Introduction

Seismic site characterization of subsurface soil profiles at a specific location is a critical endeavour for assessing site response at the surface level. This characterization helps in understanding the behaviour of the soil during a seismic event and its implication on the structures situated above these soils. Shear wave velocity \(V_{S}\) is the main factor used to assess and characterize the response of seismically active areas. Notably, the average shear wave velocity of the top 30 m (\(V_{S30}\)) of the soil profiles serves as a fundamental criterion for seismic site classification, as stipulated in the seismic design guidelines recommended by the National Earthquake Hazard Reduction Program (NEHRP) manual1,2. Subsequently, these site classifications are employed to determine seismic coefficients that are integral to the design of earthquake-resistant structures1. Furthermore, \(V_{S}\) is utilized for calculating the natural period of a site, studying soil-structure interactions, and analyzing wave amplification3,4,5,6. Designers anticipate comparable responses from sites classified within the same category when subjected to identical seismic events7,8,9,10. Several wave propagation-based geophysical tests, such as seismic cross-hole, down-hole, up-hole, and Multi-Channel Analysis of Surface Waves (MASW), are employed to determine \(V_{S}\). Among these, the seismic cross-hole test (CHST) is considered the most accurate for measuring \(V_{S}\)11, this is because it involves in-situ measurements that encompass a significant volume of soil between boreholes, utilizes undisturbed soil, employs higher frequency waves that average the properties of a relatively smaller mass of soil and offers enhanced resolution11,12,13,14. Standard penetration tests (SPT) rank among the oldest and most frequently used globally for any civil engineering projects. SPT is a well-established in-situ testing method known for its simplicity, making it highly popular in geotechnical investigations15,16. Consequently, numerous investigators have devoted extensive efforts to correlate standard penetration test (SPT) results, specifically N-values, with several critical soil properties that typically necessitate sampling and laboratory testing for determination15,17. As a result, SPT is extensively employed in assessing soil parameters such as relative density, angle of internal friction, and other key characteristics.

Although the determination of \(V_{S}\) through field experiments is preferred, conducting these measurements in situ is frequently economically unfeasible. Particularly in urban areas, where challenges such as limited space, elevated noise levels, a shortage of skilled personnel, and cost considerations prevail, soil investigation firms often eschew this testing method. To address this issue, researchers globally have explored indirect methods for measuring \(V_{S}\). In this context, numerous empirical correlations have been established between \(V_{S}\) and in-situ static tests, such as the standard penetration test (SPT) and cone penetration test (CPT), which are predominantly utilized for geotechnical site investigations8,18,19,20,21,22,23 . The correlation between SPT-N values and \(V_{S}\) also reflects an oblique connection between initial strength and soil stiffness. The main benefits of these correlations are their ease, efficacy, and computational efficiency. Seismic site categorization is of utmost importance due to its wide-ranging applications, such as developing attenuation relationships and conducting regional seismic site response assessments24,25,26.

There have been no prior seismic site classification studies to analyze the site in the current research region, and there is no recorded connection between SPT-N values and \(V_{S}\) for Noida city in the available literature. Moreover, there is a pressing need for a thorough site categorization map for the city of Noida.

Seismotectonic setting and geology of the study area

Noida, officially known as the New Okhla Industrial Development Authority, is strategically positioned with boundaries demarcated by the Yamuna River and Delhi to the west and southwest, National Highway 24 and Ghaziabad to the north, the Hindon River and Greater Noida to the east, and the confluence of the Yamuna and Hindon rivers to the south. Noida is located in a seismically active area, classified as Zone IV according to IS: 189327, indicating a high risk of seismic activity (Fig. 1). There are three significant earthquakes with magnitudes higher than 5.0 that have been reported within a 100 km radius of the study region. These earthquakes are July 15, 1720, 6.5ML near Gurugram, Haryana, October 10, 1956, 6.7ML of Faridabad, Haryana and, March 5, 2012, 5.1ML of Rohtak, Haryana. All these events are shown in Fig. 1.

Fig. 1
Fig. 1
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Earthquakes of magnitudes ML ≥ 5 occurring between the years 1720 and 2022 within a 100 km radius of the study region (Box colour legends show the earthquakes’ focal depths.) [Source: https://seismo.gov. in/MIS/riseq/earthquake] (modified after Kundu et al., 2024b30).

Broadly, two distinct geological units can be seen in Noida city—a) Older alluvium or Varanasi alluvium underlying Younger alluvial plain or upland area, and b) Younger alluvium or Terrace alluvium underlying Younger alluvial plain, i.e., the flood plains of rivers. Noida City is situated on Quaternary sediments that are part of the Indo-Gangetic alluvium. This area includes a mixture of Varanasi alluvium and Terrace alluvium28.

The region is proximal to several significant geological faults and features capable of producing moderate to large earthquakes, including the Mathura fault, Sohna fault, Delhi-Hardwar ridge, Delhi-Lahore ridge, Mahendragarh-Dehradun fault, Aravalli-Delhi fold, Moradabad fault, and the Great Boundary fault, along with numerous minor lineaments(Fig. 2). Figures 1 and 2 address the same earthquakes, however, slight variations in location may appear as the data is referenced from different seismic recording stations.

