Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 435 https://internationalpubls.com Analysis and Statistical Assessment of Liquefaction Potential Using SPT-N Approach in Bhandara Region Maharashtra: Implications for Infrastructure Development Manish V. Bawankule1, Shantanu N. Pawar2, Saurabh Naik3, Akshay Gulghane4 1 Research Scholar, Department of Civil Engineering, G H Raisoni University, Amravati, India 2 Research Supervisor, Assistant Professor, Department of Civil Engineering, G H Raisoni College of Engineering and Management, Jalgaon, Maharashtra, India 3Assistant Professor, Department of Civil Engineering, G H Raisoni College of Engineering and Management, Jalgaon, Maharashtra, India 4Assistant Professor, Department of Civil Engineering, G H Raisoni Collage of Engineering, Nagpur, Maharashtra, India manish52kule@gmail.com1, shantanu19@gmail.com2 , saurabhnaik603@gmail.com3, akshaygulghane@gmail.com4 Article History: Received: 12-04-2024 Revised: 30-05-2024 Accepted: 14-06-2024 Abstract: The Bhandara area in Maharashtra, India, has a lot of earthquakes, so its liquefaction potential needs to be studied in detail to help with building infrastructure. This research uses the Standard Penetration Test (SPT-N) method to check how easily the dirt in the area can become liquefied. When SPT-N numbers are added to soil qualities and seismic factors, they are used to figure out how likely it is that the ground will liquefy when it is loaded with earthquake energy. Different types of dirt and different levels are more or less likely to liquefy, according to the results. The makeup of the soil, the level of the groundwater table, and the history of earthquakes are some of the most important things that affect the liquefaction potential. The study finds places where there is a high risk of liquefaction that are also expected to have big building projects. These results make it clear how important it is to include liquefaction mitigating measures when designing and building roads, houses, and other important infrastructure to make sure it is safe and strong. The study also gives a plan for future earthquake risk ratings in the area, showing how important it is to keep an eye on and update records of soil data and earthquakes. Using the SPT-N method along with current geotechnical and earthquake analysis methods, this study gives a full picture of the area's liquefaction risk. The results have big effects on the growth of infrastructure because they help engineers and managers make smart choices about how to lower risks, improve design, and make infrastructure in the Bhandara region last longer and be safer. In the larger field of geotechnical engineering and crisis preparation, this study adds to it by showing how important specific studies are for building strong infrastructure in areas that are prone to earthquakes. Keywords: Liquefaction Potential, SPT-N value, Cyclic Resistance Ratio (CRR), Factor of Safety (FS). 1. Introduction Soil liquefaction caused by earthquakes can do a lot of damage to civil engineering buildings. A lot of big earthquakes have caused damage to the ground by liquefying it. Some examples are off the Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 436 https://internationalpubls.com coast of Ecuador in 1906, Assam-Tibet in 1950, Alaska in 1964, Niigata in 1964, Loma Prieta in 1989, Kobe in 1995, Sumatra in 2005, Chile in 2010, and Sendai in 2011. Since then, many people around the world have worked hard to learn more about soils and figure out how easily they can turn into liquid using a variety of experimental and analytical methods. These efforts show how important it is to know how the qualities of the soil and the way earthquakes happen affect how badly the soil liquefies in areas that are prone to earthquakes. A lot of people have died and a lot of damage has been done to both low-rise and high-rise buildings by these disasters. For organized urban planning to work, geotechnical studies of an area's earthquake possibilities are needed. To make sure people are safe and progress is made, it is important to know how natural disasters like earthquakes, floods, and subsidence affect the built environment. People are moving to cities and factories, which is causing Bhandara, which is in the eastern part of Maharashtra State and close to the middle of India, to grow. Because of movement, the city is getting a lot of new facilities and more places for people to live. In this situation, it is important to look at the liquefaction risks that might come up after an earthquake. Using SPT-N values and geotechnical studies, this paper looks at