepal |
16 | 12/11/2022 | 14:27:06 | 29.28, 81.2 | 10 | 5.4 | Dipayal, Nepal |
17 | 24/01/2023 | 8:58:31 | 29.41, 81.68 | 10 | 5.8 | Nepal |
18 | 03/10/2023 | 09:21:04 | 29.39, 81.23 | 5 | 6.2 | Nepal |
19 | 03/11/2023 | 18:02:54 | 28.84, 82.19 | 10 | 6.4 | Nepal |
This project “Earthquake Early Warning System for Uttarakhand” is being funded by USDMA, Dehradun, Government of Uttarakhand under the grant number USD-1077-DMC.
Conceptualization, K. and P.K.; Methodology, K. and P.K.; Software, P.K.; Validation, P.K.; Formal analysis, M.L.S.; Investigation, P.K.; Data curation, P.K.; Writing—original draft, P.K.; Writing—review & editing, P.K., K., M.L.S., R.S.J. and P.; Supervision, K. and M.L.S.; Project administration, K.; Funding acquisition, K. All authors have read and agreed to the published version of the manuscript.
Conflicts of interest.
The authors acknowledge no conflicts of interest recorded and declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.
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This paper examines the environmental and economic impact of cloudburst-triggered debris flow and flash flood in four villages of Uttarkashi district, Uttarakhand Himalaya. On 18th July 2021 at 8:30 p.m., a cloudburst took place on the top of the Hari Maharaj Parvat, which triggered a huge debris flows and flash floods, affecting 143 households of four villages of downstream areas. Immediately after the cloudburst occurred, the authors visited four affected villages—Nirakot, Mando, Kankrari, and Siror. A structured questionnaire was constructed and questions were framed and asked from 143 heads of affected households on the impact of debris flows and flash floods on people’s life, settlements, cowsheds, bridges, trees, forests, and arable land in and around the villages. The volume of debris, boulders, pebbles, gravels, and mud was assessed. It was noticed that all four villages got lots of destructions in terms of loss of life—people and animals, and property damage—land, crops, and infrastructural facilities. This study shows that the location of the settlements along with the proximity of the streams, which are very violent during the monsoon season, has led to the high impact of debris flow on the affected villages. We suggest that the old inhabited areas, which are located in the risk zones, can be relocated and the new settlements can be constructed in safe places using suitability analyses.
Cloudburst, a geo-hydrological hazard, refers to a sudden and heavy rainfall that takes place within a short span of time and a particular space (Sati 2013 ). The intensity of rainfall is often more than 100 mm/h (Das et al. 2006 ). The disruptive events, cloudbursts occur during the monsoon season in the Himalaya and trigger debris flows, flash floods, landslides, and mass movements (Fig. 1 ). Fragile landscape, rough and rugged terrain, and precipitous slope accentuate the magnitude of geo-hydrological hazards. Cloudburst-triggered debris flows, flash floods, landslides, and mass movements have become more intensive and frequent worldwide, mainly in the mountainous regions, causing large-scale destruction of people, land, and property (Houghton et al. 1996 ; Wang et al. 2014 ; Mayowa et al. 2015 ; Malla et al. 2020 ; Sim et al. 2022 ). Similarly, the Himalayan region is prone to the occurrences of cloudburst-triggered hazards, causing huge loss of life and property and degradation of forest and arable lands (Bohra et al. 2006 ; Allen et al. 2013 ; Balakrishnan 2015 ; Ruiz-Villanueva et al. 2017 ).
Cloudburst-triggered hazards in the Uttarakhand Himalaya
The Uttarakhand Himalaya, one of the integrated parts of the Himalaya, is the most fragile landscape and prone to geo-hydrological hazards—cloudbursts, avalanches, and glacier bursts (Sati 2019 ). It receives many hazards mainly cloudburst-triggered debris flows, flash floods, landslides, and mass movements during the monsoon season every year. The intensity, frequency, and severity of these hazards have been observed to increase during the recent past. Devi ( 2015 ) stated that the changing monsoon patterns and increasing precipitation in the Himalaya are associated with catastrophic natural hazards. However, these hazards are the least understood because of the remoteness of the areas and lacking meteorological stations (Thayyen et al. 2013 ).
The Uttarakhand Himalaya has many eco-sensitive zones, vulnerable to natural hazards mainly for geo-hydrological hazards. Every year, many cloudburst events occur here, cause to roadblocks, land degradation, forest and cropland loss, and losses of life and infrastructural facilities. One of the most devastating cloudburst-triggered debris flow events of this century occurred on the night of 16th and 17th June 2013 in the famous Hindu pilgrimage ‘Kedarnath’, which killed more than 10,000 people and devastated the entire Mandakini and Alaknanda river valleys (Upadhyay 2014 ; Sati 2013 ). The entire region had received 16 major geo-hydrological and terrestrial hazards within the last 50 years (Bhambri et al. 2016 ). Some of the devastating cloudburst-triggered debris flows and flash floods that occurred in the Uttarakhand Himalaya are Rudraprayag on 14th September 2012, Munsiyari on 18th August 2010, Kapkot on 19th August 2010, Nachni on 7th August 2009, Malpa and Ukhimath on 17th August 1998, Badrinath on 24th July 2004, and the Alaknanda River valley on 1970. About 20,000 people died and a huge loss of property took place due to these calamities (Das 2015 ). It has been noticed that these catastrophic events occurred mainly during the three months of the monsoon season—July, August, and September.
Debris flows and flash floods caused by glacier-bursts incidences were although not much frequent and intensive yet, during the recent past, their number has increased owing to changes in the climatic conditions. The increasing number of infrastructural facilities on the valley bottom has accelerated damages owing to exposed elements in risk-prone areas (Sati 2014 ; ICIMOD 2007a , b ; Chalise and Khanal 2001 ; Bhandari 1994 ; Uttarakhand 2017 ). Many drivers exist, which affect the severity of cloudburst-triggered hazards in the Uttarakhand Himalaya. Growing population and the construction of settlements and infrastructural facilities on the fragile slopes and along the river valleys have also caused severe hazards. The Uttarakhand region is home to world-famous pilgrimages and natural tourism. Mass tourism during the rainy season enhances the intensity of disasters.
Several studies have been carried out on glacier-bursts and cloudburst-triggered debris flows and flash floods in the Himalaya (Shugar et al. 2021 ; Byers et al. 2018 ; Cook et al. 2018 ; Asthana and Sah 2007 ; Bhatt 1998 ; Joshi and Maikhuri 1997 ; NIDM 2015 ; IMD 2013 ; Khanduri et al. 2018 ; Sati 2006 , 2007 , 2009 , 2011 , 2018a , b , 2020 ; Naithani et al. 2011 ). These studies were conducted from broader perspectives, mostly covering the entire Himalaya. However, the present paper looks into the case study of four villages of the Uttarakhand Himalaya, which were severely affected and damaged by cloudburst-triggered debris flows and flash floods, which occurred on July 18th, 2021. It analyses the environmental impact of cloudbursts in terms of forest and fruit trees dislocation, land degradation, and soil erosion—arable, forests, and barren land of the four affected villages. It also evaluates the human and economic losses like the killing of people, loss of existing crops, and damage of houses and cowsheds, respectively. The study suggests policy measures to risk reduction and rehabilitation of settlements from danger zones to safer areas after suitability analysis.
The Uttarakhand Himalaya is located in the north of India and south of the Himalaya. It is also called the Indian Central Himalayan Region. Out of the total 93% mountainous area, 16% is snow-capped, called the Greater Himalaya. The terrain is undulating and precipitous and the landscape is fragile, vulnerable to natural hazards. This catastrophic event occurred in the four villages of Uttarkashi district. The Uttarkashi town lies about 10 km downstream of the affected villages. A National Highway number 108, connecting Haridwar and Gangotri, is passing through Uttarkashi town. The four affected villages—Nirakot, Mando, Kankrari, and Siror are located in the upper Bhagirathi catchment, which is prone to geo-hydrological hazards. The slope gradient of these villages varies from 15° to 70°. Indravati is a perennial stream, a tributary of the Bhagirathi River that meets Bhagirathi from its left bank. All three Gadheras (streams)—Mando, Diya, and Siror are seasonal but violent during the monsoon season. Nirakot (1530 m) village is located in the middle altitude of the Hari Maharaj Parvat (2350 m) in a steep slope, Mando village (1180 m) is located on the left bank of the Bhagirathi River along the Mando Gadhera with gentle to a steep slope, Kankrari (1620 m) village is located on the moderate to the gentle slope on the bank of the Diya Gadhera, and Siror village (1280 m) is situated on the left bank of both Bhagirathi and Siror Gadhera with gentle to the steep slope (Fig. 2 ). One of the prominent eco-sensitive zones of the Uttarakhand Himalaya, the ‘Bhagirathi Eco-Sensitive Zone’ is 120 km long, spanning from Uttarkashi to Gaumukh, along the Bhagirathi River valley (Sati 2018a , b ). The rural people depend on the output of the traditional farming systems, often face intensive natural hazards. The settlements are located either on the fragile and steep slopes or on the banks of streams, which are very violent during the monsoon season when a heavy downpour occurs. Therefore, heavy losses of life and property in these areas are common, taking place every year.
Location map of cloudburst source and hit areas and their surroundings
This study was empirically tested and a qualitative approach was employed to describe data. A structured questionnaire was constructed. The main questions framed and asked from the heads of households were—human and animal death, damage to self property—houses and cowsheds, and existing crops—cereals, fruits, and vegetables. Loss to public properties such as bridges, public institutions, and forest land was assessed. Based on the questions framed, we surveyed 143 heads of households of four villages, which were partially or fully affected due to cloudburst-triggered debris flow. These villages are Nirakot, Mando, Kankrari, and Siror. To assess the debris and the damaging areas, the authors travelled from the source areas to the depositional zones and measured the volume of debris—boulders, pebbles, sands, and soils using a formula; circumference = 2πR and area = π * R 2 . The slope gradient, accessibility, economic conditions, and climate of the villages were assessed and based on which, the susceptibility analysis of the villages was carried out. The villages were divided into very high susceptibility, high susceptibility, and moderate susceptibility levels. Both environmental degradation and economic losses in four villages were assessed. We used Geographical Positioning System (GPS) to obtain the data of altitude, longitude, and latitude. Two maps—case study villages and the major cloudburst incidences—2020 and 2021 were prepared and data were also presented using graphs. Photographs of four villages were used to present the destruction of villages due to the cloudburst event.
Major cloudburst incidences in the uttarakhand himalaya.
Past incidences depict that the Uttarakhand Himalaya suffered tremendously due to cloudburst-triggered calamities. We gathered data on the major cloudburst incidences in Uttarakhand in the monsoon seasons of 2020 and 2021 from the state disaster relief force (SDRF), Dehradun. From May to September 2020, 13 major cloudburst incidences were noticed in Uttarakhand (Table 1 ). These incidences resulted in the death of 22 people and 77 animals, and 19 houses were fully damaged. Similarly, from May to September 2021, 17 major cloudburst incidences were occurred in the Uttarakhand Himalaya, resulting in the death of 34 people and 144 animals, and 106 houses were buried. Besides, it caused a huge loss to public property and landscape degradation.
The economic losses in 2021 were much higher than the losses in 2020 (Fig. 3 ). In 2021, the frequency and intensity of cloudburst-triggered calamities were also higher. The loss of animals was quite high both the years. Houses that collapsed due to calamity were six times higher in 2021 than in 2020. The loss of human life was substantial in both years. Several bridges were washed away.
Loss of human lives, livestock, houses and bridges due to cloudburst in Uttarakhand during the 2020 and 2021
District-wise major cloudburst events of 2020–2021 are shown in the map of the Uttarakhand Himalaya (Fig. 4 ). A total of 30 major cloudburst incidences were recorded, out of which, 17 occurred in 2021. The Uttarkashi district received the highest incidences (07), followed by the Chamoli district (05). Dehradun and Pithoragarh districts have recorded 04 incidences each. Rudraprayag 03 and Tehri, Almora, Bageshwar have recorded 01 each. It has been observed that cloudburst-triggered incidences mainly occurred in remote places along the fragile river valleys and middle slopes.