Fig. 2
Fig. 2
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Map of the study area’s seismic activity, highlighting significant faults and past huge earthquakes (modified after Dasgupta et al., 200031; Prakash & Shrivastava, 201232, and Kundu et al., 2024b30).

Additionally, Noida is situated approximately 200 km from the Main Boundary Thrust (MBT) and about 300 km from the Main Central Thrust (MCT), both of which are major active thrust zones within the Himalayan region29. The presence of these tectonic and the geologic features poses a potential risk of tremors that could significantly impact the city. Therefore, estimating \(V_{S}\) profiles and conducting seismic site classification for Noida will be invaluable for comprehensive seismic hazard assessments.

Importance of this study

Seismic site characterization of any site is essential for the assessment of different types of earthquake-related hazards at the level of the ground surface. A comprehensive seismic site characterization study is highly essential for advanced assessment of seismic risk for urban areas as well as carrying out earthquake-resistant design of the latest engineering works. Extensive seismic site characterization studies and seismic hazard analyses have been performed by mapping the \(V_{S}\) of in-situ soil layers. The usage of this parameter has also been witnessed in many building codes like Eurocode8, International Building Code-2009 and Building Seismic Safety Council-20011,62,63. Unlike previous site-specific correlation studies focusing on SPT versus MASW49,52,61, this study aims to develop a correlation between SPT and CHST, which is widely regarded as the most accurate method for measuring \(V_{S}\)11. To enhance data reliability and minimize mismatches, \(V_{S}\) measurements were obtained from the same boreholes where the SPT tests were conducted.

Geographically, Noida extends from latitudes 28º18′12.54" N to 28º22′36.72" N and longitudes 77º10′28.97" E to 77º15′19.83" E, marking its eastern and southeastern limits adjacent to the National Capital Territory (NCT) of Delhi (Fig. 3b).Noida city is in a seismically active area, classified as seismic zone IV according to IS: 1893–2016, the second highest seismic zone. The city has experienced a maximum seismic intensity of VII-VIII on the Modified Mercalli Intensity (MMI) Scale by the 1803 Uttarakhand earthquake64. Soft alluvial sediments and fluctuating groundwater conditions can contribute to seismic amplification, potentially causing damage to multi-story buildings65. The geological features and tectonic features, along with the city’s rapid urbanization, underscore the urgent need for seismic site characterization study and the creation of safe, durable buildings to ensure the safety and resilience of structures. Noida city currently lacks a seismic microzonation study, except for a recent seismic hazard analysis conducted by Kundu et al.29. This study highlighted the potential for future seismic site characterization and ground response analysis, emphasizing that considering local soil conditions could greatly enhance design and construction practices in urban areas. The present study is an attempt to develop a comprehensive site classification as per NEHRP guidelines. The differences between the \(N_{30}\)-based and \(V_{S30}\)-based maps are thoroughly discussed, as well as their practical application and limitations. A robust SPT-\(V_{S}\) correlation is developed for Noida region and validated the present correlation against the benchmark global and local correlations by various statistical approaches. These results reinforce the importance of region-specific empirical correlations, as applying generalized correlations might lead to inaccurate site classifications and seismic hazard assessments. Finally, the manuscript discusses the future scope of the study, including recommendations for seismic site characterization and ground response analysis. It also addresses uncertainties inherent in the methodology and outlines ways to manage these uncertainties effectively (Table 1).

Fig. 3
Fig. 3
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Test setup of Standard penetration test (SPT) (a); Location of SPT and Seismic cross-hole tests (CHST) across Noida city (b).

Table 1 Some existing global correlations between SPT-N and \(V_{S}\) are considered in the present study.
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Geotechnical investigation

Geotechnical datasets encompassing soil classification outcomes, Atterberg limits, moisture content, and unit weight, along with shear strength parameters and standard penetration test (SPT) values, were collated from the geotechnical engineering reports provided by consulting engineering firm Cengrs Geotechnica Pvt. Ltd.

SPT data collection

The standard penetration test (SPT) was conducted as per the ASTM-D158666. This test is conducted in all geotechnical boreholes at every 1.5–2 m of depth or at every layer change, whichever occurs first. A standard split sampler is lowered into the borehole and driven into the ground using a 63.5 kg hammer, free-falling from a height of 762 mm onto an anvil placed on top of the drill rod. The number of blows required for each 15 cm penetration of the sampler into the soil is recorded. The first 15 cm of drive is considered the seating drive, while the total number of blows needed for the second and third 15 cm penetration is reported as the standard penetration resistance or N value. After the test is completed, the soil sample inside the sampler can be collected for further laboratory analysis. The soil specimen contained within the sampler is retrieved for potential use in further experimental analyses that include Atterberg’s limits, grain size analysis, soil density test, moisture content, specific gravity, are mentioned in Table 2. Table 2 shows the standard geotechnical properties of a sample, collected from borehole (BH04) located near the location of CHST 1. The soil profile of CHST 1, along with its SPT-N and \(V_{S}\) value, is shown in Fig. 4. The standard penetration test setup is shown in Fig. 3(a).

Table 2 Sample borehole section (BH-04).
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Fig. 4
Fig. 4
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\(V_{S}\) profile and SPT-N change vs. depth for one sample borehole in the study area.