the liquefaction potential of empty places in the Bhandara region. The results and conclusions of these studies will be very important for figuring out how dangerous things are and where liquefaction could happen. It is a well-known fact that sandy and coarse-grained sands are more likely to melt. In the past, it was thought that liquefaction only happened in sands. However, silty and clayey soils also make evaluating liquefaction very difficult. The Kocaeli (Turkey) and Chi-Chi (Taiwan) earthquakes in 1999 liquefied compact soils, which caused some buildings to drop and weak supports to stop holding weight. Also, fine-grained sands that meet Chinese standards may be very likely to lose a lot of strength. Because of this, all the types of dirt that were found during the investigation were tested for their ability to liquefy in this study. To look at the underlying rock and find the liquefaction factor of safety, different types of soil were tested. The study's main goal is to give useful information about the liquefaction risk in the Bhandara area. This is important for making sure that built buildings are safe and for long-term urban growth. 2. Background The Bhandara region in Maharashtra, India, is very interesting because it is prone to earthquakes, which could damage buildings and other structures. Geology and soil conditions in the area make it important to know a lot about liquefaction potential to make sure that buildings, roads, and other important structures are safe and last a long time. Liquefaction is when wet soil loses a lot of its strength and stiffness in response to stress, like an earthquake. It can cause the ground to break apart badly and damage buildings. The Standard Penetration Test (SPT-N) is a well-known way to check the qualities of dirt and see how likely it is to liquefy. The SPT-N figure tells us a lot about the density and power of the soil because it shows how many hits are needed to break through a standard-sized piece of soil. These numbers, along with other structural factors, are very important for figuring out how resistant the soil is to liquefaction. Studies in the past have shown how important it is to know about the local soil conditions and how earthquakes can change the liquefaction potential. Some studies have been done on specific sites in the Bhandara area, though, to get more accurate risk estimates and more thorough information. This study tries to fill in that gap by using a lot of site and lab data to look at the liquefaction possibilities in different parts of the area. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 437 https://internationalpubls.com The goal of this study is to give a full picture of the region's ground stability by combining the SPT- N method with current analysis methods. The results are meant to help with building infrastructure and putting in place safety steps that will make buildings stronger in this earthquake-prone area. Not only does this method help make local infrastructure safer and last longer, it can also be used as a model for similar tests to be done in other places with similar earthquake and ground conditions. 3. Area of Study The location for infrastructure development in bhandara region of Maharashtra. It lies around 21.061218 latitude, 79.575455 longitude. The study area is shown in Fig. 1 below. Fig 1:- Representation Research study area 4. Geographic Location of Study Area Bhandara is located in the north-east part of Maharashtra, between 20°38' and 21°36' north latitude and 79°27' to 80°06' east longitude. The district covers a total area of 4087 square kilometres and is part of Survey of India degree sheets 55O, 55P, 64C, and 64D. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 438 https://internationalpubls.com Fig. 2:- Geology of Bhandara District Bhandara district is unique in Maharashtra since it is entirely made up of metamorphic and igneous rocks, shown in fig 2. 5. Ground water table Fig. 3:- Depths of Ground water table of Bhandara District Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 439 https://internationalpubls.com Ground water table is fluctuating as the seasonal variations, bust as shown in fig.3. GWT ranges from ground level to maximum up to 20 m. This study's liquefaction analysis relied on observed groundwater tables for inland areas, but for river and bridge sites, the worst-case scenario with GWT reaching the surface was considered. 