Location map of cloudbursts hit areas in 2020 and 2021
On July 18, 2021, a cloudburst hits the Hari Maharaj Parvat (hilltop) at an altitude of 2350 m at 8:30 p.m., which triggered huge debris flows and flash floods. The four villages—Nirakot, Mando, Kankrari, and Siror of Uttarkashi district, located down slopes of the hilltop and close to the Uttarkashi town, were severely affected due to debris flow (Table 2 ). At the cloudburst hit area, it formed three gullies, which later on merged into three streams, along which these villages are located. Debris, from the source i.e. hilltop of Hari Maharaj Parvat, equally flew in three directions. Since the cloudburst event occurred at 8:30 p.m., the people did not have time to move with their movable property and therefore, the magnitude of damage was enormous.
The villages are located from the altitudes of 1180 m (lowest) to 1620 m (highest). Mando village is located at 1180 m, Kankrari village at 1620 m, Nirakot at 1530 m, and Siror has 1280 m altitude. The two villages—Nirakot and Mando have west-facing slopes, Kankrari has a south-facing slope, and Siror has a north-facing slope. These villages are located along the tributaries of the Bhagirathi River, with 2 to 5 km distance from the road. The intensity and volume of debris were different in different villages, therefore, the casualties and losses were also varied. The villages are surrounded by agricultural and forestlands. The farmers mainly grow subsistence cereal crops—paddy, wheat, pulses, oilseeds, fruits, and vegetables. Forest types comprise pine (sub-tropical) and oak and coniferous forests (temperate), used for fodder, firewood, and wild fruits.
Located at the high-risk zones, these villages face several disaster incidences every year. Out of the total 143 heads of households surveyed, more than 80% of heads were in favour of rehabilitating them in the safer areas. They wanted to relocate their houses and cowshed within the village territory with financial assistance from the state government. The streams, along which the settlements are constructed, are fragile and highly vulnerable to landslide hazards. Further, the cloudburst incidences are increasing due to climate change, the heads of households perceived.
Figure 5 shows four villages—Nirakot, Mando, Kankrari, and Siror, which were severely affected by cloudburst-triggered debris flow and flash flood. The volume of debris and boulders can be seen in all the villages. These villages are surrounded by dense sub-tropical and temperate forests that vary from pine to mixed-oak and deodar. Kharif crops were growing in the arable land whereas a large cropland has been washed away.
Cloudburst affected villages a Nirakot, b Mando, c Kankrari, d Siror; Photo: by authors
Environmental impact.
The environmental impact of cloudburst-triggered debris flow and flash flood in four villages of Uttarkashi district was analyzed (Table 3 ). The major variables were the number of forest trees dislocated, total land degradation, land degradation under existing crops, number of fruit trees dislocated, land degradation under arable land, number of buildings were damaged, number of bridges damaged, and boulders’ volume. Forest trees, which dislocated were pine in the middle altitude and mixed-oak and deodar in the higher altitude. A total of 770 forest trees were dislocated from all four villages, out of which, 500 were from the Kankrari village (highest). The lowest trees dislocated were from Siror village (70). The total land degradation from the cloudburst hit areas to the affected areas was huge, however, we have measured the land which was within and surrounding each village. The total land degradation was 52.5 acres with the highest in Kankrari (45 acres) and the lowest in Siror (0.5 acres). The land degradation under existing crops was 22.6 acres in all four villages, varying from 0.1 acres in Siror to 20.6 acres in Kankrari. The total number of fruit trees dislocated was 486. Land degradation under arable land was 22.6 acres. It includes the area under existing crops both agriculture and horticulture. A total of 19 buildings were damaged whereas a total of 14 bridges, connecting the affected villages were washed away.
The economic impact due to cloudburst calamity was tremendous in the forms of a household affected, loss of human and animal life, building loss, forest loss, loss of existing crops including fruits, loss of arable land, and loss of bridges (Table 4 ). The value of all these assets was calculated in Indian Rupees (INR) at the current price. The total number of households affected was 143, of which, 100 households belonged to the Kankrari village (highest) and three households (lowest) were from Siror village. Four people died due to the calamity—three women from Mando village and 1 man from Kankrari village. Two cows from Mando village died. The total loss from the collapse of the building was 1.7 million INR, with the highest (1.1 million INR) from Kankrari village. A total of 0.77 million INR was lost due to forest loss, and the loss from existing crops was 3.35 million INR. Loss from dislocation of fruit trees was noted high, which was about 0.5 million INR. A large portion of arable land was flown which value was 11.3 million INR. About 14 million INR was lost due to the collapse of bridges. As a whole, about 31.62 million INR was lost due to cloudburst calamity. Per household loss by the cloudburst calamity was noted 0.22 million INR.
We calculated the average circumference, area, and volume of boulders in the case study villages using a formula: circumference = 2πR; Area = π * R 2 ; volume = length × width × depth (Table 5 ). We noticed that the highest average area of boulders was in Mando village, which is 28.3 m 2 followed by Kankrari 19.6 m 2 , Nirakot 12.57 m 2 , and Siror 7.1 m 2 . In terms of the total volume of debris, it was the highest in Kankrari village, followed by Mando, Nirakot, and Siror villages.
Figure 6 shows the average diameter of boulders in the cloudburst-affected villages. We drew the figure with a scale of 1 cm is equal to 1 m. The average biggest diameter of boulders was found in Mando village (6 m), followed by Kankrari (5 m) and Nirakot (4 m) villages. The average smallest diameter of boulders was found in Siror village (3 m).
Village-wise average diameter of boulders
Based on the above description, susceptibility analysis of the case study villages was carried out (Table 6 ). The main variables of susceptibility were slope gradient, accessibility of villages, economic conditions of households, and climatic conditions. We noticed that Nirakot village has very high susceptibility, Kankrari has high, and Siror and Mando have moderate susceptibility.
The Uttarakhand Himalaya is highly vulnerable to geo-hydrological disasters because of its geological formation (Vaidya 2019 ). It is an ecologically fragile, geologically sensitive, and tectonically and seismically very active mountain range (Sati 2019 ). The geo-hydrological events—cloudbursts and glacier bursts-triggered catastrophes are very common and devastating. The monsoon season poses severe threats to natural hazards because of heavy downpours. About 93% of the Uttarakhand Himalaya is mountainous mainland, of which 16% is snow-capped. The undulating and precipitous terrain and remoteness are the most vulnerable for disaster risks.
This study reveals that most of the cloudbursts incidences in 2020–21 occurred mainly in the remote mountainous districts of the Uttarakhand Himalaya. The villages in the Uttarakhand Himalaya are located on the sloppy land and along the river valleys, which are fragile and very vulnerable to disasters. The rivers flow above danger marks during the monsoon season cause threats to rural settlements. The roads of Uttarakhand are constructed along the river banks and on fragile lands. These roads lead to the highland and river valley pilgrimages where the number of tourists and pilgrims visit every year mainly during the monsoon season. There are many locations along the river valleys where the houses are constructed on the debris, deposited by rivers during debris flow events. Therefore, the environmental and economic losses due to debris flows and flash floods are high. The construction of hydropower projects along the river valleys without using sufficient technology further accentuates the vulnerability of debris flows and flash floods. One of the recent examples is the Rishi Ganga tragedy in Chamoli district where more than 200 people died with a huge loss to property (Sati 2021 ). We observed that the cloudburst triggered calamity in 2021 was higher than in 2020. The trend of occurring natural hazards has been increasing. Similarly, the intensity and frequency of natural hazards were observed high.
The present study shows that the environmental and economic loss in the four villages of the Bhagirathi River valley was huge due to cloudburst-triggered debris flows and flash floods. Almost every household of the villages were affected by cloudburst calamity. There were large forest and arable land degradation, forest and fruit trees were dislocated, loss of life—human and animal, and the houses and bridges were collapsed. The calamity also poses threat to the future, in terms of, the large deposition of debris including boulders, pebbles, and gravels in the villages along the streams and gullies. The rural people are poor and their livelihood is dependent on practicing subsistence agriculture. Many of them are living below the poverty line in these villages. Because the existing crops have been lost, they are facing food insecurity. Further, the psychological problems are immense. The fear of another calamity is always there in the mind of people as all villages are situated in very high to moderate susceptible areas. The national highway is passing through the right bank of the Bhagirathi River and the affected villages are situated on the left bank. The connectivity problem is immense all the time in these villages. The entire rural areas of the Uttarakhand Himalaya are facing similar problems.
Cloudburst-triggered debris flows and flash floods are natural calamities in the Himalayan regions. They occur naturally and cannot be stopped. The losses—environmental and economic are also huge. However, the severity of these natural calamities can be minimized. For example, the high impact of cloudburst-triggered debris flow on the four study villages was mainly due to their location along the streams and on the fragile slopes. This can be avoided by constructing the settlements in safer places generally away from the violent streams. In the disaster risk zones, scenario analysis can be carried out under which, identifying driving forces of disaster risks is the first step. Then, the critical uncertainties are to be identified, and finally, a possible scenario can be developed. Nature-based eco-disaster risk reduction can be adopted to prevent further disaster risks. A large-scale plantation drive in the degraded land will restore the fragile landscape. Both pre and post-disaster risk reduction measures can be adopted to reduce the economic and environmental impact of debris flows. There must be policies implementation programmes for providing immediate relief packages for the affected people in terms of food and shelters. In a long run, susceptibility analyses should be carried out to understand the risk to the settlements so that the settlements can be replaced on the safer side if needed. A special budget can be allocated to hazard-prone villages during adverse situations.
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Vishwambhar Prasad Sati & Saurav Kumar
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Sati, V.P., Kumar, S. Environmental and economic impact of cloudburst-triggered debris flows and flash floods in Uttarakhand Himalaya: a case study. Geoenviron Disasters 9 , 5 (2022). https://doi.org/10.1186/s40677-022-00208-3
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Paritosh Yadav
Smriti Saraswat , Gautam Mayuresh
‘Koti Banal’ architecture of Uttarakhand is a reflection of indigenous realities and community involvement. It demonstrates a profound knowledge of local materials and native sensibilities. Investigations suggest that this is an earthquake-safe construction style done in timber and stone, which evolved as early as 1000 years ago. This paper is an attempt to study the Koti Banal architecture of Uttarakhand and understand the craft nurtured by the indigenous communities using locally available materials in response to earthquakes. In fact, the Koti Banal architecture is much like the framed construction of modern times. The structural design suggests that these buildings responded well to the forces likely to act upon them during an earthquake. The paper further investigates what are the modifications that have happened in this style of architecture with respect to morphology and materials, through three case studies done in the Garhwal region. This is primarily a descriptive research based on a case study (field study) approach, which focuses on traditional knowledge systems; indigenous building materials; community involvement; and, craft skills of Uttarakhand. Keywords Koti Banal Architecture; Uttarakhand; Indigenous; Craft; Materials; Community; India
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The existing Reinforced Concrete (RC) buildings stock is often characterized by a significant seismic vulnerability, due to the absence of capacity design principles, even in regions with high seismic hazard, such as Italy. Approximately 67% of existing RC buildings in Italy have been designed without considering seismic actions (GLD), resulting in very low transverse reinforcement amount in beams and, particularly, in columns. Additionally, beam-column joints typically totally lack stirrups. Consequently, shear failures under seismic actions are very likely for this pre-code building typology, often limiting their seismic capacity. However, the assessment of shear failures in beams/columns or joints varies significantly from code to code worldwide. The main goal of this work is to quantify the impact of different code-based brittle capacity models on the seismic capacity assessment and retrofit, focusing on GLD Italian pre-1970 RC buildings. This comparative analysis is carried out by first considering three current codes, emphasizing their, even significant, differences: European (EN 1998-3-1. 2005), Italian (D.M. 2018), and American (ASCE SEI/41 2017) standards. Then, shear capacity models prescribed by the current drafts of the next generation of Eurocodes are implemented and compared to the current models. The assessment includes: ( i ) a parametric comparison among models; ( ii ) the evaluation of case-study buildings capacity in their as-built condition and after shear strengthening interventions. The latter is performed on 3D “bare” models, due to the lack of practical guidance in most codes on modelling masonry infills.