In the collected data sets, out of 117 bore logs, 26 were selected that were close to the CHST test locations (see Fig. 3b) and were used for development of SPT- \(V_{S}\) correlation using non-linear regression analysis. The remaining 91 bore logs are available but not close to the CHST locations. The developed correlation further used to estimate the shear wave velocity (\(V_{S}\) ) profile at all 117 borehole locations.

The majority of boreholes reach up to a depth of 30 to 35 m, while approximately 10 boreholes are extended to greater depths ranging from 40 to 50 m. Typically, within the upper soil strata, the SPT-N values are relatively low, showing a gradual increase with depth. This rise in SPT-N values is likely due to the densification of soil layers caused by overburden pressure. Changes in SPT-N and \(V_{S}\) with depth for one sample borehole (CHST-1) located in Sec 62, Noida is shown in Fig. 4.

Geophysical investigation

Cross-hole tests require a minimum of three boreholes positioned at specific distances to ensure accurate \(V_{S}\) measurements. This setup needs ample open space, which is often unavailable in densely populated urban areas. Apart from that, permission from local authorities and ambient noise in urban environments are the biggest challenges faced during the field test. In this study, fourteen seismic cross-hole experiments were performed to assess the in-situ shear wave velocity (\(V_{S}\)), following the ASTM D4428/D4428M standards68. The CHST were well distributed across the city, similar methodology has been adopted for site characterization study of Lucknow51 and Varanasi59 by SPT and MASW, which are densely populated and located on the Indo-Gangetic plain, characterized by Quaternary alluvium consisting of older and newer alluvium. This implies lithological characteristics similar to those of our study area.

The survey employed equipment from Olson Instruments Inc., USA, which consisted of a Freedom Data PC (seismograph) with a high-speed data acquisition card, an electromechanical source (EMS), triaxial geophones (with vertical, radial, and transverse components), cables, and supplementary accessories (Fig. 5a). The experimental configuration consisted of three boreholes, namely one source hole and two receiver holes, which were positioned at a distance of 5 m from each other (Fig. 5b). After the completion of all the boreholes, PVC casings were inserted into each borehole. The area between the borehole wall and the casing was completely filled with a cement-bentonite grout of the correct density to guarantee proper contact with the surrounding soil.

Fig. 5
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Cross-hole test equipment (a); Cross-hole test arrangements (b).

In our study, hydrophones were utilized, which are interchangeable as both source and receiver. These hydrophones have a sampling frequency of 42 kHz, which is well-suited for capturing the full range of seismic wave frequencies encountered during the tests.

The subsequent phases entailed equipment installation and data acquisition:

  1. 1.

    A pneumatically activated piston lowered the electromagnetic P-SV source (EMS) to the measuring depth and was clamped to the casing walls.

  2. 2.

    Orthogonal down-hole sensors (Tri-axial geophones) were lowered to the same depth as the source. Dummy slope inclinometer probes were used to maintain the correct receiver orientation.

  3. 3.

    After reaching the desired depth, the bladders attached to each receiver geophone were inflated with air so that the geophones were properly clammed onto the casing.

  4. 4.

    All the communication cables in the source and receivers were connected to the amplifier module of the Freedom Data PC, together with the trigger cable.

  5. 5.

    The source was triggered from the surface to generate shear and compression wave energy at depth. Both upward and downward polarized energy was generated to duplicate data, and to measure shear wave arrival effectively.

  6. 6.

    The vertical component of the receiver was used to capture the vertically polarized shear waves (SV). The radial component senses the propagating compression waves (P), and the tangential component senses the horizontally propagating shear waves (SH).

  7. 7.

    The acquisition system captures both the EMS source input and the outputs from the receivers. The collected data are stored on the seismograph’s hard disk and transferred to a computer for post-processing.

  8. 8.

    Data analysis is conducted using the WinGEO(Version 2.1) analysis software provided by Olson Instruments, Inc.

Considering the objective of this paper, data analysis is limited to shear wave velocities. The data was stored in a seismograph at the time of data acquisition, and the data was transferred to a computer for post-processing. The processing involves picking the first arrivals. In case of noisy data, there are intermediate steps of data processing using filtering, amplitude corrections, etc. Velocity calculation is done based on the distance between the source and receiver boreholes. The shear wave energy was generated by triggering the source in both horizontal directions. In our study, a wooden plank is used to generate the shear wave.

In seismic down-hole testing, the challenge of distinguishing the first arrival of shear waves from compression waves is addressed by reversing the polarity of the source generating the wave pattern. This involves measuring the shear wave pattern twice using a horizontally directed sledgehammer strike on a firmly embedded post. The post is initially struck parallel to the ground surface, followed by a second strike applied 180 degrees out of phase (in the opposite direction) (Fig. 6). By reversing the direction of the energy input. The shear wave pattern is recorded in the reverse direction, while the compression wave pattern remains largely unchanged. This method effectively differentiates shear wave signals from compression wave signals. Figure 6 exhibits the standard chronological records of shear wave trains seen at two receivers, demonstrating a set of signals generated by hits from opposing directions. Shear wave energy is often detected when the polarized waves undergo a 180° phase shift, which is depicted by a vertical orange line. In this case, the occurrence times are 41,360 microseconds for Receiver 1 and 48,600 microseconds for Receiver 2, respectively. The \(V_{S}\) is determined using the formula, \(V_{S} = D/t\) where, D represents the distance between the source and receiver borehole, and t denotes the shear wave arrival time. This procedure is conducted at 1.5 m intervals along the depth of the borehole. Five data stacks were collected at each interval. After the computation of the wave velocity, a graph was assembled to show a velocity profile with depth (Fig. 4).