6. Geotechnical investigation and Data collection This study gathered data on SPT, laboratory tests, and groundwater table levels from actual field geotechnical investigation work. We obtained 10 borehole data from 10 places from study area. Most geotechnical investigations have been limited to depths between 35.0. Fig. 4 shows the borehole sites. Geotechnical investigations are conducted in areas around bhandara to evaluate the region's subsurface lithology and stratified profile. A total of 10 boreholes of 35.0 m. depths were drilled in different places as indicated on the map in Fig. 4. Fig. 4:- Borehole locations for the research in Bhandara District. 7. Characterization of soil Laboratory test parameters were analyzed to assess the soil characteristics of the soils. The soil type of 10 boreholes was determined using the Indian Standard Classification System. Fig. 5:- Geological profile for the study area Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 440 https://internationalpubls.com Testing was done on clayey sand up to 14.00 m then hard silty sandy strata is present till final depth of 35.0 m and is represented in the geological profile below in Fig 5. 8. Assessment of liquefaction potential In this section methodology adopted for evaluation of liquefaction potential is explained. The water table's location, the SPT blow count, and the fines content of the soil met at a definite depth are among the data needed to define the vulnerability to liquefaction. • Analysis and Assessment of Liquefaction Potential Using SPT-N Approach 𝑆𝑡𝑒𝑝 1: 𝐶𝑜𝑟𝑟𝑒𝑐𝑡 𝑆𝑃𝑇 − 𝑁 𝑉𝑎𝑙𝑢𝑒𝑠 1. 𝑂𝑣𝑒𝑟𝑏𝑢𝑟𝑑𝑒𝑛 𝑆𝑡𝑟𝑒𝑠𝑠 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 (𝑁₁₆₀): (𝑁1)60 = 𝑁 × 𝐶𝑁 × 𝐶𝐸 × 𝐶𝑆 × 𝐶𝐵 × 𝐶𝑅 𝑤ℎ𝑒𝑟𝑒: − 𝑁 = 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑆𝑃𝑇 𝑏𝑙𝑜𝑤 𝑐𝑜𝑢𝑛𝑡 − 𝐶_𝑁 = 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑜𝑣𝑒𝑟𝑏𝑢𝑟𝑑𝑒𝑛 𝑠𝑡𝑟𝑒𝑠𝑠 − 𝐶_𝐸 = 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑒𝑛𝑒𝑟𝑔𝑦 𝑟𝑎𝑡𝑖𝑜 − 𝐶_𝑆 = 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑏𝑜𝑟𝑒ℎ𝑜𝑙𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 − 𝐶_𝐵 = 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑟𝑜𝑑 𝑙𝑒𝑛𝑔𝑡ℎ − 𝐶_𝑅 = 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑠𝑎𝑚𝑝𝑙𝑒𝑟 𝑡𝑦𝑝𝑒 𝑆𝑡𝑒𝑝 2: 𝑂𝑣𝑒𝑟𝑏𝑢𝑟𝑑𝑒𝑛 𝑆𝑡𝑟𝑒𝑠𝑠 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟 (𝐶_𝑁) 2. 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟 (𝐶_𝑁): 𝐶𝑁 = ( 𝑃𝑎 𝜎{𝑣𝑜} ′ ) {0.5} 𝑤ℎ𝑒𝑟𝑒: − 𝑃_𝑎 = 𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑖𝑐 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑡𝑦𝑝𝑖𝑐𝑎𝑙𝑙𝑦 100 𝑘𝑃𝑎) − 𝜎′_{𝑣𝑜} = 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑜𝑣𝑒𝑟𝑏𝑢𝑟𝑑𝑒𝑛 𝑠𝑡𝑟𝑒𝑠𝑠 𝑆𝑡𝑒𝑝 3: 𝐶𝑦𝑐𝑙𝑖𝑐 𝑆𝑡𝑟𝑒𝑠𝑠 𝑅𝑎𝑡𝑖𝑜 (𝐶𝑆𝑅) 3. 𝐶𝑦𝑐𝑙𝑖𝑐 𝑆𝑡𝑟𝑒𝑠𝑠 𝑅𝑎𝑡𝑖𝑜 (𝐶𝑆𝑅): 𝐶𝑆𝑅 = 0.65 × ( 𝜏{𝑚𝑎𝑥} 𝜎{𝑣𝑜} ′ ) 𝑤ℎ𝑒𝑟𝑒: − 𝜏{𝑚𝑎𝑥} = 0.65 × 𝑎{𝑚𝑎𝑥} × 𝜎{𝑣𝑜} 𝑔𝑎 _ −{𝑚𝑎𝑥} = 𝑝𝑒𝑎𝑘 𝑔𝑟𝑜𝑢𝑛𝑑 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 − 𝜎_{𝑣𝑜} = 𝑡𝑜𝑡𝑎𝑙 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑜𝑣𝑒𝑟𝑏𝑢𝑟𝑑𝑒𝑛 𝑠𝑡𝑟𝑒𝑠𝑠 − 𝑔 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑢𝑒 𝑡𝑜 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑆𝑡𝑒𝑝 4: 𝐶𝑦𝑐𝑙𝑖𝑐 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅𝑎𝑡𝑖𝑜 (𝐶𝑅𝑅) 4. 𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒 𝐶𝑅𝑅 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛: 𝐶𝑅𝑅{7.5} = 1 (34 – (𝑁1)60) 𝑆𝑡𝑒𝑝 5: 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑆𝑐𝑎𝑙𝑖𝑛𝑔 𝐹𝑎𝑐𝑡𝑜𝑟 (𝑀𝑆𝐹) 5. 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑆𝑐𝑎𝑙𝑖𝑛𝑔 𝐹𝑎𝑐𝑡𝑜𝑟 (𝑀𝑆𝐹): Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 441 https://internationalpubls.com 𝑀𝑆𝐹 = 10 {( −2.24 𝑀𝑤− 2.56 )} 𝑤ℎ𝑒𝑟𝑒: − 𝑀_𝑤 = 𝑚𝑜𝑚𝑒𝑛𝑡 𝑚𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑎𝑟𝑡ℎ𝑞𝑢𝑎𝑘𝑒 𝑆𝑡𝑒𝑝 6: 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝐶𝑅𝑅 6. 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝐶𝑅𝑅 𝑓𝑜𝑟 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 (𝐶𝑅𝑅): 𝐶𝑅𝑅 = 𝐶𝑅𝑅{7.5} × 𝑀𝑆𝐹 𝑆𝑡𝑒𝑝 7: 𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑆𝑎𝑓𝑒𝑡𝑦 (𝐹𝑆) 7. 𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑆𝑎𝑓𝑒𝑡𝑦 𝑎𝑔𝑎𝑖𝑛𝑠𝑡 𝐿𝑖𝑞𝑢𝑒𝑓𝑎𝑐𝑡𝑖𝑜𝑛: 𝐹𝑆 = 𝐶𝑅𝑅 𝐶𝑆𝑅 𝑆𝑡𝑒𝑝 8: 𝐼𝑛𝑡𝑒𝑔𝑟𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑂𝑣𝑒𝑟𝑏𝑢𝑟𝑑𝑒𝑛 𝑆𝑡𝑟𝑒𝑠𝑠 8. 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑂𝑣𝑒𝑟𝑏𝑢𝑟𝑑𝑒𝑛 𝑆𝑡𝑟𝑒𝑠𝑠 (𝜎′_{𝑣𝑜}): 𝜎{𝑣𝑜} ′ = ∫ (𝛾 − 𝛾𝑤)𝑑𝑧 𝑧 0 𝑤ℎ𝑒𝑟𝑒: − 𝛾 = 𝑢𝑛𝑖𝑡 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑜𝑖𝑙 − 𝛾_𝑤 = 𝑢𝑛𝑖𝑡 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 − 𝑧 = 𝑑𝑒𝑝𝑡ℎ 𝑆𝑡𝑒𝑝 9: 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃𝑒𝑎𝑘 𝐺𝑟𝑜𝑢𝑛𝑑 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 (𝑃𝐺𝐴) 9. 𝑃𝑒𝑎𝑘 𝐺𝑟𝑜𝑢𝑛𝑑 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 (𝑃𝐺𝐴): 𝑎_{𝑚𝑎𝑥} = 𝐹 × 𝑆 × 𝑍 × 𝑇 𝑤ℎ𝑒𝑟𝑒: − 𝐹, 𝑆, 𝑍, 𝑇 = 𝑓𝑎𝑐𝑡𝑜𝑟𝑠 𝑑𝑒𝑝𝑒𝑛𝑑𝑖𝑛𝑔 𝑜𝑛 𝑠𝑖𝑡𝑒 𝑐ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐𝑠, 𝑠𝑜𝑖𝑙 𝑡𝑦𝑝𝑒, 𝑎𝑛𝑑 𝑠𝑒𝑖𝑠𝑚𝑖𝑐 𝑧𝑜𝑛𝑒 𝑆𝑡𝑒𝑝 10: 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝐹𝑖𝑛𝑒𝑠 𝐶𝑜𝑛𝑡𝑒𝑛𝑡 (𝐹𝐶) 10. 