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Post-earthquake surveys worldwide have brought to light the significant impact of shear failures in beams, columns, or beam-column joints on the seismic performance of existing reinforced concrete (RC) buildings. Recent catastrophic seismic events (e.g., Verderame et al. 2014 ; Masi et al. 2019 ) have highlighted the detrimental effects of inadequate transverse reinforcements or the absence of seismic detailing, especially in joint regions and columns, on the structural response. Consequently, ensuring the accurate estimation of shear capacity is imperative for a comprehensive evaluation of the structural performance (Karakas et al., 2022 ; Lupoi et al. 2004 ) and the design of effective retrofitting strategies.
In the literature, a multitude of shear capacity models for existing beam-column elements have been formulated by means of an empirical approach. Several of these (Priestley et al. 1994 ; Sezen and Moehle 2004 ; Biskinis et al. 2004 ; Kowalsky and Priestley 2000 ) forecast a deterioration in shear strength under seismic cyclic loading as ductility demand rises. Nonetheless, despite being conceptually rooted in the same theory, these models exhibit significant differences. Shear resistance is primarily attributed to two factors: one associated with the presence of transverse reinforcements, and the other reliant on the concrete resisting mechanisms. Nevertheless, some models relegate the strength cyclic degradation to the concrete resisting contributions only (e.g, Priestley et al. 1994 ), owing to a progressive reduction in load-carrying capacity with crack propagation. Other models extend the shear strength degradation to the contribution of transverse reinforcement, considering the potential loss of anchorage and bond capacity of the reinforcement due to concrete cracking (Sezen and Moehle 2004 ; Biskinis et al. 2004 ). In addition, among the various capacity models, there is not unanimous agreement on the definition of resistance contributions, especially about the concrete strength contribution. For example, Sezen and Moehle ( 2004 )’s model evaluates this contribution using the Mohr’s circle approach including the influence of axial load. In contrast, Biskinis et al. ( 2004 )’ s model considers the axial load with an additional resistance contribution, not subjected to any cyclic degradation effect.
In addition to empirical capacity models, the shear strength of RC elements can be assessed through the application of the Modified Compression Field Theory (Vecchio and Collins 1986 ) or its simplified variants (Bentz et al. 2006 ; CSA Standard, 2006 ; Model Code, 2010 ; Marcantonio et al. 2015 ). This theory represents the latest advancement of an approach that originated in the early 1900s, according to which the shear strength of a RC element is governed by a truss mechanism (Ritter 1899 ; Morsch 1909 ) with compressive stresses inclined at 45° to the longitudinal axis of the element. This very first model neglected any contribution by the cracked concrete, potentially resulting in overly conservative estimates of shear strength for elements with limited transverse reinforcement. Moreover, studies from the 1980s revealed that the inclination angle is seldom exactly 45°. The necessity for a rational determination of this angle gave rise to the Compression Field Theory (CFT, Collins 1978 ), subsequently modified to consider the tensile stresses in the cracked concrete (MCFT, Vecchio and Collins 1986 ). The method estimates the inclination angle based on the strain distribution in the cross-section of the element and it has been suggested by the Model Code ( 2010 ) - with different levels of approximations (Model Code, 2010 ; Biskinis and Fardis 2020 ).
In last years, many experimental works have been conducted focusing on the estimation of the shear strength of beam-column joints without transverse reinforcement, which typically characterize existing buildings. Most of these studies focus on exterior joints (e.g., Vollum and Newman 1999 ; Pantelides et al. 2002 ; Tsnos, 2007 ), generally more vulnerable, identifying the parameters that can most significantly affect joint strength. Among these parameters, in addition to joint configuration (interior or exterior) and concrete compressive strength (Priestley 1997 ; Kim and LaFave 2012 ), the joint aspect ratio, the beam longitudinal reinforcement ratio (Park and Mosalam 2012 ), and the column axial load (Priestley 1997 ) were identified as key factors, as also confirmed by Jeon et al. ( 2014 ) based on a wide experimental dataset. Nevertheless, there is not a full consensus within the research community about the influence of some factors on the joint shear strength. For example, several studies acknowledge the influence of axial force only on the deformability of the joint and not on its strength (e.g. Fujii and Morita 1991 ; Park and Mosalam 2012 ). An increase in column axial load has not or limited influence on interior and exterior joints strength respectively, according to Fujii and Morita ( 1991 ). A detrimental effect on the joint shear strength due to high axial loads has been observed by Li et al. ( 2015 ).
The discrepancies among the different brittle capacity models proposed in the literature, both for beam/column elements and beam-column joints, have been integrated into various national standards (e.g., EN 1998-3, 2005 ; D.M. 2018 ; ASCE/SEI-41, 2017 ; NZS 3101, 2006 ), and, thus, the assessment of the seismic capacity of RC buildings is based on technical codes that rely on (often very) different capacity models.
This study aims at investigating the potential impact of using different code-based brittle capacity models first in terms of parametric comparison and, then, by applying them on the seismic assessment and retrofit of RC case-study buildings. This assessment is conducted through nonlinear static pushover analysis within the N2 framework (Fajfar 2000 ) on Italian pre-1970 (“pre-code”) case-study buildings with different numbers of stories, in both the as-built condition and after the implementation of a retrofitting strategy that addresses brittle tensile-only failures (De Risi et al. 2023a ). Three current code prescriptions are considered herein: the current Eurocode 8 (labelled “EC8 2005” in what follows) (EN 1998-3, 2005 ), Italian technical code D.M. ( 2018 ) (labelled “NTC 2018” hereinafter), and American standards “ASCE/SEI” (ASCE/SEI-41, 2017 ). Based on European and Italian codes (EC8 2005 ; NTC 2018) approach, the building capacity at the Severe Damage (SD) Limit State (LS) is always assessed as that corresponding to the first failure attained at that LS. It is worth noting that this choice of “failure” criterion is certainly conservative with respect to the “real” (sidesway or gravity load) collapse of a building (Shoraka, 2013 ), as well know, but it is also more conservative with respect to other code-based approach (e.g. Turkish TBEC 2018 , according to which a certain percentage of RC members can reach a given LS). Due to the main aim of this study, the sole distinction among the code cases applied herein lies in the implemented brittle capacity models, while the framework for determining the seismic capacity remains consistent with the European codes: the seismic demand is uniform across all code cases (in contrast to Dhanvijay and Nair, 2015 ), and the ductile capacity of beam/column elements is always defined as prescribed by EC8 2005 (and NTC 2018).
Within the codes framework, brittle failures are typically identified through post-processing the data obtained from (linear or) nonlinear analyses. However, it is worth noting that American standards also explicitly provide tools to model the nonlinear behaviour of shear-sensitive elements, including beam-column joints (i.e., scissor model, Alath and Kunnath 1995 ), providing the backbone for their implementation (ASCE/SEI-41, 2017 ; Hassan 2011 ; Hassan and Elmorsy 2022a , b ).
Lastly, it is worth noting that, very recently, some works from the literature focused on the analysis of the capability of code prescriptions to catch real capacity and seismic damage extend and severity in existing buildings. Cook et al. ( 2023 ) and Sen et al. ( 2023 ) analysed the results of structures experimentally damaged via shake tables testing, to compare the experimental response with the simulated outcomes following ASCE/SEI 41 application, aiming at promoting its improvement. Similarly, in European context, a challenging work is currently ongoing by several European research groups to update the current European standards (e.g., Fardis ( 2021 ), Biskinis and Fardis ( 2020 ), Franchin and Noto ( 2023 ), Maranhão et al. ( 2024 ), among others). Therefore, a focus on the brittle capacity models of the (current draft of the) incoming second-generation Eurocode 8 - currently ongoing and in its final steps of development - is carried out in this work. Some studies from the literature have already started analysing the main differences compared to the current version. For instance, the design of moment resisting frame RC buildings according to the second-generation code has been compared to the previous EC8 version in Maranhão et al. ( 2024 ). The next-generation EC8 will modify the current shear strength model of beam-column joints (Fardis 2021 ) and change significantly the brittle capacity model to be used for beam/column members, moving from the empirical model by Biskinis et al. ( 2004 ) (EC8 2005 ) to a MCFT-based approach (Biskinis and Fardis 2020 ). Such novelties could potentially be very impactful and, thus, they are investigated in this work.
In this section, a description of some of the main shear capacity models currently adopted worldwide for beams/columns and joints is provided. The capacity models adopted by the current European (EC8 2005 ), Italian (NTC 2018; Circolare 2019 ), and American (ASCE/SEI) technical standards are analysed. A parametric comparison is also carried out to identify hierarchies and trends in resulting strengths.
Nowadays, worldwide, the shear strength of existing RC beam/column elements is generally evaluated using “degrading” models (De Luca and Verderame 2013 ), which predict a decreasing shear strength as the plastic displacement demand increases.
According to EC8 2005, the shear strength (V R ) of a beam/column element is calculated as proposed by Biskinis et al. 2004 ( \(\:{\text{V}}_{\text{R},\text{B}\text{I}\text{S}}\) ), namely, as the sum of three contributions:
In Eq. ( 1 ), the coefficient γ el , accounting for uncertainties in fitting experimental data, is equal to 1.15 for primary elements. \(\:{\text{V}}_{\text{N}}\) is the contribution due to the presence of compressive axial load N (Paulay and Priestley 1992 ). The latter is limited to 55% of the maximum axial load that the concrete section can sustain (i.e., \(\:{\text{A}}_{\text{c}}{\text{f}}_{\text{c}}\) , being \(\:{\text{A}}_{\text{c}}\) the area of the concrete cross-section and \(\:{\text{f}}_{\text{c}}\) the concrete compression strength). \(\:\text{h}\) is the section height, x the neutral axis depth, and \(\:{\text{L}}_{\text{v}}\) the element shear span. The contribution of the post-cracking concrete resistance mechanisms, \(\:{\text{V}}_{\text{c}}\) , can be expressed as α times √f c \(\:{\cdot\:\text{A}}_{\text{c}}\) . The term α depends on the total geometric percentage of the longitudinal reinforcement, \(\:{{\rho\:}}_{\text{t}\text{o}\text{t}}\) , and on the slenderness of the element, \(\:{\text{L}}_{\text{V}}/\text{h}\) . Lastly, the contribution of the transverse reinforcement, \(\:{\text{V}}_{\text{w}}\) , is the same proposed by Ritter-Morsch model (Ritter 1899 ; Morsch 1909 ). Thus, it depends on the stirrups area ( \(\:{\text{A}}_{\text{s}\text{w}}\) ), yielding strength ( \(\:{\text{f}}_{\text{y}\text{w}}\) ), and spacing (s), and on the internal lever arm (z) - assumed hereinafter as 0.9 times the cross-section effective depth, d.
According to EC8 2005, V R degrades by means of the coefficient, \(\:\text{k}.\) The latter decreases as displacement ductility demand (µ Δ ) increases (Fig. 1 ), moving linearly from 1 (no degradation) to 0.75 (maximum degradation).
Shear capacity model according EC8-2005 and NTC 2018 ( a ); degradation coefficient according to EC8 2005 and ASCE/SEI-41 ( b )
It is worth underlying that the EC8 2005 provides materials strengths reduction factors for safety check at SD LS. In particular, the mean strengths resulting from in-situ tests must be divided by the partial safety factor (γ c = 1.50 for concrete and γ s = 1.15 for steel) and by the Confidence Factor (i.e., CF) depending on the Knowledge Level (KL). In this work, a comprehensive KL has been always assumed, and, thus, CF = 1.00.