Fig. 6
Fig. 6
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Typical recorded time history of shear wave trains recorded at 6.0 m depth: (a) Receiver 1; (b) Receiver 2.Black colour- shear wave signal generated by the source when sledgehammer stroke parallel to the ground surface; Pink colour- shear wave signal generated by the source when sledgehammer stroke 180 degrees out of phase (i.e., in the opposite direction) [The vertical red line is used for computing the arrival time of the shear wave, it indicates the time where the polarized share waves become 180 degrees out of phase].

Correlation between \(V_{S}\) and SPT-N

Although various empirical relationships exist between \(V_{S}\) and SPT blow counts, these correlations are specific to particular areas and are not universally applicable across different regions. It is well established that SPT and \(V_{S}\) data collected at identical depths within the same borehole yield more accurate correlations than those obtained from disparate locations. In order to minimize inaccuracies in data collection and the determination of shear wave velocity, SPT-N values, and shear wave velocities were obtained from the exact same depths and boreholes.

This study aims to establish a correlation between \(V_{S}\) and the uncorrected standard penetration test value (SPT-N) for Noida city for all soil types. It has been observed that the correlation between uncorrected SPT-N—\(V_{S}\) gives better fitting, and also, the majority of the proposed correlations are based on the uncorrected SPT-N value49,52. Due to the lack of geophysical data covering the entire area, the empirical correlations were initially developed using the SPT-N values from boreholes and \(V_{S}\) values obtained from the seismic cross-hole test. SPT data obtained from 26 boreholes have been paired with seismic cross-hole test (CHST) derived 1D \(V_{S}\) profiles. For the current correlation study, a total of 179 data pairs of \(V_{S}\) and SPT-N were utilized. The fitted non-linear equation mentioned in Eq. 1 has a coefficient of regression (\(R^{2}\)) of 0.8811 for all soil types (see Fig. 7).

$$V_{S} = 59.271N^{0.4392}$$
(1)
Fig. 7
Fig. 7
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Non-linear correlation between SPT-N and \(V_{S}\).

Validation of the developed SPT-N – \(V_{S}\) relationship

Non-linear regression is used to develop the relationship between SPT-N values and \(V_{S}\). Non-linear regression can incorporate multiple forms of relationships (e.g., exponential, power-law), which align more closely with the underlying geotechnical and geophysical principles of soil behaviour. This flexibility improves the model’s predictive accuracy for \(V_{S}\) with varying SPT-N values. Non-linear regression allows the derived SPT-\(V_{S}\) correlation to be compared effectively with global and regional correlations. In the present study, the correlation aligns with established models from other regions, further supporting its validity. Also, the result of non-linear regression was found to be more accurate than the linear regression analysis for developing the SPT-\(V_{S}\) correlation of Indore city58.

The non-linear regression correlation equations developed for the study area were further evaluated using the coefficient of determination (R2) value and graphical methods. A R2 value of 0.8811 indicates a high correlation between \(V_{S}\) and the uncorrected standard penetration resistance (SPT-N). While the R2 value describes the best-fit relationship across the entire dataset used in the analysis, graphical methods were employed to validate the developed correlations between measured and predicted values. Various graphical approaches were utilized to confirm the correlation between \(V_{S}\) and SPT-N values following the similar methodology adopted by Aas and Sinha61 for developing the SPT-\(V_{S}\) correlation of a site in New Delhi, India.

Plot of measured \(V_{SM}\) and predicted shear wave velocity \(V_{SP}\)

Figure 8(a) displays the plot of predicted \(V_{SP}\) from Eq. 1 alongside derived \(V_{SM}\) from CHST. The plot clearly shows that the \(V_{SP}\) predicted by non-linear correlations closely align with the CHST-derived \(V_{SM}\), as the majority of the data points are clustered near the 1:1 slope line. Additionally, the data points lie within the lines of slopes 1:1.25 and 1:0.8, indicating a highly accurate prediction for the soil examined in the current study area, and the predictions are within + 25%, -20% of the actual dataset.

Fig. 8
Fig. 8
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Plot of measured and predicted shear wave velocity (a); Plot of predicted velocity vs residual velocity (i.e., measured velocity – predicted velocity) (b); Plot of SPT-N and Normal consistency ratio, \(C_{d}\) as defined by Dikmen59 (c); Plot of Scaled error percent and Cumulative frequency (d).

Graphical residual plot

Figure 8(b) displays the distribution of residuals calculated as the difference between CHST derived \(V_{S}\) (\(V_{SM}\)) and predicted \(V_{S}\) (\(V_{SP}\)) and plotted against the projected shear wave velocity for the regression equation developed in the study. The figure demonstrates that the residuals have a uniform and horizontal distribution along the horizontal axis, with about equal variance. The distribution indicates that the regression model is well-suited to the data.