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝐹𝑖𝑛𝑒𝑠 𝐶𝑜𝑛𝑡𝑒𝑛𝑡: (𝑁1)60𝑐𝑠 = (𝑁1)60 × (1 + 𝐹𝐶 100 ) 𝑤ℎ𝑒𝑟𝑒: − 𝐹𝐶 = 𝑓𝑖𝑛𝑒𝑠 𝑐𝑜𝑛𝑡𝑒𝑛𝑡 𝑖𝑛 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑆𝑡𝑒𝑝 11: 𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑓𝑜𝑟 𝑂𝑣𝑒𝑟𝑏𝑢𝑟𝑑𝑒𝑛 𝑆𝑡𝑟𝑒𝑠𝑠 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 11. 𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑂𝑣𝑒𝑟𝑏𝑢𝑟𝑑𝑒𝑛 𝑆𝑡𝑟𝑒𝑠𝑠 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 (𝑓𝑜𝑟 𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑎𝑛𝑎𝑙𝑦𝑠𝑖𝑠): 𝑑(𝐶𝑁) 𝑑(𝜎{𝑣𝑜} ′ ) = −0.5 × 𝑃𝑎 {0.5} 𝜎{𝑣𝑜} ′{1.5} 𝑆𝑡𝑒𝑝 12: 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑖𝑒𝑑 𝐼𝑛𝑡𝑒𝑔𝑟𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝐶𝑆𝑅 𝑜𝑣𝑒𝑟 𝐷𝑒𝑝𝑡ℎ 12. 𝐼𝑛𝑡𝑒𝑔𝑟𝑎𝑡𝑒𝑑 𝐶𝑆𝑅 𝑜𝑣𝑒𝑟 𝐷𝑒𝑝𝑡ℎ: 𝐶𝑆𝑅{𝑎𝑣𝑔} = ∫ (0.65 × 𝜏{𝑚𝑎𝑥}(𝑧) 𝜎{𝑣𝑜}(𝑧) ′ ) 𝐷 0 𝑑𝑧 𝑤ℎ𝑒𝑟𝑒: − 𝐷 = 𝑑𝑒𝑝𝑡ℎ 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 442 https://internationalpubls.com When the PGA value is unavailable, (amax/g) might be assumed to be equivalent to the seismic zone factor Z. Considering that this is stated in IS 1893 (Part 1):2016 and that Nagpur is located in zone II on the seismic zoning map of India, this liquefaction potential assessment uses (amax/g) = 0.10. The final corrected SPT-N value and other parameters of the soil under research, such as fine content (FC), are used to calculate the Cyclic Resistance Ratio (CRR) using the following expressions. For an earthquake of magnitude of Mw=7.5, a high overburden stress level, and a high initial static shear stress, CRR must be adjusted to the comparable uniform shear stress. 𝐶𝑅𝑅 = 𝐶𝑅𝑅 7.5 (𝑀𝑆𝐹) 𝐾𝜎 𝐾𝛼 Where, CRR 7.5 = CRR for an earthquake of magnitude 7.5 calculated using SPT data MSF = magnitude scaling factor and can be calculated as follows 𝑀𝑆𝐹 = ( 102.24 𝑀𝑊2.56 ) Kσ = Correction for high overburden stress , when depth of assessment is greater than 15 m, then correction for high overburden stresses is required and can be calculated as below; 𝐾𝜎 = (𝜎’ 𝑣𝑜 𝑃𝑎 ) (𝑓 − 1) Where, Pa = atmospheric pressure and f = exponent that is depending on the relative density Dr and when Dr is in between 40% to 60% then f will be 0.8 to 0.7 and when Dr is in between 60% to 0% then f will be 0.7 to 0.6 Examining the SPT-N number and relative density correlations, the values for Dr are tabulated as follows in Table 1 based on field N number. In a laboratory, relative density cannot be determined from the SPT samples because it requires sufficient samples. Table 1. Relative density and SPT-N values. Relative Density SPT-N Value Dr (%) Very loose 0- 4 0 Loose 5 - 10 15 Medium 11 -30 35 Dense 31- 50 65 Very Dense > 50 85 Kα = is only necessary for sloping terrain and is not essential for standard engineering practice; as a result, this value is taken to be 1 for the purposes of this work. Numerous adjustments and corrections are needed for filed N60 for hammer efficiency of 60% in order to calculate the CRR value based on the field SPT-N value as N60=NC60. As per IS 1893 (Part 1) : 2013 if Non-standard method is used for conducting SPT then corrections will be require as given in clause F-1, Step:6(a) and Table 12 of IS 1893 (Part 1) : 2013. But in this research work standard method is adopted for conducting SPT hence no corrections is required and C60 = 1 is considered. Further it required normalizing this computed N60 value with effective overburden Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 443 https://internationalpubls.com pressure, as(𝑁1)60 = 𝐶𝑁𝑁60. Here CN is effective overburden correction factor and can be found as, 𝐶𝑁 = √(𝑃𝑎/𝜎’𝑣𝑜) ≤ 1.7 The graph in Fig.8 of IS 1893 (Part 1): 2013, which is based on the (N1)60 value for a specific percentage of FC, can be used to calculate CRR7.5 for MW = 7.5. Since MW=7.0 is taken into account in this study and the fine contents differ from what is specified in the code, further calculations are made in order to increase the correctness and dependability of the findings and research. By discovering (N1)60CS and correlating (N1)60, it is reasonable to explain the effect of FC in percent in the following way. (𝑁1)60𝐶𝑆 = 𝛼 + 𝛽 (𝑁1)60 Where, values and conditions for α & β is given in IS IS 1893 (Part 1): 2013 Figure.8 of IS 1893 (Part 1): 2013 can be utilised in estimation of CRR7.5, with (N1)60CS being used in place of (N1)60 and just the SPT clean sand based curve being utilised, regardless of the amount of particles. However, it is not required to meet clean sand every time; hence, the CRR7.5 is determined using the equation below. 