The same shear capacity model is (partially) adopted also by Italian technical code (NTC 2018), which introduces a modification for low µ Δ levels, by using the truss model of shear resistance with variable inclination diagonals (Biskinis and Fardis 2004 ). The latter is hereinafter referred to as Variable Inclination Truss (i.e., VIT) model. In particular, V R is the same provided by EC8 2005 model when µ Δ ≥ 3 (i.e., V R, NTC18 =V R, EC8 ). When µ Δ ≤ 2, V R is the maximum between the values provided by EC8 2005 model and VIT model. Lastly, for intermediate ductility demand, V R, NTC18 is obtained by linearly interpolating between the two models (Fig. 1 a). As well known, according to VIT model (prescribed for not-seismic loadings by NTC 2018 and EN 1998-1, 2004 ), the shear strength ( \(\:{\text{V}}_{\text{R},\text{V}\text{I}\text{T}}\) ) is the minimum between compressed strut strength, \(\:{\text{V}}_{\text{R}\text{c}}\) , and the tensile strength of the transverse reinforcement, \(\:{\text{V}}_{\text{R}\text{s}}\) , i.e. (in case of stirrups):
In Eq. ( 2 ), \(\:{\theta\:}\) is the inclination angle of the compressed struts with respect to the longitudinal axis of the element, b the web width, \(\:\stackrel{-}{{\nu\:}}\) is equal to 0.5, and \(\:{{\alpha\:}}_{\text{c}}\) is a function of N. According to Italian code, \(\:\text{c}\text{o}\text{t}{\theta\:}\) in Eq. ( 2 ) mut be limited between 1.00 and 2.50.
Similarly to European code, Italian guidelines also require that materials strengths must be divided by the partial materials factors and by the CF for safety checks at SD LS.
The model adopted by ASCE/SEI ( \(\:{\text{V}}_{\text{R},\text{A}\text{S}\text{C}\text{E}}\) ) is based on Sezen and Moehle ( 2004 )’s model, i.e. an additive degrading model relying on two contributions: \(\:{\text{V}}_{\text{c}}\) , due to concrete post-cracking mechanisms and axial load, and \(\:{\text{V}}_{\text{w}}\) .
where \(\:{\text{V}}_{\text{w}}\) has the same meaning of Eq. ( 1 ). According to this model, the degradation coefficient \(\:\text{k}\) is equal to 1.00 for µ Δ ≤ 2, and 0.70 for µ Δ ≥ 6, varying linearly between these two bounds (Fig. 1 b). ASCE/SEI model predicts a higher strength degradation compared to EC8 2005. Indeed, on one hand, the “residual” strength is derived from a lower degradation coefficient \(\:\text{k}\) ( \(\:\text{k}=0.70\) ); on the other hand, this coefficient multiplies all the strength contributions (even that related to the axial load).
The material strengths to be used for assessment are, also in this case, the reduced strengths. However, while γ c assumes the same value provided by European codes, γ s is higher (i.e., 1.25). Furthermore, this standard prescribes that, in case of “comprehensive” knowledge (maximum level), CF is equal to the 1.
In existing structures, especially if designed for gravity loads only, structural elements often have low transverse reinforcement ratios. In this hypothesis, the strength provided by the VIT model, coincides with \(\:{\text{V}}_{\text{R}\text{s}}\) evaluated with \(\:\text{c}\text{o}\text{t}{\theta\:}=2.5\) . Thus, in these cases, \(\:{\text{V}}_{\text{R},\text{V}\text{I}\text{T}}=\text{min}({\text{V}}_{\text{R}\text{c}};{\text{V}}_{\text{R}\text{s}})={\text{V}}_{\text{R}\text{s}}={\text{V}}_{\text{w}}\text{c}\text{o}\text{t}{\theta\:}=2.5{\text{V}}_{\text{w}}\) .
For high plastic demands, Italian and European codes provide the same shear strength. On the contrary, a difference is observed when µ Δ ≤ 3. This difference (Eq. ( 4 )) is maximized in absence of strength degradation ( \(\:\text{k}=1\) ) and can be expressed as the sum of three terms. They depend on five parameters: axial load ratio \(\:{\nu\:}=\text{N}/\left({\text{A}}_{\text{c}}{\text{f}}_{\text{c}}\right)\) , mechanical percentage of shear reinforcement \(\:{{\omega\:}}_{\text{s}\text{w}}={\text{A}}_{\text{s}\text{w}}{\text{f}}_{\text{y}}/\left(\text{b}\cdot\:\text{s}\cdot\:{\text{f}}_{\text{c}}\right)\) , the above-defined \(\:{\text{L}}_{\text{V}}/\text{h}\) , \(\:{{\rho\:}}_{\text{t}\text{o}\text{t}}\) , and the mean concrete compressive strength, \(\:{\text{f}}_{\text{c}\text{m}}\) .
In Eq. ( 4 ), \(\:{\Delta\:}{{\text{V}}_{\text{R}}}^{\text{E}\text{C}8-\text{V}\text{I}\text{T}}\) is the difference between \(\:{\text{V}}_{\text{R},\text{E}\text{C}8}\) and \(\:{\text{V}}_{\text{R},\text{V}\text{I}\text{T}}\) , and it is normalized with respect to the quantity \(\:{\text{A}}_{\text{c}}{\cdot\:\text{f}}_{\text{c}\text{m}}\) . So, when the combination of the five parameters above leads to positive values of ΔV R , \(\:{\text{V}}_{\text{R},\text{E}\text{C}8}\) > \(\:{\text{V}}_{\text{R},\text{V}\text{I}\text{T}}\) . Note that \(\:{\text{f}}_{\text{c}}\) and \(\:{\text{f}}_{\text{c}\text{m}}\) represent both the concrete compressive strength, but the latter is a mean value (derived from in-situ tests), whereas the former is evaluated as \(\:{\text{f}}_{\text{c}}={\text{f}}_{\text{c}\text{m}}/\left(\text{C}\text{F}\cdot\:{{\gamma\:}}_{\text{c}}\right)\) .
The same normalized difference can be evaluated by comparing the non-degraded shear strengths resulting from the European and American codes, as shown in Eq. ( 5 ) (which results quite similar to Eq. ( 4 )):
Note that the expressions above assume that:
\(\:{{\rho\:}}_{\text{t}\text{o}\text{t}}\) is not lower than 0.50% (in tune with the definition of α in Eq. ( 1 ));
\(\:{{\omega\:}}_{\text{s}\text{w}}\) is compatible with the assumption of a weakly reinforced element (i.e., not exceeding 0.07, value which provides \(\:\text{c}\text{o}\text{t}{\theta\:}\) always limited to 2.5), as typical in existing buildings;
\(\:{\text{L}}_{\text{V}}/\text{h}\) ranges between 2 and 4 (considering the limitations of ASCE model);
the cross-section height, h, has been confused with its effective depth, \(\:\text{d}\) , for sake of simplicity.
Figure 2 shows the isocurves corresponding to \(\:{{\Delta\:}\text{V}}_{\text{R}}=0\) resulting from Eq. ( 4 ) (in grey scale) and Eq. ( 5 ) (in blue scale). They display when the code models provide the same strength. Three possible values of \(\:{\text{L}}_{\text{V}}/\text{h}\) and \(\:{\text{f}}_{\text{c}\text{m}}\) are assumed in Fig. 2 (i.e., \(\:{\text{L}}_{\text{V}}/\text{h}=2;3;4,\) and \(\:{\text{f}}_{\text{c}\text{m}}=10;20;30\:\) MPa). The axial load ratio \(\:{\nu\:}\) varies between 0 and 0.5. Each isocurve corresponds to a different value of \(\:{{\rho\:}}_{\text{t}\text{o}\text{t}}\) (ranging between 0.50% and 2.00%). It can be noted that:
Isocurves corresponding to \(\:{\varDelta\:V}_{R}=0\) , varying \(\:\frac{{L}_{V}}{h}\) , \(\:{f}_{c}\) , \(\:{\omega\:}_{sw}\) , \(\:\nu\:\) , and \(\:{\rho\:}_{tot}\) , resulting from the comparison between \(\:{V}_{R,EC8}\) with \(\:{V}_{R,VIT}\) (in gray scale) and with \(\:{V}_{R,ASCE}\) (in blue scale)
for low values of \(\:{{\omega\:}}_{\text{s}\text{w}}\) and high values of \(\:{\nu\:}\) , \(\:{\text{V}}_{\text{R},\text{E}\text{C}8}\) results higher than the other two models. Actually, according to NTC 2018, for \(\:{\text{V}}_{\text{R},\text{E}\text{C}8}\) > \(\:{\text{V}}_{\text{R},\text{V}\text{I}\text{T}}\) , \(\:{\text{V}}_{\text{R},\text{N}\text{T}\text{C}18}{=\text{V}}_{\text{R},\text{E}\text{C}8}\) , and, thus, both codes provide exactly the same shear strength;
the area where \(\:{{\Delta\:}\text{V}}_{\text{R}}>0\) covers wider ranges of \(\:{{\omega\:}}_{\text{s}\text{w}}\) and \(\:{\nu\:}\) values when \(\:{{\rho\:}}_{\text{t}\text{o}\text{t}}\) is high;
the latter effect is more pronounced when comparing \(\:{\text{V}}_{\text{R},\text{E}\text{C}8}\) and \(\:{\text{V}}_{\text{R},\text{A}\text{S}\text{C}\text{E}}\) , and when considering upper bounds of \(\:{\text{f}}_{\text{c}\text{m}}\) and lower bounds of \(\:{\text{L}}_{\text{V}}/\text{h}\) .
Another useful representation of the differences among the considered models is shown in Fig. 3 . A “central” value of \(\:{{\eta\:}}^{\text{E}\text{C}8-\text{V}\text{I}\text{T}}\) (and \(\:{{\eta\:}}^{\text{E}\text{C}8-\text{A}\text{S}\text{C}\text{E}}\) ) is calculated by using mean values (within the above-defined ranges of variation) of the 5 key parameters (central value of \(\:{{\eta\:}}^{\text{E}\text{C}8-\text{V}\text{I}\text{T}}\) and \(\:{{\eta\:}}^{\text{E}\text{C}8-\text{A}\text{S}\text{C}\text{E}}\) results − 0.010 and 0.021, respectively). Then, the 5 parameters have been varied one-by-one to assume their upper or lower bound values (within the above-defined ranges of variation), and corresponding \(\:{{\eta\:}}^{\text{E}\text{C}8-\text{V}\text{I}\text{T}}\) (and \(\:{{\eta\:}}^{\text{E}\text{C}8-\text{A}\text{S}\text{C}\text{E}}\) ) are evaluated. Lastly, the relative variation (Ω) of \(\:{{\eta\:}}^{\text{E}\text{C}8-\text{V}\text{I}\text{T}}\) (and \(\:{{\eta\:}}^{\text{E}\text{C}8-\text{A}\text{S}\text{C}\text{E}}\) ) with respect to the central value is plotted in Fig. 3 a (and b). It is clear that \(\:{{\omega\:}}_{\text{s}\text{w}}\) has the greatest influence on \(\:{{\eta\:}}^{\text{E}\text{C}8-\text{V}\text{I}\text{T}}\) , followed by ν, L V /h and ρ tot . The latter three parameters become more influent on \(\:{{\eta\:}}^{\text{E}\text{C}8-\text{A}\text{S}\text{C}\text{E}}\) , whereas f cm always has a quite small importance in these comparisons (especially when comparing EC8 and ASCE).