Normal consistency ratio (NCR)

The Normal consistency ratio, \(C_{d}\) 59, is defined as the ratio of the difference between the measured shear wave velocity and the calculated shear wave velocity to the recorded standard penetration test number (SPT-N). It is expressed as follows:

$$C_{d} = \frac{{V_{sm} - V_{sp} }}{SPT - N}$$
(2)

where, \(V_{sm}\) and \(V_{sp}\) represent the measured and predicted shear wave velocities, respectively, using Eq. (1), and SPT − N is the recorded penetration number at the depth corresponding to the measured \(V_{sm}\). It can be noticed from Fig. 8(c) that most of the \(C_{d}\) values are close to the horizontal zero axis, and the developed correlation gives a maximum error of 5%, which suggests that the predicted \(V_{sp}\) is close to the measured \(V_{sm}\).

Scale error percent (\(S_{er}\))

The scaled error percent (\(S_{er}\)) was employed to evaluate the effectiveness of the developed correlation equation against observed data. It is defined as follows59.

$$S_{er} = \frac{{V_{sp} - V_{sm} }}{{V_{sp} }}$$
(3)

It is observed from Fig. 8(d) that more than > 80% of the predicted \(V_{sp}\) falls within the ± 15% (bounded by Red dotted line). This suggests that the developed correlation equations are capable of predicting shear wave velocity values with minimal error. This threshold aligns with similar studies in the field, such as seismic site classification study of Lucknow51and Varanasi59, where ± 15% is considered acceptable for practical applications in seismic site classification and earthquake-resistant design.

Comparison of the developed correlation with other existing correlations

Initially, equal weight was assigned to the most representative correlations between \(V_{S}\) and SPT-N, as shown in Table 1, to calculate \(V_{S}\) values. Subsequently, these \(V_{S}\) values were paired with corresponding SPT-N values. Following this, a power model was applied in the non-linear regression analysis. In .

Figure 9(a), a comparative analysis is shown between the proposed correlation and globally established correlations. Additionally, as depicted in Fig. 9(b), the proposed correlation is compared with correlations available for different regions of India. The analysis reveals that the proposed correlation exhibits a trend similar to that of the correlations from Japan33,35,39, etc.], and India22,48,49 etc.

Fig. 9
Fig. 9
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Comparison of proposed correlation with worldwide existing correlations (a); Comparison of proposed correlation with existing relations developed for different parts in India (b); Comparison of scaled percent error of predicted \(V_{S}\) with existing global correlations (c); Comparison of scaled percent error of predicted \(V_{S}\) with existing Indian correlations(d).

Figure 9 demonstrates that the newly developed non-linear equation closely aligns with those established by Mehta and Thaker57 and Ohta and Goto37. Some correlations, such as those identified by Lee40, Singh et al.59, and Anbazhagan70, produce relatively high \(V_{S}\) values as SPT-N values increase. Conversely, relationships documented by Sisman43 and Uma Maheswari et al.49 predict lower \(V_{S}\) values. Discrepancies between the developed and existing correlations may be attributed to factors such as geotechnical site conditions, fluctuations in the water table, compaction, and geological age, among others. Additionally, variations in SPT equipment and methodologies significantly influence the blow counts recorded. Moreover, some of these variations could also stem from different \(V_{S}\) measurement techniques utilized by various researchers.

Figure 9(c) and (d) provide a comparative view of the scaled error percentage for various global and regional correlations:

Global correlations, Examples such as Kalteziotis et al.42 and Lee40 display broader error margins, ranging from approximately -100% to + 30%. This higher variability stems from the fact that global correlations are developed based on datasets covering diverse geotechnical conditions, and as a result, they do not account for the specific lithology and geotechnical characteristics of the Noida region. Their performance highlights the limitations of applying global trends to region-specific studies.

Regional studies such as Anbazhagan and Sitharam48 or Singh et al.59, which were developed for sites with geological similarities to Noida, show significantly smaller error margins (± 10–20%). These studies are primarily based on quaternary alluvium deposits found in the Indo-Gangetic plains, comprising fine to medium-grained sand, silt, and clay, closely resembling Noida’s geological conditions. The proposed correlation aligns well with these regional correlations, demonstrating its reliability in capturing the geotechnical characteristics specific to the Noida region.

Furthermore, we have highlighted the findings of Uma Maheswari et al.49, who observed similar trends while developing SPT-\(V_{S}\) correlations for Chennai soils. These findings support the observation that regionally tailored correlations, such as the one proposed in this study, offer better accuracy and lower variability compared to global correlations.

In conclusion, while global correlations provide broader applicability, their performance is limited by the lack of site-specific calibration. Regional correlations, including the one developed in this study, prove to be more effective in minimizing error margins and providing accurate predictions tailored to local geotechnical properties.

Uncertainties in the SPT-\(V_{S}\) correlation

Soil shear wave velocity (\(V_{S}\)) can be determined through various testing methods, ranging from low to high-strain tests, conducted both in the field and laboratory. However, these measurements face three key types of uncertainty (as per Kuili,71):

  • Natural Variability (Inherent):

    • Caused by the complex geological processes responsible for soil deposition and stress history.

    • Includes spatial randomness due to varying depositional behaviors of soil layers.

    • Independence of external measurement or procedural errors and cannot be reduced by gaining moreknowledge​.

  • Testing Accuracy (Measurement):

    • Arises from inaccuracies in testing equipment, procedural errors, and operator handling.

    • Includes disturbances to soil samples prior to testing and precision-related errors (random and systematic) during field or laboratory tests​.