𝐶𝑅𝑅7.5 = 1 34 − ((𝑁1)60𝐶𝑆 + (𝑁1)60𝐶𝑆 135 + 50 [10𝑋(𝑁1)60𝐶𝑆 + 45]2 + 1 200 The examination of liquefaction susceptibility results is presented as a factor of safety (FS) concern and is calculated as 𝐹𝑆 = 𝐶𝑅𝑅 𝐶𝑆𝑅. It is considered that soil is liquefiable if FS<1. The soil is assumed to be marginally liquefiable when the FS is between 1.1 and 1.2, and not liquefiable when the FS is more than 1.2. The findings of the liquefaction study utilizing the aforesaid methodology are assessed for FS vs Depth in Figure 6, and (N1)60 vs CSR in Fig. 8, which specifies the liquefiable condition. Additionally, rd vs Depth in Fig. 9 and σ'vo vs Kσ is analyzed in Fig.10 (1) (2) Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 444 https://internationalpubls.com (3) (4) (5) (6) (7) (8) (9) (10) Fig. 6 Different study factor in depth Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 445 https://internationalpubls.com 9. Calculation of liquefaction potential An example location from the entire study region was chosen to elaborate on the computation of liquefaction calculations, as shown in Fig. 4. This detailed analysis is crucial for understanding the specific conditions and risks associated with this site. The borehole (BH-1) data provides a comprehensive profile of the soil stratification, including SPT-N values, which are fundamental to assessing liquefaction potential. • Soil Stratification and SPT-N Values The soil stratification at this location, as illustrated in Fig. 7, includes three distinct layers: Clayey Soil: The uppermost layer, characterized by lower SPT-N values, indicating a relatively loose and potentially less stable soil structure. Sandy Silty Soil: This intermediate layer exhibits varying SPT-N values, reflecting changes in density and composition. Sandy silty soils are particularly susceptible to liquefaction due to their granular nature and the presence of fine particles. Rock Strata: The deepest layer consists of rock, which provides a stable foundation and typically has high SPT-N values, indicating high resistance to penetration and low liquefaction susceptibility. • Liquefaction Potential Assessment The Factor of Safety (FOS) with respect to liquefaction potential is a critical metric used in this assessment. For an earthquake magnitude of MW=7.0, the calculation at BH-1 involves several steps: Determine Cyclic Stress Ratio (CSR): CSR is calculated using the earthquake magnitude, site- specific seismicity, and overburden pressure. It represents the shear stress induced by the earthquake. Calculate Cyclic Resistance Ratio (CRR): CRR is derived from the SPT-N values, considering soil type and depth. It indicates the soil's capacity to resist liquefaction. Compute Factor of Safety (FOS): The FOS is the ratio of CRR to CSR. A FOS greater than 1.0 implies that the soil can resist liquefaction, while a FOS less than 1.0 indicates potential liquefaction. • Detailed Results at BH-1 Clayey Soil Layer: The SPT-N values in this layer are relatively low, leading to a lower CRR. Given the CSR induced by an MW=7.0 earthquake, the FOS may be close to or less than 1.0, suggesting a potential risk of liquefaction. Sandy Silty Soil Layer: This layer shows variability in SPT-N values. Zones with lower SPT-N values have a higher risk of liquefaction, especially if the CRR is insufficient to counteract the CSR. The FOS in these zones can be less than 1.0, highlighting areas of concern. Rock Strata: With high SPT-N values, the CRR is significantly higher than the CSR, resulting in a FOS much greater than 1.0. This indicates no risk of liquefaction in this layer. 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝐿𝑖𝑞𝑢𝑒𝑓𝑎𝑐𝑡𝑖𝑜𝑛 𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑆𝑡𝑒𝑝 1: 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝐶𝑦𝑐𝑙𝑖𝑐 𝑆𝑡𝑟𝑒𝑠𝑠 𝑅𝑎𝑡𝑖𝑜 (𝐶𝑆𝑅) 1. 𝐶𝑦𝑐𝑙𝑖𝑐 𝑆𝑡𝑟𝑒𝑠𝑠 𝑅𝑎𝑡𝑖𝑜 (𝐶𝑆𝑅): 𝐶𝑆𝑅 = 0.65 × (𝜏_{𝑚𝑎𝑥} / 𝜎′_{𝑣𝑜}) 𝑤ℎ𝑒𝑟𝑒: − 𝜏_{𝑚𝑎𝑥} = 0.65 × 𝑎_{𝑚𝑎𝑥} × 𝜎_{𝑣𝑜} / 𝑔 − 𝑎_{𝑚𝑎𝑥} = 𝑝𝑒𝑎𝑘 𝑔𝑟𝑜𝑢𝑛𝑑 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 446 https://internationalpubls.com − 𝜎_{𝑣𝑜} = 𝑡𝑜𝑡𝑎𝑙 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑜𝑣𝑒𝑟𝑏𝑢𝑟𝑑𝑒𝑛 𝑠𝑡𝑟𝑒𝑠𝑠 − 𝜎′_{𝑣𝑜} = 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑜𝑣𝑒𝑟𝑏𝑢𝑟𝑑𝑒𝑛 𝑠𝑡𝑟𝑒𝑠𝑠 − 𝑔 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑢𝑒 𝑡𝑜 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑆𝑡𝑒𝑝 2: 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝐶𝑦𝑐𝑙𝑖𝑐 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅𝑎𝑡𝑖𝑜 (𝐶𝑅𝑅) 2. 𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒 𝐶𝑅𝑅 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛: 𝐶𝑅𝑅_{7.5} = 1 / (34 − (𝑁₁)₆₀) 𝑤ℎ𝑒𝑟𝑒: − (𝑁₁)₆₀ = 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑆𝑃𝑇 𝑏𝑙𝑜𝑤 𝑐𝑜𝑢𝑛𝑡 𝑆𝑡𝑒𝑝 3: 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑆𝑐𝑎𝑙𝑖𝑛𝑔 𝐹𝑎𝑐𝑡𝑜𝑟 (𝑀𝑆𝐹) 3. 