Tornado diagrams for sensitivity analysis
A similar comparison can also be carried out focusing on the residual shear strength. The latter comparison makes sense only if \(\:{\text{V}}_{\text{R},\text{E}\text{C}8}\) and \(\:{\text{V}}_{\text{R},\text{A}\text{S}\text{C}\text{E}}\) are compared, since, when µ Δ ≥ 3, \(\:{\text{V}}_{\text{R},\text{N}\text{T}\text{C}18}{=\text{V}}_{\text{R},\text{E}\text{C}8}\) . By using the maximum degradation factors (i.e., k equal to 0.70 and 0.75 respectively for \(\:{\text{V}}_{\text{R},\text{A}\text{S}\text{C}\text{E}}\) and \(\:{\text{V}}_{\text{R},\text{E}\text{C}8}\) ), a small modification is observed in the coefficients of Eq. ( 5 ) (the values 0.40, 11.40, and 0.12 are replaced with 0.28, 8.52, and 0.05, respectively). The isocurves in Fig. 2 tend to shift towards lower \(\:{\nu\:}\) and higher \(\:{{\omega\:}}_{\text{s}\text{w}}\) values, making the area with positive \(\:{{\Delta\:}\text{V}}_{\text{R}}\) much wider than that obtained for the non-degraded strength.
The capacity models of beam-column joints prescribed by current global standards differ to each other significantly both for reinforced (Del Vecchio et al. 2023 ) and unreinforced joints, especially when comparing the European approach with the American one.
According to EC8 2005, the shear strength of a beam-column joint is evaluated as in EN 1998-1, 2004, for newly designed buildings, by means of two safety checks (related to a tensile and a compressive failure mode). These checks can be reformulated in terms of joint shear stress \(\:{{\tau\:}}_{\text{j}}={\text{V}}_{\text{j}}/{\text{A}}_{\text{j}}\) (where \(\:{\text{V}}_{\text{j}}\) is the joint shear load and \(\:{\text{A}}_{\text{j}}\) the joint horizontal area, according to EN 1998-1, 2004 ) and normal vertical stress \(\:{{\sigma\:}}_{\text{v}}=\text{N}/{\text{A}}_{\text{c}}\) (due to the axial force related to the column above the joint). By assuming a joint without stirrups (as typical in existing buildings), Eq. ( 6a ) represents the tensile failure check, whereas Eq. ( 6b ) the compressive failure check:
In Eq.s (6), η is equal to 0.60(1 - f ck /250) for interior joints and 0.48(1 - f ck /250) for exterior ones; f ct is the concrete tensile strength (according to EN 1992-1-1, 2004 ). This strength, as well as the concrete compressive strength \(\:{\text{f}}_{\text{c}}\) , is intended to be the mean strength reduced by CF and partial materials safety factors (EC8 2005 ). Thus, \(\:{\text{f}}_{\text{c}\text{t}}={\text{f}}_{\text{c}\text{t}\text{m}}/(\text{C}\text{F}\cdot\:{{\gamma\:}}_{\text{c}})\) with \(\:{\text{f}}_{\text{c}\text{t}\text{m}}=0.30\sqrt[3]{{\left({\text{f}}_{\text{c}\text{k}}\right)}^{2}}\) ). Conversely, \(\:{\text{f}}_{\text{c}\text{k}}\) is a characteristic concrete compression strength value, assumed equal to \(\:({\text{f}}_{\text{c}\text{m}}-8)\text{M}\text{P}\text{a}\) (EN 1992-1-1, 2004 ).
For existing buildings, the Italian standard (Circolare 2019 , C8.7.2.3.5) prescribes a double strength check for joints that are not fully confined according to Eq.s (6), as well. Nevertheless, it assumes \(\:{\eta\:}=0.50\) and \(\:{\text{f}}_{\text{c}\text{t}}=0.30\sqrt{{\text{f}}_{\text{c}}}\) (with \(\:{\text{f}}_{\text{c}}={\text{f}}_{\text{c}\text{m}}/(\text{C}\text{F}\cdot\:{{\gamma\:}}_{\text{c}})\) ). As a results, comparing Italian and European codes, a difference in safety checks results is obtained even if both use Eq.s (6). Figure 4 shows this difference, distinguishing between exterior (“EXT J”) and interior (“INT J”) joints, and assuming three f cm values to fix ideas.
Beam-column joint strengths according to EC8 2005 and NTC2018, given the joint configuration and the concrete compressive strength (tensile check with solid lines; compressive check with dotted lines)
For low values of f cm (f cm = 10 MPa), NTC 2018 model provides higher tensile joint strength (solid lines in Fig. 4 ) compared to EC8 2005; conversely, at higher values of f cm (f cm = 30 MPa), the hierarchy is reversed, with almost coincident strengths if f cm = 20 MPa.
Regarding the compressive safety check (dotted lines in Fig. 4 ), EC8 2005 model provides a lower resistance in the case of exterior joints and a higher strength for interior ones.
However, for both European standards, the joint strength results as the minimum between those produced by Eq.s (6), given the value of ν. In other words, for low values of axial load ratio, the joint strength is limited by that corresponding to diagonal cracking (i.e. tensile failure), while for high ν, the joint fails due to compression failure.
According to American standard (ASCE/SEI), a joint shear stress capacity equal to \(\:{\lambda\:}{\gamma\:}^{\prime\:}\sqrt{{\text{f}}_{\text{c}}\:}\) is assumed, being λ = 1 for normal-weight aggregate concrete. The γ′ coefficient (see Table 1 ) depends on various parameters: joint typology (i.e., interior, exterior, or knee joint), presence/absence of transverse beams, presence/absence of “conforming” transverse reinforcement. Note that according to the American Code, if the stirrup spacing in the joint is less than or equal to half the column cross-section height, then the joint is considered as conforming . Otherwise, the joint is nonconforming . Thus, unlike EC8 2005 and NTC 2018, American standard prescribes a single safety check (Eq. ( 7 )):
It should be noted that, while European standards lead to a joint strength variation with N, the American guideline always provides the same joint strength irrespective of the axial load level.
Another main difference of ASCE/SEI approach compared to European codes lies in the possibility of explicitly modelling the behaviour of the joint - possibility that could significantly impact the assessment outputs. This modelling is allowed by European standards as well, which, however, do not provide specific reference models.
In Fig. 5 , the trend of the joint strength (expressed as \(\:{{\tau\:}}_{\text{j}}/\sqrt{{\text{f}}_{\text{c}\text{m}}}\:\) ) is provided for fixed values of \(\:{\text{f}}_{\text{c}\text{m}}\) , depending on ν, according to all the strength models above.
Strength domains of beam-column joints according to NTC2018, EC8 2005 and ASCE/SEI, given the joint configuration and the concrete compressive strength
For European models, the joint strength is evaluated for each axial load value as the minimum between tensile and compressive strength. This type of representation can be considered as a strength domain. Indeed, considering a given joint typology (i.e., interior or exterior) and a given \(\:{\text{f}}_{\text{c}\text{m}}\) , the demand joint shear load (i.e., \(\:{\text{V}}_{\text{j}}\) ) and axial load (i.e., N) allow deriving the \(\:{{\tau\:}}_{\text{j}}-{\nu\:}\) coordinates of a “demand point”. If this point is inside or belongs to the boundary of the domain (related to the specific strength model), then the joint is on the safe side. The ascending branches of these domains represent the tensile check; the descending branches the compressive check.
Regarding American Code, joints are assumed as non-conforming herein, since, typically, stirrups in joints are totally missing in existing buildings. For interior joint (especially with transversal beams and low \(\:{\text{f}}_{\text{c}\text{m}}\) values), the joint strength is overestimated by ASCE/SEI compared with the European codes. Conversely, for exterior joints, the hierarchy among the models depends on ν and on \(\:{\text{f}}_{\text{c}\text{m}}\) values.
Moreover, ASCE/SEI provides a different strength for knee joints (i.e., γ′ = 4 √MPa). Being located on the top floor of the building, for these joints, zero axial load can be assumed. Thus, the joint strength according to European models can be obtained assuming \(\:{{\sigma\:}}_{\text{v}}=0\) in Eq.s (6) (i.e., ν = 0 in Fig. 5 ), generally resulting lower than joint strength by ASCE/SEI.
In the previous section, the capacity models prescribed by current standards have been analysed and compared. However, a paramount work is currently ongoing by European research groups to update the current European standards with a second-generation of Eurocodes in the next years. Significant changes will be carried out to the shear strength models of both beam/column elements and beam-column joints, as highlighted by the recently published works from the literature (Biskinis and Fardis 2020 ; Fardis 2021 ; Franchin and Noto 2023 ). Thus, in this section, the capacity models introduced by the incoming second-generation of Eurocodes will be first analysed, emphasizing their evolution with respect to the current version. The current available drafts of the second-generation of Eurocodes adopted herein are prEN 1998-3:2023, FprEN 1998-1-1: 2024 (along with its previous draft FprEN 1998-1-1: 2022 ), and FprEN 1992-1-1:2023, along with the relevant references from the literature, recalled in the next sub-paragraphs.
In the second-generation of Eurocode 8-part 3 (prEN 1998-3: 2023 ), the shear capacity of existing RC beams and columns must be evaluated according to a model based on the variable inclination, θ, between the compression stress field in the member web and the member axis (Biskinis and Fardis 2020 ).
PrEN 1998-3:2023 prescribes to evaluate the shear strength, \(\:{\text{V}}_{\text{R},\text{E}\text{C}8-2\text{n}\text{d}}\) , according to FprEN 1998-1-1:2024, by using the mean values of the material properties and also following FprEN 1992-1-1:2023 suggestions, even if with some modifications explained below. \(\:{\text{V}}_{\text{R},\text{E}\text{C}8-2\text{n}\text{d}}\) can be expressed as in Eq. ( 8 ):
In Eq. ( 8 ), V N is evaluated similarly to Eq. ( 1 ), and the variable inclination θ has the same meaning of the VIT model, ranging between 1 and \(\:{\text{c}\text{o}\text{t}{\theta\:}}_{\text{m}\text{i}\text{n}}\) (see Eq. ( 9 )). The latter depends on the axial load, \(\:\text{N}\) .
However, \(\:\text{c}\text{o}\text{t}{\theta\:}\) may exceed the upper limit, \(\:{\text{c}\text{o}\text{t}{\theta\:}}_{\text{m}\text{i}\text{n}}\) , if the deformation state of the cross-section is analysed. In fact, the value of \(\:\stackrel{-}{{\nu\:}}\) is not necessarily a constant value (i.e., 0.5 as prescribed by the VIT model), and it can be obtained based on the state of strains of the member according to Eq. ( 10 ) (FprEN 1998-1-1: 2024 ):
where the reduction factor 1/1.6 is applied to account for cycling loading (Biskinis and Fardis 2020 ), and \(\:{{\epsilon\:}}_{\text{x}}\) is the average strain between the bottom and top chords, ranging between 0 and 0.02 (FprEN 1998-1-1: 2024 ). Note that, strictly speaking, according to FprEN 1998-1-1:2024 draft, \(\:\stackrel{-}{{\nu\:}}\) in seismic loading conditions should be always higher than 0.5/1.6 (= 0.31). However, the latter prescription was not present in the previous draft (FprEN 1998-1-1: 2022 ), nor in original works by Biskinis and Fardis ( 2020 ); additionally, it would result very close to the TIV model and in a not safe-sided prescription. Thus, it has not been applied in what follows.
\(\:{{\epsilon\:}}_{\text{x}}\) is calculated as in Eq. ( 11 ) (FprEN 1992-1-1: 2023 ):
where \(\:{\text{A}}_{\text{s}\text{t}}\) and \(\:{\text{A}}_{\text{s}\text{c}}\) are the areas of the longitudinal reinforcement in the flexural tension chord and flexural compression chord, respectively; \(\:{\text{A}}_{\text{c}\text{c}}\) is the area of the flexural compression chord. Lastly the “chord forces”, \(\:{\text{F}}_{\text{t}\text{d}}\) and \(\:{\text{F}}_{\text{c}\text{d}}\) , are defined as a function of the flexural ( \(\:{\text{M}}_{\text{E}\text{d}}\) ) and shear ( \(\:{\text{V}}_{\text{E}\text{d}}\) ) demand, and of axial force.