  • Conversion Uncertainty (Transformation):

    • Stems from the use of empirical correlations or transformation models to estimate shear wave velocity from other geotechnical data (e.g., SPT results).

    • Introduces variability due to the idealized nature of empirical relationships, which may not fully represent site-specific conditions.

When these uncertainties combine throughout the testing and analysis process, they can significantly affect the final results. This is particularly important when researchers use various empirical relationships to convert between different soil parameters, as each conversion step can introduce additional uncertainty into the final values72,73.

The adherence to different types of uncertainty in all geotechnical tests is inevitable, and the variability on account of such uncertainties is bound to induce disparity in choosing a reliable outcome. As noted in our research, several factors contribute to these discrepancies, including geotechnical site conditions, variations in water table levels, geological age, SPT equipment, methodologies, and different measurement techniques adopted by researchers. We will discuss in detail how we can deal with these uncertainties.

  • Standardization of SPT measurements: Recognizing that variations in SPT equipment and methodologies influence recorded blow counts, we emphasize the need for adopting standardized procedures (e.g., ASTM D1586) during field testing. This standardization minimizes variability and ensures consistency across studies.

  • Account for site-specific factors: To account for site-specific factors such as geological age and water table fluctuations, we can adopt several ways to incorporate their effect in our analysis. Regular monitoring of groundwater levels with application of correction factors for water table variations. Verify site-specific geological conditions from the standardized documents (e.g., Report of the Geological Society of India). It helps to mitigate site-specific biases.

  • Incorporating robust statistical analysis: The developed correlations can be statistically validated using relevant statistical techniques, e.g., regression analysis, which helps in quantifying and reducing prediction errors.

  • Cross-validation with independent datasets: We can compare our findings with independent datasets from diverse geotechnical settings to ensure the robustness of the developed correlations. This demonstrates the approach is reliable even when applied to varying conditions.

  • Sensitivity analysis: A sensitivity analysis may be conducted to evaluate the influence of individual parameters, such as compaction and geological age, on the developed correlations.

Seismic site characterization of Noida city

Characterizing seismic sites in areas vulnerable to seismic activity is crucial. Most importantly, this is one of the major outcomes of the present study, and based on this output, the competent administrative authority can make decisions for building disaster resilience infrastructure. Seismic site characterization involves assessing the subsurface properties through seismic site classification. Various seismic codes, such as Eurocode 874, IS 189327, and NEHRP (BSSC)1, provide frameworks for seismic site classification. These codes incorporate one or more of the following approaches: average standard penetration blow count (\(N_{30}\)), average shear wave velocity (\(V_{S30}\)), and average undrained shear strength (\(C_{U30}\)). These parameters can be obtained from Eq. 4, which is given below.

$$\begin{array}{*{20}c} {V_{S30} } & {or} & {N_{30} } & {or} & {C_{U30} = \frac{{\sum\limits_{i = 1}^{n} {d_{i} } }}{{\sum\limits_{i = 1}^{n} {\left( {\frac{{d_{i} }}{{\begin{array}{*{20}c} {V_{i} } & {or} & {N_{i} } & {or} & {C_{Ui} } \\ \end{array} }}} \right)} }}} \\ \end{array}$$
(4)

Where, \(d_{i}\) represents the thickness of the i-th layer in meters; n is the total number of layers within the top 30 m of the soil profile; and \(V_{i}\) , \(N_{i}\) and \(C_{Ui}\) denotes the shear wave velocity, standard penetration test number (SPT-N), and undrained shear strength of the i-th layer, respectively. In this study, seismic site classification was conducted using \(N_{30}\) and \(V_{S30}\) values for all the boreholes. The developed regression relationship, as expressed in Eq. 1, was utilized to estimate the shear wave velocity across different layers.

To develop an seismic site classification -based map utilizing SPT-N values, the \(N_{30}\) value at each of the 117 borehole locations was determined using Eq. 4. These values were then interpolated between boreholes using the Kriging interpolation technique, as recommended by Anbazhagan et al.51. Utilizing the determined \(N_{30}\) values, a seismic site classification map was developed for Noida city, as depicted in Fig. 10(a), following the NEHRP (National Earthquake Hazard Reduction Program) site classification scheme1 in accordance with Table 3. The NEHRP classification scheme categorizes subsoil into three seismic site classification categories C, and D based on \(N_{30}\) values, as outlined in Table 3. It has been observed that most of Noida falls in seismic site class C, which includes Sector 62,63,122, and very few locations fall into site class D (Fig. 10a). Analyzing Fig. 10(a), reveals that 82% of the boreholes were classified as site class C and 18% as site class D. This implies the presence of weathered soft rock at shallow depth in most places. Site Class C (\(N_{30}\) > 50) attributed to the borehole with loose to medium clayey or silty soil over the dense fine sand(as seen in Fig. 4. Whereas, very few places come under site class D (15 < \(N_{30}\) < 50), i.e., loose to medium clayey or silty soil because if an average up to 30 m gives an \(N_{30}\) of 51 , it will come as site class C (\(N_{30}\) > 50).

Fig. 10
Fig. 10
Full size image

Seismic site classification map of Noida city based on \(N_{30}\)(a); based on \(V_{S30}\)(b).