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑆𝑐𝑎𝑙𝑖𝑛𝑔 𝐹𝑎𝑐𝑡𝑜𝑟 (𝑀𝑆𝐹): 𝑀𝑆𝐹 = 10^(−2.24 / 𝑀_𝑤 − 2.56) 𝑤ℎ𝑒𝑟𝑒: − 𝑀_𝑤 = 𝑚𝑜𝑚𝑒𝑛𝑡 𝑚𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑎𝑟𝑡ℎ𝑞𝑢𝑎𝑘𝑒 𝑆𝑡𝑒𝑝 4: 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝐶𝑦𝑐𝑙𝑖𝑐 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅𝑎𝑡𝑖𝑜 (𝐶𝑅𝑅) 4. 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝐶𝑅𝑅 𝑓𝑜𝑟 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 (𝐶𝑅𝑅): 𝐶𝑅𝑅 = 𝐶𝑅𝑅_{7.5} × 𝑀𝑆𝐹 𝑆𝑡𝑒𝑝 5: 𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑆𝑎𝑓𝑒𝑡𝑦 (𝐹𝑆) 𝑎𝑔𝑎𝑖𝑛𝑠𝑡 𝐿𝑖𝑞𝑢𝑒𝑓𝑎𝑐𝑡𝑖𝑜𝑛 5. 𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑆𝑎𝑓𝑒𝑡𝑦 𝑎𝑔𝑎𝑖𝑛𝑠𝑡 𝐿𝑖𝑞𝑢𝑒𝑓𝑎𝑐𝑡𝑖𝑜𝑛: 𝐹𝑆 = 𝐶𝑅𝑅 / 𝐶𝑆𝑅 Example Calculation: Given: - Observed SPT blow count N = 20 - Overburden correction factor C_N = 1.2 - Peak ground acceleration a_{max} = 0.3g - Total vertical overburden stress σ_{vo} = 100 kPa - Effective overburden stress σ'_{vo} = 80 kPa - Moment magnitude of the earthquake M_w = 7.5 Step-by-Step Calculation: 1. Corrected SPT-N Value: (𝑁1)60 = 𝑁 × 𝐶𝑁 = 20 × 1.2 = 24 2. Cyclic Stress Ratio (CSR): 𝜏{𝑚𝑎𝑥} = 0.65 × 𝑎{𝑚𝑎𝑥} × 𝜎{𝑣𝑜} = 0.65 × 0.3 × 100 = 19.5 𝑘𝑃𝑎R = 0.65 × (19.5 / 80) = 0.158 3. Cyclic Resistance Ratio (CRR): CRR_{7.5} = 1 / (34 - 24) = 1 / 10 = 0.1 4. Magnitude Scaling Factor (MSF): MSF = 10^(-2.24 / 7.5 - 2.56) ≈ 1 (for M_w = 7.5, MSF is often considered as 1) 5. Adjusted CRR: CRR = CRR_{7.5} × MSF = 0.1 × 1 = 0.1 6. Factor of Safety (FS): Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 447 https://internationalpubls.com FS = CRR / CSR = 0.1 / 0.158 ≈ 0.63 Fig. 7 Representation of soil layers, Standard Penetration Test (SPT) N-values, Factor of Safety (FOS) against liquefaction 10. Result and Discussions:- 10.1 Soil Characterization In study locations, 10 boreholes were bored to a depth of 35.0 m. A typical penetration test was performed each 1.5 m up to this depth. SPT-N results varying from 11 to above 50 (refusal). Bhandara soils are predominantly Clayey soils followed by coarse-grained (sand and gravel) with tiny amounts of silt and fine clay, forming alluvial deposits. The thickness of these layers varies significantly. Non-plastic inorganic silts were discovered in an every location after clayey soils. The majority of the coarse-grained component is classified as SM. Fine-grained soils have plasticity indexes ranging from 7.81 to 21.48%, with most falling within the 20% to 22% range. The 10 drilling logs revealed that the majority of the water table was within 0-5 m of the ground surface. The presence of granular soil and a near-surface water table can lead to liquefaction during earthquakes. Fig 5 shows typical soil profiles from four locations in the Bhandara region where the study is conducted. The image shows varied soil layers with a significant concentration of sand and gravel D e p th B el o w E G L , m T y p e o f S tr a ta O b se rv e d S P T v a lu e F in e C o n te n t (% ) S tr e ss r e d u c ti o n f a c to r (r d ) S a tu r a te d d e n si ty (g m /c c ) V e r ti ca l O v e r b u r d e n S tr e ss ( σ v o ) ( t/ m 2 ) E ff e c ti v e V e r ti ca l O v er b u r d e n S tr e ss ( σ ' v o ) (t /m 2 ) C y c li c S tr e ss R a ti o C S R C N N 6 0 C o r re c te d S P T ( N 1 ) 6 0 (N 1 ) 6 0 C S C R R 7 .5 R e la ti v e d e n si ty , D r% f K σ M a g n it u d e s c a li n g f a c to r M S F C y c li c R e si st a n ce R a ti o C R R F O S D is cr ip ti o n 1.5 C H 18 89 0.9 89 1.8 7 2.80 5 1.30 5 0.1 38 1.7 18 30. 6 37. 22 - 0.0 4 35 0.8 3 1.4 3 1.1 9 - 0.0 7 - 0.5 Liquefiable 3.0 C H 20 56 0.9 77 1.8 9 5.67 2.67 0.1 35 1.7 20 34 41. 3 0.1 6 35 0.8 3 1.2 6 1.1 9 0.2 4 1.8 Non Liquefiable 4.5 S 25 48 0.9 1.9 8.73 4.23 0.1 1.5 25 38. 46. 0.2 35 0.8 1.1 1.1 0.3 2.8 Non Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 448 https://internationalpubls.com D e p th B el o w E G L , m T y p e o f S tr a ta O b se rv e d S P T v a lu e F in e C o n te n t (% ) S tr e ss r e d u c ti o n f a c to r (r d ) S a tu r a te d d e n si ty (g m /c c ) V e r ti ca l O v e r b u r d e n S tr e ss ( σ v o ) ( t/ m 2 ) E ff e c ti v e V e r ti ca l O v er b u r d e n S tr e ss ( σ ' v o ) (t /m 2 ) C y c li c S tr e ss R a ti o C S R C N N 6 0 C o r re c te d S P T ( N 1 ) 6 0 (N 1 ) 6 0 C S C R R 7 .5 R e la ti v e d e n si ty , D r% f K σ M a g n it u d e s c a li n g f a c to r M S F C y c li c R e si st a n ce R a ti o C R R F O S D is cr ip ti o n C 66 4 3 4 5 7 6 3 6 9 6 Liquefiable 6.0 S C 27 46 0.9 54 1.9 5 11.7 5.7 0.1 27 1.3 2 27 35. 64 43. 27 0.2 1 35 0.8 3 1.1 1.1 9 0.2 7 2.1 Non Liquefiable 7.5 S C 32 46 0.9 43 1.9 6 14.7 7.2 0.1 25 1.1 8 32 37. 