Moreover, in member end-zones expected to enter the inelastic range, the values of \(\:{\text{M}}_{\text{E}\text{d}}\) and \(\:{\text{V}}_{\text{E}\text{d}}\) from the analysis should be multiplied by the chord rotation ductility factor, \(\:{{\mu\:}}_{\varDelta\:}\) . It is worth noting that the approach proposed in Eq. ( 12 ) is a simplified approach, based on the assumption of the equal displacement rule. Nevertheless, the effective average strain \(\:{{\epsilon\:}}_{\text{x}}\) should be rigorously evaluated, considering the curvature and the neutral axis depth of the cross-section (Biskinis and Fardis 2020 ).
The additional tensile axial load, \(\:{\text{V}}_{\text{E}\text{d}}\text{c}\text{o}\text{t}{\theta\:},\) and factor \(\:\stackrel{-}{{\nu\:}}\) depend on \(\:\text{c}\text{o}\text{t}{\theta\:}\) , resulting in an iterative procedure to derive the inclination θ and, thus, the shear capacity \(\:{\text{V}}_{\text{R},\text{E}\text{C}8-2\text{n}\text{d}}\) .
Lastly, in the code-based safety check at SD LS, the shear resistance of existing members (prEN 1998-3: 2023 ), should be divided by the corresponding safety factor related to the resistance, γ Rd (prEN 1998-3: 2023 ). The latter accounts for uncertainty in the shear strength assessment and is evaluated as in Eq. ( 13 ) (Franchin and Noto 2023 ):
In Eq. ( 13 ), α R is the resistance sensitivity factor, equal to 0.85 according to FprEN 1998-1-1:2024 and Franchin and Noto ( 2023 ). The target reliability index in a 50-years reference period, β LS, CC, depends on both the considered limit state and the consequence class. According to the Annex F of FprEN 1998-1-1:2024, for SD LS and CC2 (second consequence class), β LS, CC is equal to 1.60. Lasty, the total logarithmic standard deviation \(\:{{\sigma\:}}_{\text{l}\text{n}\text{R}}\) for existing members with rectangular cross-section is equal to 0.40 (prEN 1998-3:2023- Table 8.5) when the KL3 is attained, as assumed herein. As a result, \(\:{{\gamma\:}}_{\text{R}\text{d}}=1.72\) is obtained herein.
According to PrEN 1998-3:2023, the shear resistance of existing beam-column joints should be evaluated as prescribed for new elements (prEN 1998-1-1: 2024 ). Based on prEN 1998-1-1:2024, for unreinforced joints a cracking strength (V Rj, cr ) only is provided. Vice-versa, in presence of transverse reinforcement, V Rj, cr can be overcome and joint strength estimated based on studies by Fardis ( 2021 ). Nevertheless, prEN 1998-1-1:2024 also specifies that, in a safe-side and simplified approach, joint strength can be calculated as the maximum between the shear resistance at the first cracking and a minimum value of joint strength (V Rj, min ), the latter related to the absence of transverse reinforcement and axial load:
In Eq. ( 14 ), α is equal to 0.5 for exterior joints and 1.2 for interior ones, h b and h c are the beam and column depth, respectively, and other parameters have been defined above. Eq. ( 14 ) is applied herein to calculate the shear strength of unreinforced joints according to the second-generation Eurocode. Thus, a first comparison with EC8 2005 can be easily carried out, as shown in Fig. 6 , in terms of shear stress τ j /√f cm , and, assuming four h b /h c ratios (i.e., 500 mm/[300 400 500 600]mm). It is worth noting that, ν in Fig. 6 is defined as a function of f cm , both for EC8 2005 (contrary to what Fig. 5 shows) and for the incoming-code, for sake of comparison. Additionally, the application of \(\:{{\gamma\:}}_{\text{R}\text{d}}\) factor for joints is not foreseen in the currently available drafts (i.e., \(\:{{\gamma\:}}_{\text{R}\text{d}}\) =1). However, it is reasonably very likely that in the final version of Eurocode 8, a \(\:{{\gamma\:}}_{\text{R}\text{d}}\) factor similar to those used to reduce the shear strength of beams/columns will be introduced. For this reason, herein, the joint strength has been assessed with a twofold assumption: \(\:{{\gamma\:}}_{\text{R}\text{d}}\) =1 and \(\:{{\gamma\:}}_{\text{R}\text{d}}\) =1.72.
Strength domain for unreinforced beam-column joints: comparison between first- and second-generation of Eurocodes
Unlike EC8 2005, the current draft of the second-generation Eurocode does not explicitly provide a compression limitation for unreinforced joints, leading to a different shear strength-axial load trend for high axial load ratios (even for ν < 0.3 for exterior joints). Instead, the presence of a minimum strength leads to higher V j, EC8−2nd in the case of interior joint, especially for low axial loads and high values of the h b /h c . Therefore, moving from the first to the second generation, a lower number of joint failures can be expected for the top floors interior joints (if characterized by lower h c values, i.e., higher h b /h c ratios and lower axial loads). Moreover, the use of a \(\:{{\gamma\:}}_{\text{R}\text{d}}\) coefficient higher than 1 significantly reduces the joint strength, and, consequently, its hierarchy with respect to the current Eurocode (see Fig. 6 ).
According to the ISTAT ( 2011 ) census, roughly 1/3 of Italian RC buildings have been built before 1970, when most of the national territory (about 6700 municipalities) was classified as not-seismic prone area. About 2% of municipalities not seismically classified before 1970 are nowadays classified as first seismic zone, based on expected value of acceleration on stiff soil (a g ) with 10% probability of exceedance in 50 years exceeding 0.25 g. 23% is classified as second seismic zone (0.15 \(\:<\) a g \(\:\le\:\) 0.25 g), about the 60% as third (0.05 \(\:<\) a g \(\:\le\:\) 0.15 g) and the 17% as fourth (a g \(\:\le\:\) 0.05 g) seismic zone.
In this section, two case-study buildings have been selected to analyse the difference among code-based brittle capacity models described in Sects. 2 and 3. They are RC residential buildings designed according to the technical regulations in force in Italy until 1970 (Royal Decree, R.D. 2229, 1939 ), to withstand only gravity loads, located in the about 6700 municipalities mentioned above. Case-study buildings haves the same floor area, but different number of stories, Ns (2 and 4), being buildings with Ns ≤ 4 the most widespread in Italian building stock (ISTAT 2011 ).
The selected case study buildings are in line with the prevalent construction practices in force in Italy before ‘70s. Each structure has a Moment Resisting Frame (MRF) system, consisting of 2D parallel resisting frames in the longitudinal (X) direction (see Fig. 7 a), without interior beams in the transverse (Y) direction. Buildings are symmetric in both directions (X and Y). Floor slabs are 20 cm width, and the inter-story height is 3.00 m (see Fig. 7 b).
Plan view ( a ) of case-study buildings and related representative frames ( b ); cross-sections of typical beams ( c ) and columns ( d ) (dimensions in millimetres)
The cross-section dimensions and reinforcement details are based on a simulated design (Verderame et al. 2010 ; De Risi et al. 2023b ) according to the Italian code in force during the construction period (R.D.2229, 1939 ). A maximum allowable stress of 5.0 or 6.0 MPa was considered for concrete (depending on compressive loads or bending actions, respectively), and of 140 MPa for reinforcing plain bars (type AQ42). All the beams have a 30 × 50 cm² cross-section, with a geometrical percentage of longitudinal reinforcement (ρ l ) ranging from 0.40% to about 0.90%– see Fig. 7 c. Column sections (Fig. 7 d) vary from 30 × 30 cm² (for the upper storeys) to 30 × 40 cm² (for the central columns of the ground floor of the 4-storey building), with a decreasing reinforcement ratio from the ground floor of the 4-storey building (ρ l ≈ 0.80%) to the last floor (ρ l ≈ 0.60%). The minimum requirement specified by the R.D.2229 ( 1939 ) is adopted as transverse reinforcement (Fig. 7 c, d). Note that no transverse reinforcement was placed within beam-column joints, since the technical code in force at the construction time did not require any design nor reinforcement of joints. Additional information about the main buildings features is reported in De Risi et al. ( 2023a ).
Lastly, f cm and mean yielding strength of rebars (f ym ) used for buildings assessment are assumed equal to 20 MPa and 322 MPa, respectively, according to Verderame et al. ( 2010 ) and Masi et al. ( 2019 ), for the relevant time period.
Resulting first mode periods (T X and T Y ), mass participation ratios (m p, x and m p, y ) in both the main directions, and the seismic weight (W), ranging between 8.6 and 10 kN/m 2 , are also shown in Table 2 .
Each building is modelled in the OpenSees platform (McKenna 2011 ) with 3D “bare” frames. Beams and columns are modelled as ductile elements using a lumped plasticity approach to simulate their flexural response (see Fig. 8 ). This approach is implemented by elastic BeamColumn Elements in series with Zero-Length Elements (featuring by the Pinching4 Uniaxial Material ) at both ends of each beam/column. The flexural response is a moment (M)-chord rotation (θ) relationship calibrated for RC elements reinforced with plain bars (Verderame and Ricci 2018 ), by means of a four-point envelope, integrated herein by an additional point corresponding to the first cracking (Fig. 8 ).
Adopted lumped plasticity approach ( a ); envelope of the flexural response of beams and columns ( b )
Masonry infills are only considered in terms of masses and loads. It is acknowledged that masonry infills play a crucial role on seismic performance of RC buildings. Nevertheless, despite decades of research about this topic, often codes worldwide do not provide comprehensive provisions for numerical modelling of masonry infills and relevant safety checks. This is the case of Italian code (D.M. 2018 ), and of the current European code (CEN, 2004 ) as well. As an example, no information about the in-plane nonlinear response, or, more simply, the elastic stiffness of the infill panels is provided within these codes. Additionally, even the evaluation of infills mechanical properties (e.g., Young modulus or compressive strength) in existing buildings is still a challenging issue in common practice. As a result, in common practice, both for the design of new buildings and the assessment/retrofit of existing ones, infills are neglected (except than as loads and masses). Since this work is intended to be a code-based study, masonry infills are not explicitly modelled. Nevertheless, it is worth noting that a comprehensive risk-based analysis should certainly consider explicitly the presence of infills, if the main aim is a more “realistic” assessment of seismic performance and its improvement, along with a realistic estimation of seismic losses (De Risi et al. 2020a ; Del Gaudio et al. 2021 ).
Similarly, following a typical practice-oriented approach, joints are assumed to be rigid elements, and the floors stiff in their own plane. Lastly, potential shear failures have been identified in post-processing, considering all models introduced in Sects. 2 and 3.
The code-based assessment at a given LS can be expressed through a capacity-to-demand ratio. NTC 2018 allows to synthetically express this ratio in terms of Peak Ground Acceleration (PGA). The demand mainly depends on the considered LS and the construction location and use. The capacity depends on the attainment of a certain failure condition, generally the first failure occurring at the considered LS (NTC 2018, EC8 2005). The adopted capacity model certainly affects the capacity. This is particularly true for the shear strength models, since brittle failures generally limit the seismic capacity of existing buildings (De Risi et al. 2023a ).
Therefore, in this section, the first achievement and the evolution of brittle failures at SD LS is illustrated, depending on the adopted shear capacity models. Then, the influence of the capacity models on the buildings seismic assessment is analysed, assuming as possible buildings locations all Italian municipalities classified as seismic-prone only after 1970.
The seismic capacity assessment is performed within the N2 framework (Fajfar 2000 ). Nonlinear static pushover analyses are carried out, considering a lateral load distribution proportional to the first vibration modal shape in each direction. The resulting capacity curves (obtained as suggested by European codes, NTC 2018 and EC8 2005), are shown in Fig. 9 , as spectral displacement (S d ) -versus- pseudo-acceleration (S a (T) up to the occurrence of the first ductile failure (DF) at the SD LS. As suggested by the Italian code, such failure occurs when the demand in terms of chord rotation θ reaches ¾ of the capacity calculated according to Biskinis and Fardis ( 2010 ). Since the focus of the present work is on brittle failures models, such definition of DF capacity point is always kept constant in what follows.