Table 3 NEHRP based site characterization1.
Full size table

For the development of the seismic site classification map, \(V_{S}\) values at all borehole locations were obtained directly from the SPT-N values, by using Eq. (1). Then \(V_{S30}\) values were estimated from the \(V_{S}\) using Eq. (4) and applied for seismic site classification. Once the \(V_{S30}\) values at all borehole locations were estimated, and intermediate values were interpolated using the Kriging interpolation method, referencing the methodology described by Anbazhagan et al.51 for Lucknow. Figure 10(b) displays the seismic site classification contour map for Noida city based on \(V_{S30}\) values. Although a major part of the city falls in site class C (62%), about 38% of the location falls into site class D. The calculated \(N_{30}\) and \(V_{S30}\) values vary from 34 to 120 and 260 to 481 m/s, respectively. Figure 10 also reveals that locations classified as Site Class D based on \(N_{30}\) values correspondingly fall into the same site class according to \(V_{S30}\) classification. Additionally, the majority of the city is categorized as Site Class C (very dense soil and soft rock) according to both classification systems. As discussed previously in site characterization using geotechnical data, the weathered soft rock in the study area lies at a shallow depth. Site classification considering \(V_{S30}\) included rock velocity, because there was a shallow mass of rock within 30 m, which may lead to a higher site classification. While, as compared to site classification using \(V_{S30}\), an additional 20% of the area falls into site Class D(180 < \(V_{S30}\), < 360), than the site classification by \(N_{30}\) values. This is due to the averaging of \(V_{S}\) values up to 30 m. More boreholes fall under this higher site class according to NEHRP based site characterization1. This disparity in site classification under both approaches can also be seen in the seismic site characterization of Bangalore city, conducted by Anbazhagan et al.70.

Robustness of the developed correlations

The robustness of the empirical correlations developed between standard penetration test (SPT-N) values and shear wave velocities (\(V_{S}\)) is discussed through several key aspects.

Statistical validity:

  • High regression coefficient (R2 = 0.8811) indicating strong correlation.

  • Graphical residual plots show uniform and horizontal distribution.

  • Over 80% of predicted \(V_{S}\) values fall within ± 15% error range.

  • Normal consistency ratio (NCR) shows maximum error of only 5%.

Benchmarking against existing studies:

  • The study compares the newly developed correlation with globally and locally established relationships, such as those from Japan, India, and other regions.

  • The proposed correlation aligns closely with those by Ohta and Goto37, Mehta and Thaker57, and other studies, particularly for similar soil conditions.

  • This alignment suggests that the correlation reflects realistic soil behaviour and shear wave velocity trends.

Region-specific data:

  • Unlike general/global correlations, this study uses site-specific data from 26 boreholes and 14 seismic cross-hole tests and, totaling 179 SPT-N and \(V_{S}\) data pairs has been used for developing SPT-\(V_{S}\) correlation.

  • Shear wave velocity profile is generated at all 117 boreholes using the developed correlation and site specific SPT data.

  • The close proximity of SPT and \(V_{S}\) measurements (same borehole and depth) minimize data mismatches and increases reliability.

Limitations of the study

While the correlation is robust, there are some inherent limitations to its applicability:

Geographical constraints:

  • Correlations are specifically developed to address Noida’s soil conditions.

  • It may not be applicable to other regions with different geological settings.

  • Limited to the specific soil types found in Noida (primarily sandy soil with silt and clay patches).

  • A more extensive and evenly distributed borehole dataset across Noida city would be required, which could significantly improve the reliability and accuracy of the interpolation.

Depth limitation:

  • The study uses data from boreholes with depths ranging mostly between 30–35 m and some extending to 40–50 m.

  • For deeper soil profiles, the correlation’s applicability might be limited since, \(V_{S}\) behaviour could change with increasing depth and pressure.

SPT and \(V_{S}\) measurement variations:

  • The standard penetration test (SPT) is susceptible to errors due to operator variability, equipment type, hammer energy, and borehole conditions. These errors could propagate into the developed correlation.

  • Similarly, the seismic cross-hole tests used to measure \(V_{S}\), rely on proper borehole grouting, accurate source-receiver alignment, and noise filtering. Any deviations could introduce uncertainties.

Influence of soil conditions:

  • The study primarily focuses on sandy soils interspersed with silt and clay patches, which are characteristic of Noida.

  • Variations in soil type, water table conditions, and compaction across other locations could affect the accuracy of the correlation.

Potential applications

Despite the limitations, the correlation offers a significant advancement in understanding Noida’s subsurface properties for seismic site characterization:

  • The correlation can be used to estimate \(V_{S}\) profiles in the absence of direct field measurements, which are often cost- and time-prohibitive.

  • It provides a foundation for generating seismic site classification maps, aiding urban planning, and improving earthquake-resistant building design.

  • However, for critical infrastructure or high-seismic risk areas, direct \(V_{S}\) measurements (e.g., cross-hole or MASW tests) are still recommended for greater accuracy.

Future scope

  • Future studies should focus on increasing the density of boreholes and \(V_{S}\) measurement locations to capture finer-scale heterogeneity in Noida’s subsurface conditions.

  • Consider deeper investigation depths beyond 30 m.

  • Integrate additional geophysical methods like multi-channel analysis of surface waves (MASW) and refraction microtremor (ReMi) and compare their results with the current findings. Integrating MASW and ReMi with existing methods could enable finer-scale heterogeneity studies at a greater depth, compared to CHST and improves the validation of the correlations.