76 45. 81 0.2 5 65 0.6 8 1.1 1 1.1 9 0.3 3 2.6 Non Liquefiable 9.0 S C 43 44 0.9 31 1.9 7 17.7 3 8.73 0.1 23 1.0 7 43 46. 01 55. 71 0.3 6 65 0.6 8 1.0 5 1.1 9 0.4 5 3.7 Non Liquefiable 10. 5 S C 50 43 0.8 94 1.9 8 20.7 9 10.2 9 0.1 17 0.9 9 50 49. 5 59. 9 0.4 65 0.6 8 0.9 9 1.1 9 0.4 7 4.0 Non Liquefiable 12. 0 S C 50 42 0.8 54 1.9 9 23.8 8 11.8 8 0.1 12 0.9 2 50 46 55. 7 0.3 6 65 0.6 8 0.9 5 1.1 9 0.4 1 3.7 Non Liquefiable 13. 5 S C 50 25 0.8 14 1.9 9 26.8 65 13.3 65 0.1 06 0.8 6 50 43 52. 45 0.3 3 65 0.6 8 0.9 1 1.1 9 0.3 6 3.4 Non Liquefiable 15. 0 S M 50 10 0.7 74 1.9 9 29.8 5 14.8 5 0.1 01 0.8 2 50 41 42. 69 0.2 65 0.6 8 0.8 8 1.1 9 0.2 1 2.1 Non Liquefiable 16. 5 S M 50 12 0.7 33 1.9 9 32.8 35 16.3 35 0.0 96 0.7 8 50 39 41. 72 0.1 7 65 0.6 8 0.8 5 1.1 9 0.1 7 1.8 Non Liquefiable 18. 0 S M 50 10 0.6 93 1.9 9 35.8 2 17.8 2 0.0 91 0.7 5 50 37. 5 39. 12 0.0 9 65 0.6 8 0.8 3 1.1 9 0.0 9 2.0 Non Liquefiable 19. 5 S M 50 10 0.6 53 1.9 9 38.8 05 19.3 05 0.0 85 0.7 2 50 36 37. 59 0.0 9 65 0.6 8 0.8 1 1.1 9 0.0 9 3.0 Non Liquefiable 21. 0 S M 50 8 0.6 13 1.9 9 41.7 9 20.7 9 0.0 8 0.6 9 50 34. 5 35. 14 0.6 2 65 0.6 8 0.7 9 1.1 9 0.5 8 7.3 Non Liquefiable 22. 5 S M 50 8 0.5 73 1.9 9 44.7 75 22.2 75 0.0 75 0.6 7 50 33. 5 34. 13 7.4 4 65 0.6 8 0.7 7 1.1 9 6.8 2 90. 9 Non Liquefiable 24. 0 S M 50 9 0.5 52 1.9 9 47.7 6 23.7 6 0.0 72 0.6 5 50 32. 5 33. 71 3.6 9 65 0.6 8 0.7 5 1.1 9 3.2 9 45. 7 Non Liquefiable 25. 5 S M 50 7 0.5 4 1.9 9 50.7 45 25.2 45 0.0 71 0.6 3 50 31. 5 31. 94 0.7 2 65 0.6 8 0.7 4 1.1 9 0.6 3 8.9 Non Liquefiable 27. 0 S M 50 5 0.5 28 1.9 9 53.7 3 26.7 3 0.0 69 0.6 1 50 30. 5 30. 5 0.5 1 65 0.6 8 0.7 3 1.1 9 0.4 4 6.4 Non Liquefiable 28. 5 S M 50 8 0.5 16 1.9 9 56.7 15 28.2 15 0.0 67 0.6 50 30 30. 6 0.5 2 65 0.6 8 0.7 1 1.1 9 0.4 4 6.6 Non Liquefiable 30. 0 S M 50 2 0.5 04 1.9 9 59.7 29.7 0.0 66 0.5 8 50 29 29 0.4 1 65 0.6 8 0.7 1.1 9 0.3 4 5.2 Non Liquefiable Table 2. Sample calculation for liquefaction potential evaluation. 10.2 Liquefaction potential of the area:- Given the importance of Bhandara, this study aims to map the study region in terms of liquefaction risk and provide data for technocrats to use in constructing structures and preventing liquefaction- related risks, as indicated in Table 3. The lithological differences acquired from 10 boreholes demonstrate that the study region contains distinct layers of soil types and gradations of gravels, sand, silt, and clay. The stratification seen in boreholes varies in thickness and shape depending on location. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 449 https://internationalpubls.com Table 3. Estimated FOS and Potential to Liquefaction. BH No Depth of liquefiable layer in meter F.O.S Description BH-1 1.50 -0.5 Liquefiable BH-2 3.00 0.4 Liquefiable 4.50 1.1 Marginally Liquefiable 6.00 -2.0 Liquefiable BH-3 4.50 0.90 Liquefiable 6.00 1.00 Marginally Liquefiable BH-5 3.00 0.40 Liquefiable BH-7 1.50 0.50 Liquefiable BH-8 1.50 0.50 Liquefiable Some layers of the bore hole in various sections of Bhandara under study were found to be sensitive to liquefaction; two of them showed marginal liquefaction activity, while six showed evidence of liquefaction potential. The depths of liquefaction layers vary depending on the stratification and this might be due to the existence of a significant amount of sand in that layer, but it is not limited to that; certain layers contain clay and exhibit liquefaction capabilities, as shown in Table 4. Many parameters were evaluated in this study to directly evaluate the liquefaction potential if an investigation is conducted and to reduce the time-consuming calculations. IS 1893 (Part 1):2016 provides a curve for estimating CRR7.5, but this curve is limited to clean sand, which is not a condition in every location where clean sand is encountered. To overcome this, in this study, a curve is evolved as shown in Fig. 8, based on actual field and laboratory testing, and CRR7.5 can be estimated directly for the bhandara region. Fig. 8 Representation of Correlation for Earthquake It was looked at up to a depth of 35 meters in this study, which is deeper than the 23-meter limit set by IS standards. Scholars have found different results when they try to connect rd and depth, which has led to different readings. The calculations here tried to make things clearer by increasing the depth range to 35 meters, as shown in Fig. 9. Figure 9 shows that as depth goes up, the stress reduction factor goes down. It is this drop in rd that causes the Cyclic Stress Ratio (CSR) to go down and the Factor of Safety (FOS) against liquefaction to rise. There is a clear trend in the