Capacity curves up to the first DF with the relevant collapse mechanisms; evolution of the brittle failures at SD LS according to all considered code-based capacity models
In addition to the capacity curves, also the relevant collapse mechanisms are shown in Fig. 9 . A global collapse mechanism is always observed in the transverse (Y) direction, whereas local mechanisms are observed in the longitudinal (X) direction. Each capacity curve also shows the achievement of all the failure typologies at SD LS, i.e. the first joint failure (JF), and the first shear failure (SF) in beams or columns, according to the considered capacity models. Moreover, the percentage of failing elements is provided in each step of the pushover analysis.
Regarding the beams/columns SFs (which occur only in the X direction on the lowest storeys of the case-study buildings), the most conservative capacity model for the analysed case-study buildings is that proposed by EC8 2005. Only according to this model, even the 2-story building exhibits SFs (especially in the longitudinal exterior beams at the first floor). Considering the other two codes, ASCE/SEI results the less conservative model.
About beam-column joints, current European technical regulations (NTC 2018, EC8 2005) prescribe a dual check. The tensile failure is hereinafter referred to as JF(T). The compression failure is labelled JF(C). It is worth noting that a joint does not necessarily reaches its maximum capacity when diagonal cracking first occurs (Hakuto et al. 2000 ). In these cases, the occurrence of JF(T) could severely limit the actual joint capacity.
Considering JF(T) according to NTC 2018, failures occur in both directions for all the case studies, with a maximum percentage of failing elements in X direction that exceeds 50% of all the joints. The number of failures is about the same moving from the NTC 2018 to EC8 2005 model. Indeed, the diagonal tensile check according to NTC 2018 and EC8 2005 provides very similar capacity when f cm = 20 MPa (Fig. 5 ).
On the contrary, JF(C), which represent a more appropriate failure criterion (Hakuto et al. 2000 ; Park and Mosalam 2012 ; NZS 3101, 2006 ), involves fewer joints (always below 10% of all the joints) of the tallest building, according to NTC 2018 and EC8 2005 models. The joints exhibiting JF(C) are typically interior joints with high axial loads. For this type of joints, EC8 2005 provides higher capacity than NTC 2018 (Fig. 5 ), thus delaying the first JF(C) (of the interior 8-11-14-17 joints at the first floor– see numeration in Fig. 7 a).
Only one safety check is performed according to the American code for joints. Its relevant failure evolution is plotted in Fig. 5 with JF(T) of European codes, since that generally limits the building capacity. ASCE/SEI results less conservative than European codes (see Fig. 5 ), especially for interior joints.
The seismic capacity assessment at the SD LS is, lastly, carried out according the next-generation Eurocodes, assuming a double option for \(\:{{\gamma\:}}_{\text{R}\text{d}}\) (1 or 1.72), as explained above.
With respect to the current EC8, the shear strength model by the second-generation Eurocodes leads to a lower number of SFs in beams/columns, even by using \(\:{{\gamma\:}}_{\text{R}\text{d}}\) =1.72. Such failures primarily involve the internal longitudinal beams of the central spans and the central columns (i.e., 8-10-14-16) on the ground floor of the 4-storey building. Note that, if \(\:{{\gamma\:}}_{\text{R}\text{d}}\) =1 was used, shear failures in beams/columns are not observed at all.
About JFs(T), the current European model provides intermediate results compared to those of the future Eurocode 8 considering the two \(\:{{\gamma\:}}_{\text{R}\text{d}}\) bounds (coherently with Fig. 6 ). However, for the 2-story building, the number of JFs(T) is approximately the same when applying the strength model of the current Eurocode or that of the second generation with \(\:{{\gamma\:}}_{\text{R}\text{d}}\) =1.72. As the number of stories increases, the maximum axial load increases at the bottom stories, and, thus, the unreinforced joint strength from the second-generation Eurocode tends to coincide with that related to cracking, leading to an increase in JF(T) failures even for interior joints (with \(\:{{\gamma\:}}_{\text{R}\text{d}}\) =1.72) (see Fig. 6 ). If \(\:{{\gamma\:}}_{\text{R}\text{d}}\) =1, a lower number of joint failures is always obtained with respect to the current Eurocode 8.
As clearly highlighted above, the shear failure of joints can significantly limit the building seismic capacity. It is worth noting that the safety check of beam-column joints is often very penalizing because of the use of a force-based approach (i.e., a comparison between shear load and shear strength), in conjunction with the definition of LS achievement when the first element fails. A possible alternative is offered, among the investigated codes, by ASCE/SEI guidelines. ASCE/SEI explicitly introduces the possibility to model the nonlinear response of beam-column joints, for example using the so-called scissors model, shown in Fig. 10 (a) (ASCE/SEI 41, 2017 ; Alath and Kunnath 1995 ). ASCE/SEI also explicitly provides the characterization of the joint nonlinear response and the joint shear strain (γ j ) thresholds to be used for each LS safety check, thus actually introducing the possibility of a displacement-based approach also for elements like joints.
Scissors model for beam-column joints ( a ); nonlinear response of the beam-column joint according to ASCE/SEI ( b )
Both the strain thresholds and the whole joint nonlinear response depend on the joint typology, the axial load ratio, the shear load level, and the presence of (conforming or not) stirrups. A typical nonlinear response of the beam-column joints according to ASCE/SEI suggestion is reproduced in Fig. 10 (b) (ASCE/SEI 41, 2017 ; Hassan 2011 ). These prescriptions by American guidelines have been applied to the buildings analysed herein for a brief comment, in this sub-section only, about the influence of joint modelling, by:
implementing the scissors model (Alath and Kunnath 1995 ) as in Fig. 10 (a);
converting the joint shear stress into joint moment (M j ) as suggested in the literature based on equilibrium equations (Celik and Ellingwood 2008 ; De Risi et al. 2017 ); and.
assuming that the joint rotational spring is equal to γ j (Celik and Ellingwood 2008 ; De Risi et al. 2017 ).
The joint spring is characterized based on f cm as concrete compressive strength, without any reduction coefficient. The achievement of SD LS is (conservatively) assumed herein as the attainment of the beginning of the joint softening response (i.e., when the second point of Fig. 10 (b) is reached for the first time in a joint spring). Pushover curves are updated following this modelling approach.
As a result, for the analysed 2- and 4-storey buildings, joint failures are not detected at all, thus highlighting the great difference in safety check depending on the check approach.
For each building and direction, the capacity curve is bi-linearized according to NTC 2018, obtaining an elastic-perfectly-plastic curve. Since the focus of the present work is on brittle failures models, the bi-linearization approach is kept always constant in what follows.
Starting from the inelastic capacity point, C IN (i.e., the attainment of the first failure at the SD LS on the elasto-plastic bilinear curve), the corresponding elastic capacity point, C EL , is derived by means of Vidic et al. ( 1994 ) relationships. Vidic et al. ( 1994 ) proposal depends on the ratio between the building effective period, T eff , and the corner period T C . The latter is a function of the building location according to NTC 2018, always used herein to characterize seismic hazard. Considering the demand elastic spectra at the SD LS (with return period 475 years) for all the considered sites– always assuming soil type A (NTC 2018, EC8 2005)–, the equal-displacement condition always applies herein (being T eff, X =0.55s and T eff, Y =0.99s for Ns = 2, and T eff, X =0.77s and T eff, Y =1.46s for Ns = 4). The elastic spectral pseudo-acceleration capacity, S a,C (T eff ), is shown in Fig. 11 for each building/direction/code.
As-built capacity in terms of S a (T eff ) at SD LS: X-( a ) and Y-( b ) direction
In almost all buildings/codes, the very first failure occurs on the linear branch of the bilinear capacity curve (resulting in C EL =C IN ). The exceptions are the first failures in the Y direction for all buildings, and in the X direction for the 2-story building, according to ASCE/SEI and next generation EC8 wth γ Rd = 1. Note that in these cases, the values of S a, C (T eff ) were cut off from the plot, being very high (see Table 3 ). In general, the S a, C (T eff ) evaluated according to American standards is significantly higher compared to those obtained with (current or incoming) European models. Instead, the values provided by Italian and European standards are quite similar to each other, especially in Y direction (see Table 3 ).
The pseudo-acceleration spectrum passing through the elastic capacity point C EL allows associating a capacity PGA value (PGA C ) to each site (as described in De Risi et al. 2023a ). An example is shown in Fig. 12 a. Given C EL point and the spectral parameters of each site at SD LS (according to NTC 2018), as many spectra passing through C EL as the considered sites can be derived. Each of these spectra is characterised by a PGA C value. Thus, PGA C exhibits a certain variability, which clearly stems from the variability of the spectral shape associated with the building location (NTC 2018). Table 3 provides the median values and the 16th and 84th percentiles of PGA C values (PGA C,50 , PGA C,16 , and PGA C,84 , respectively) for both directions. The minimum value of PGA C is always in Y direction.
Example of PGA C derivation (4-storey building in X direction, according to EC8 2005 code) ( a ); PGA C depending on Ns and code, assuming A soil type ( b ) and varying the soil typology ( c )
In Fig. 12 b, the PGA C (hereinafter, the minimum value between the two directions) is provided, showing median values, 16th and 84th percentiles. The capacity values according to EC8 2005, NTC 2018 and next-generation Eurocode derive from the same kind of failure (i.e., JF(T) in Y direction). According to the ASCE/SEI code, too, the capacity at the SD LS is due to a JF, which nevertheless generally occurs for higher displacement demands (see Fig. 9 ), resulting in higher PGA C values (especially for Ns = 2). The coefficients of variation (CoV) of PGA C are quite small (about 18% for both case studies in accordance with ASCE/SEI and next-generation EC8 with γ Rd = 1; about 10% for the other cases).
Lastly, Fig. 12 c shows the PGA C ratios between the value corresponding to flexible soil types - from B to D (NTC 2018) - and that related to soil A (Fig. 12 b), assumed as a reference. Moving from a rock soil (type A) to a more deformable soil (type D), PGA C progressively decreases for all codes, up to about 50%.
Lastly, the as-built assessment explained above has been repeated by changing f cm , assuming 10 MPa and 30 MPa, as in Sects. 2–3. Table 4 summarizes the results of this further analysis in terms of variation of PGA C,50 (soil A) with respect to the results presented above (for f cm =20 MPa), namely in terms of ΦPGA C,50 = PGA C,50,fcm /PGA C,50,fcm=20MPa . A lower value of f cm leads to lower PGA C (and more brittle failures); vice-versa if f cm increases. Nevertheless, such a variation has different weight depending on the considered building and, above all code. For the 2-storey building:
according to NTC 2018, the considered variation in f cm leads to percentage variation lower than 30% in PGA C ; the first failure always is a JF(T);
according to EC8 2005, higher variations are observed. When f cm decreases, in particular, JF(T) occurs even for gravity loads only, thus leading to a null PGA C (i.e., ΦPGA C,50 =0). Vice-versa, when f cm increases the first failure typology becomes a beam SF;
according to ASCE/SEI, a reduction in f cm leads to very premature JF; whereas, if f cm increases, joints failures disappear and the very first failure is a DF; similar outcomes are obtained according to the next generation EC8 if γ Rd = 1.00 is assumed;
according to the next generation EC8 with γ Rd = 1.72, JFs(T) are very sensitive to a reduction in f cm , leading to a significant PGA C reduction due to joint failures under gravity loads only (as for EC8 2005).
For the 4-storey building, similar outcomes are obtained, except for the NTC 2018 case. In this case a f cm reduction leads to considerable increments in axial load levels, and, thus, a very premature attainment of JF(C), even under vertical loads only (ΦPGA C,50 =0). Anyway, the “reference” case (f cm =20 MPa) only is analysed in what follows.