  • In the present work, the focus remains on providing a single, robust correlation applicable to the diverse subsurface conditions of Noida, and therefore, the present correlation can be applicable to all soil types of Noida region, but one may explore the possibility of separate correlations for specific soil types for further analysis.

  • Accounting the water level fluctuations and adopting suitable correction factors for water table variations can improve the reliability of the proposed correlation.

  • This study can be very useful for the evaluation of site amplification effects that can further classify the city into multiple zonation with low to high amplification, which are essential for urban planning and liquefaction study.

  • The classification maps should be incorporated into urban planning and zoning regulations to guide construction practices, particularly in high-risk zones identified as Site Class D. It is very important to integrate these microzonation results in the current building codes.

  • The current regional correlation balances practical applicability and variability management. Future studies may incorporate stochastic evaluations (e.g., Monte Carlo simulations, Importance sampling) to establish confidence intervals and reliability indices for seismic site classification.

  • By incorporating sensitivity analysis, key factors that significantly influence the relationship between SPT-N and \(V_{S}\) can be identified. This is achieved by systematically varying input parameters. The dependent parameter is \(V_{S}\), and the independent parameters are depth of water table, corrected and uncorrected SPT-N and different soil types (i.e., input parameters). Sensitivity analysis allows for measuring the effect of changes in independent variables on the dependent variable (\(V_{S}\)), thereby improving correlation accuracy.

  • With the help of these site classification maps, we can prepare the site-specific design spectra, by incorporating strain-dependent dynamic soil properties, such as damping and non-linear shear modulus and conducting site-specific ground motion simulations and validating them with observed seismic events will improve ground response analysis. The final design spectra is crucial for any earthquake-resistant building design in the city.

Conclusions

In this study, we aimed to develop empirical correlations between SPT-N values and \(V_{S}\) profiles for all soil types in Noida city, located in Northern India, using a non-linear regression technique. This approach allows for the estimation of Vs profiles in the absence of direct field measurements. Noida is primarily composed of sandy soil interspersed with significant amounts of silt and occasional clay patches up to borehole depth. The correlations proposed herein align well with both global and local established correlations, with a regression coefficient (R2) of 0.88, indicating a robust fit. The study further includes several graphical validations of the proposed correlation against \(V_{S}\) data derived from CHST tests at 14 locations, demonstrating consistently low error ranges. These novel correlations could significantly contribute to regional seismic microzonation efforts. It is noteworthy that the correlation for all soil types of mirrors trends found in existing studies from Japan and India. Additionally, seismic site characterization was carried out using \(N_{30}\) and \(V_{S30}\) methodologies, as recommended by NEHRP provisions. Both methods predominantly classified most areas of Noida as Class C, indicating very dense soil or soft rock. Regardless of the depth of the weathered bedrock and N values, sites with dense soil and high SPT N values up to shallow bedrock exhibit a comparable site class70. On the other hand, sites with loose and medium soil values up to shallow engineering bedrock exhibit a distinct site class in terms of N values and bedrock depth. When the weathered bedrock is at a shallow depth, the SPT N value, which represents loose-to-medium soil layers, may not be accurate and should not be used for site characterization purposes. These findings were consistent with those of Anbazhagan et al.70 and Naji et al.75, who used both SPT-N and \(V_{S}\) to characterize Bangalore (India) and Kahramanmaras(Turkey) respectively, in accordance with NEHRP guidelines.

These variations arise due to the distinct methodologies and assumptions inherent in deriving \(N_{30}\) and \(V_{S30}\) values. While \(N_{30}\) values are derived from geotechnical tests that provide direct data from boreholes, \(V_{S30}\) values rely on geophysical testing or empirical correlations, potentially introducing variability. These differences in methodology can be reflected in the seismic site classification results. According to the NEHRP guidelines, the most suitable approach for determining the seismic site class is by calculating the average shear wave velocity (\(V_{S30}\)). In the absence of shear wave velocity data, generalized correlations between shear wave velocity and standard penetration test (SPT) blow counts can be utilized. If these data are also unavailable, site-specific geotechnical information, such as the average SPT-N (\(N_{30}\)), can be employed for seismic site classification. Using shear wave velocity information for site classification is more reliable as it incorporates seismic wave components based on a geophysical approach, whereas SPT-based site classification relies solely on geotechnical data and localized soil conditions.

The \(N_{30}\) based map may be more relevant in areas where direct geotechnical data is readily available, offering insights tailored to localized soil conditions. The \(V_{S30}\) based map, on the other hand, aligns with global practices such as NEHRP guidelines and is widely recognized for its earthquake-resistant design. For practical applications, including urban planning and construction, the \(V_{S30}\) based map is recommended as the primary guidance, as it adheres to international standards for seismic hazard assessment.

The findings of this study are intended to enhance the estimation of earthquake risk, ground displacements, liquefaction potential, and the generation of site-specific synthetic ground motions for Noida City. This pioneering work on developing correlations and seismic site classifications for Noida will enhance future studies in seismic hazard analysis, ground response analysis, liquefaction potential assessment, and the creation of site-specific synthetic ground motions. This geospatial analysis can aid in targeted interventions, optimizing locations for construction projects, and improving emergency preparedness and response strategies in the context of seismic risks.