graph. The Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 450 https://internationalpubls.com rate of drop in rd is slower up to 20 meters, but then it speeds up. The research shows that the stress reduction factor decreases slowly up to 20 meters, but it becomes more noticeable after that. Inferring from this that deeper layers of dirt have much lower CSR makes them more resistant to liquefaction. This connection is very important for building infrastructure because it shows how important it is to do more in-depth soil studies to correctly figure out and lower the risks of liquefaction in areas that are prone to earthquakes. Fig. 9 Representation of depth rate factor Stress too much Kπ is an adjustment factor for initial shear stress and effective top pressure. It changes depending on the type of soil and how dense and pressurized the air is. In this study, detailed data from both the site and the lab were used to figure out Kπ for each place. Figure 10 shows the connection between Kπ and effective overburden stress. It shows that as effective overburden stress rises, so does Kπ. This image makes it easier to figure out the liquefaction potential for the study area. This saves time and cuts down on the amount of data that needs to be collected to figure out Kπ, which makes risk estimates more accurate. Fig. 10 Overview representation variation correlation factor Laboratory test results on soil samples for grain size measurement demonstrate that as depth increases, fine content drops significantly, as illustrated in Fig. 11. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 451 https://internationalpubls.com Fig. 11 Representation of Fine consent Vs depth 11. Conclusion According to the Standard Penetration Test (SPT-N) method, this study gives a full look at the liquefaction potential in the Bhandara area of Maharashtra. The results show that liquefaction susceptibility varies a lot depending on the type of soil and how deep it is. The depth of the research was increased from the usual 35 meters set by IS standards. This study gives a better picture of the physical qualities of the area. The stress reduction factor (rd) study shows that rd drops slowly up to a depth of 20 meters, but drops more quickly after that. This means that in deeper layers, the Cyclic Stress Ratios (CSR) are lower and the Factors of Safety (FOS) against liquefaction are higher. This information is very important for correctly figuring out the risk of liquefaction and using it to build and create strong infrastructure. The study also stresses how important it is to look at overload stress Kπ in each place individually. We found the link between effective overload stress and Kπ by using thorough data from both the site and the lab. This gives us a useful way to quickly check the liquefaction potential. The connection graph speeds up math, cutting down on the need to collect large amounts of data and shortening the time it takes to evaluate danger. What this means for building up facilities is very important. Finding high-risk areas lets you take specific steps to protect buildings, like stabilizing the dirt, building deep foundations, and improving drains. This makes sure that buildings last and are safe. This localized assessment approach not only makes infrastructure in the Bhandara region more resistant to earthquakes, but it can also be used as a model for similar assessments of seismic risk in other places. References [1] Sladen, J. A., Holeander, R. D., and Krahn, J., 1985. The liquefaction of sands- a collapse surface approach; Canadian Geotechnical Journal., v.22, pp: 564-578. [2] Idriss, I. M., and Boulanger, R. W., 2004. “Semi empirical procedure for evaluation liquefaction potential during earthquake” Proceeding joint conference, The 11th International conf. of soil dynamics and earthquake engineering (SDEE), the 3rd international conf. on Earthquake Geotechnical Engineering (ICEGE), Berkeley California. pp: 32-56. [3] Seed, R. B., Cetin, K. O., Moss, R. E. S., Kammerer, A. M., Wu, J., Pestana, J. M., Riemer, M.F., Sancio, R.B., Bray, J.D., Kayen, R. E., and Faris, A., 2003. “Recent Advances in SoilLiquefaction Engineering: A Unified and Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 452 https://internationalpubls.com Consistent Framework”, 26th Annual ASCE Los Angeles Geotechnical Spring Seminar, Keynote Presentation, H.M.S. Queen Mary, Long Beach, California, April 30, 2003. [4] Wang, W.(1979). Some findings in soil liquefaction; water conservancy and Hydroelectric power scientific research institute, Bejing, China. 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