Building capacity can be improved in several ways, mainly grouped into four strategies: (i) increment of lateral strength and stiffness (e.g., by means of shear walls), (ii) increment of displacement capacity only (e.g., by fibre-reinforced polymer (FRP) wrapping or steel cages); (iii) mixed implementation of (i) and (ii); (iv) reduction of the demand (e.g., by using seismic isolators or dissipation devices). However, when shear failures significantly limit the building capacity, as in the above-analysed cases, a possible retrofitting strategy could just aim at solving the detected shear failures. This would make possible the achievement of (more favourable) ductile failures, even without any change in lateral stiffness nor in collapse mechanism. This latter retrofitting approach is one of the less invasive and less expensive strategies, and it is applied herein to analyse its effectiveness depending on the adopted code.
The main objective of the adopted strengthening strategy is the enhancement of the seismic capacity at the SD LS by solving all the (tensile-only) shear failures, without modifying the lateral stiffness of the structural elements. All details about the retrofitting design procedure can be found in De Risi et al. ( 2023a ).
FRP wrapping (e.g., Del Vecchio et al. 2015 ; Pohoryles et al. 2018 , 2023 ) is employed to mitigate shear failures in beams and columns. The number of uniaxial FRP fabrics has been designed according to CNR-DT 200/ 2004 guidelines. The plastic shear is used as shear demand for the design to convert shear-sensitive elements in ductile elements. The design results in a maximum number of uniaxial carbon-FRP plies (with high elastic modulus, 230 GPa, and an equivalent thickness equal to 0.166 mm) ranging from one to three. For columns, a continuous wrapping along the height is assumed. This FRP wrapping leads to an improved tensile strength ranging from 1.9 to 2.7 times the V w (as defined in Sect. 2) for columns, resulting in capacity-to-demand ratios ranging from 1.1 to 1.5. On the contrary, beams ending portions are wrapped (until a maximum extension of 50% of the beam length), namely only where the shear demand (assumed as plastic shear at the beams ends) overcomes the as-built shear strength. One FRP ply is always sufficient for beams, leading to capacities at least 1.8 times higher than the plastic shear load.
Pre-stressed steel strips, applied as “external stirrups”, are used to effectively solve tensile shear failures in beam-column joints. The number of pre-stressed strips is designed to prevent diagonal cracking of the joint or support the maximum tensile force coming from the converging beams (Verderame et al. 2022 ), in tune with CEN 2005. As a result, a maximum of about twenty pre-stressed 0.9 × 19 mm 2 strips of stainless steel (420 MPa yielding strength) is obtained. A maximum of three holes per beam is necessary for this intervention.
Nevertheless, the adopted techniques do not allow solving the compressive failures, as defined by CEN 2005 and NTC 2018. This failure can be an issue not for beams or columns (always characterised by a tensile shear failure in the investigated buildings), but for joints (especially when characterised by high axial load levels). In other words, if a JF(C) failure occurs before the first DF (according to CEN 2005 and NTC 2018), the building capacity is limited to the first JF(C), instead than the first DF (De Risi et al. 2023a ). Therefore, this intervention is intended to be applied to all shear-sensitive elements that fail during the pushover analysis up to the first DF (see Fig. 9 ) or the first JF(C), if any. It is also worth noting that, if JF(C) occurred for gravity loads only (as when f cm is very low), such strengthening strategy would have no sense, and thus, it should be replaced with a more comprehensive and likely “heavier” retrofitting approach.
Moving towards the next-generation Eurocode, shear strength of joints strengthened with pre-stressed steel strips has been assessed based on prEN 1998-1-1:2024 and Fardis ( 2021 ), assuming that steel strips act as exterior stirrups (as for CEN 2005 ). Joint shear strength of (thus reinforced) joints, evaluated according to prEN 1998-1-1:2024, increases with respect to unreinforced joints, and overcomes the joint maximum shear demand for the analysed buildings. Therefore, joint shear failures result completely solved after retrofitting according to the incoming code.
Contrary to European approaches, according to ASCE/SEI, the joint transverse reinforcement is conforming if, in the joint region, the spacing of the hoops does not exceed half of the height of the column’s cross-section. Therefore, it is assumed that joints strengthening - designed as described above - is able to transform non-conforming joints into conforming joints (Cosgun et al. 2019 ). A conforming joint has higher capacity (i.e., higher γ′ coefficients in Table 1 ) than a relevant non-conforming joint. This leads to a higher displacement capacity (Fig. 13 ), and, in tune, higher Sa c (T eff ) (Fig. 14 ), if compared with the ante-operam condition. Therefore, the post-operam capacity according to ASCE/SEI model is the minimum between the Sa c (T eff ) corresponding to the first DF and that corresponding to the occurrence of a conforming joint failure.
Capacity curves up to the first DF with relevant brittle failures at SD LS in the post-operam condition (second row) compared to the ante-operam condition (first row)
Post-operam capacity in terms of S a, C (T eff ) ( a ) and comparison with ante-operam capacity ( b )
Lastly, note also that any possible increment in column displacement capacity due to FRP wrapping is herein neglected, since it does not significantly affect the analysis of the effectiveness of the selected strengthening techniques.
Figure 13 shows the S d capacity increments, moving from ante - to post-operam condition.
Among current codes, the highest displacement capacity increments are observed for European/Italian codes (ranging from + 83% to + 94%), especially in Y direction (where no JF(C) occurs). About ASCE/SEI, displacement capacity increment reaches + 60% (for Ns = 4 in X direction); whereas, for Ns = 2, the displacement capacity increment is null or very low since, already in as-built condition, shear failures, if any, only occur very close to the first DF.
Figure 14 a shows that, for the 2-story building, after retrofit, S a, C (T eff ) is limited by the first DF failure for all considered codes and in both directions, thus reaching the same value for all codes (Fig. 14 b). The high ante-operam S a, C (T eff ) according to ASCE/SEI model results in a small capacity increment in Y direction (about + 20%). Vice-versa, in X direction, the ASCE/SEI-based S a, C (T eff ) remains unchanged between the ante- and post-operam conditions, since in both conditions, the first DF defines the capacity. On the contrary, the two current Italian and European codes provide about the same S a, C (T eff ) increment for the 2-storey building (about + 85% and + 95% in X and Y direction, respectively), moving from the first JF(T) to the first DF.
For the 4-storey building, the post-operam capacity is limited by the occurrence of a JF(C) in X direction according to NTC 2018 and EC8 2005, and of conforming JFs according to ASCE/SEI. The S a, C (T eff ) in X direction according to ASCE/SEI is due to the failure of an exterior joint. On the contrary, according to European standards, the post-operam capacity is associated with the JF(C) of an interior joint. In this case, the highest capacity increment (among current codes) is reached with EC8 2005 capacity model (about + 90%), which allows moving from the first SF to the first JF(C). In Y direction, instead, both the current Italian and European codes provide the same S a, C (T eff ) (corresponding to the first DF), higher than the ASCE/SEI-based S a, C (T eff ). In this latter case, indeed, exterior (conforming) joints fail before any element reaches its ductile capacity, limiting the corresponding capacity increment (about + 65%).
Lastly, Fig. 14 also shows how the current Eurocode leads to an as-built seismic capacity quite similar to that of the future Eurocode with \(\:{{\gamma\:}}_{\text{R}\text{d}}\) =1.72, in tune with observed failure evolution.
Even with the same retrofitting strategy, the resulting the post-operam capacity can be very different if second-generation Eurocodes is used (Fig. 14 ). For the 2-story building the capacity always corresponds to the first DF, thus leading to the same S a, c (T eff ) of the previously considered current codes. Vice-versa, for the 4-storey building, the capacity provided by the current Eurocode 8 is limited by the JF(C), contrary to what happens by using the second-generation Eurocodes in its current draft. This outcome leads to higher post-operam S a, c (T eff ) values if the incoming code is used.
Pre-code RC buildings are particularly vulnerable to shear failures during seismic events, thus emphasizing the paramount role of a reliable estimation of shear capacity of RC elements. The scientific literature proposes different capacity models, and technical codes worldwide have significant differences as well. This study provides an overview and a comparison of shear strength models adopted by Italian, European and American codes.
About the current shear strength models for low-standard beam/column elements, a first parametric comparison found that:
the current European standard is generally penalizing, when compared to American code;
the model adopted by Italian code provides intermediate resistances between the European and American standards; it is derived from European one but modifies the latter for low ductility demand.
Additionally, significant differences exist in the current capacity models used to assess unreinforced beam-column joints in the European and American contexts:
the joint resistance significantly varies with the axial load according to European and Italian models; on the contrary, in the American model, the axial load has not any role on unreinforced joint strength, which only depends on the joint geometrical configuration and the number of converging beams;
the current European and Italian codes generally provide a lower joint resistance compared to American standard, for interior joints; for exterior joints this comparison strongly depends on axial load ratio;
the current European and Italian models have same theoretical approach, but their hierarchy in terms of strength is strongly influenced by the joint configuration, concrete compressive strength, and axial load ratio.
All the models have been applied and compared to each other in terms of seismic capacity assessment of case-study pre-code RC buildings. They were designed for gravity loads only, with 2 or 4 stories. The assessment, at Severe Damage Limit State, based on pushover analyses, revealed that:
the seismic capacity is severely limited by joint failures in a force-based approach for almost all buildings/codes;
the seismic capacity in terms of elastic spectral acceleration based on the American standard overcomes that of European models (at least + 65%), while the Italian code generally falls between the other two current codes (but closely to the EC8 2005 outcome);
an explicit modelling of the beam-column joint behaviour and a displacement-capacity safety check approach is explicitly allowed by American standard only. It leads to very less conservative results for the investigated buildings than force-based safety checks.
The incoming second generation of Eurocodes has been also investigated and applied herein based on their current available drafts and background literature. With respect to the current European standards:
a generally less conservative safety check for beams/columns shear strength is obtained;
a similar outcome is confirmed for beam-column intersections, mainly due to the absence of an explicit diagonal compressive safety check for unreinforced joints.
The seismic capacity of the case-study buildings was also reassessed after implementing a retrofitting strategy that addresses all tensile-only brittle failures. It was found that:
post-operam capacity is due to the occurrence of the first ductile failure for the shortest building, whichever the code;
for the tallest building, post-operam capacity is due to the first joint compressive failure as for the current European and Italian standards (which has always to be checked also for reinforced joints), or to a conforming joint failure as for American standard;
the incoming shear strength model (next-generation Eurocode) for beam/column elements was found to be significantly less penalizing than the current one, thus also requiring fewer retrofitting efforts;
the current draft of the next-generation Eurocode, unlike the current European code, leads to higher post-operam capacities. This is particularly due to the new model adopted for beam-column joints, according to which joint strength can increase with transverse reinforcement.
Buildings seismic assessment herein has been performed on 3D models neglecting infills, due to the lack of practical guidance in most codes on modelling them and the code-based framework of this study.
Nevertheless, further works, if aimed at more comprehensive fragility analysis of as-built and retrofitted buildings, should consider the paramount presence of infill panels. Lastly, it is worth noting that some further details (e.g., safety factors) have to be still defined and could somehow modify the current available versions of the second-generation Eurocodes and, thus, in this eventuality, some discussed results could be affected.
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This study was developed within the activities of the ReLUIS-DPC 2024–2026 research programs, funded by the Presidenza del Consiglio dei Ministri—Dipartimento della Protezione Civile (DPC).
This work was supported by Reluis-DPC project, funded by Presidenza del Consiglio dei Ministri—Dipartimento della Protezione Civile (DPC).
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Scala, S.A., De Risi, M.T. & Verderame, G.M. Code-based brittle capacity models for seismic assessment of pre-code RC buildings: comparison and consequences on retrofit. Bull Earthquake Eng (2024). https://doi.org/10.1007/s10518-024-02016-6
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DOI : https://doi.org/10.1007/s10518-024-02016-6
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