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Limitations of the Yang’s breaking wave force formula and its improvement under a wider range of breaker conditions

  • Xing Yang EMAIL logo and Kaixi Cai
Published/Copyright: December 22, 2022
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Open Geosciences
From the journal Open Geosciences Volume 14 Issue 1

Abstract

Some commonly used empirical formulas (e.g., Soviet CHиПII57-75, Ikeno-Tanaka, Führböter-Sparboom, and Stanczak) for estimating plunging breaker wave slamming pressure on sea dike surface do not take into account the comprehensive influence of the wave steepness, slope angle, and breaker height and depth on the loads, and the Yang formula eliminates the drawback. The Yang formula is derived based on an analysis of the impulse in the breaking wave tongue and the kinetic and potential energy in the wave tongue. But the limited range of the Yang formula is 0.5 ≤ ξ ≤ 3.3 and 0.01 ≤ tan α ≤ 0.44; otherwise, its prediction error will greatly increase. In addition, some parameters in the Yang formula need to be optimized. The aim of this project is to revise the Yang formula for improving its performance and making it suitable for a wider range of hydraulic conditions and bottom slope conditions. A constant term in the Yang formula is replaced by the function obtained by analysis, and the calculation method of breaking wave height in the formula is also changed. The resulting formula is of interest because the comparison of the formula with some measurements is done well.

Keywords: plunging breaker; sea dike; slamming pressure; empirical formula; prediction error

1 Introduction

Sloping sea dikes are commonly used types of coastal protection structures [1,2] to withstand wave and tide impacts in extreme weather and climate events (e.g., typhoon and tsunami). Wave breaking is a common phenomenon on seaward sea dikes [3]. Compared with a non-breaking wave, breaking wave can produce extremely high slamming pressure on the sea dike surface in a short period of time [4], which may lead to the failure of the sea dike. Therefore, breaking wave impinging induced by strong waves is one of the main causes of sea dike failure [5,6]. Experimental, numerical, and theoretical investigation of breaking waves based on wave flume experiments (including numerical wave flumes) can be found in some literature [7,8,9,10,11,12,13]. Only a few results of the field measurements are available because field measurement is very difficult [14,15,16,17].

Results from previous studies mentioned above show that plunging breaker is the most destructive of the three types (i.e., spilling breaker, plunging breaker, and surging breaker), which is characterized by acceleration of the fluid near the crest, causing the jet with air bubbles impinging and the devastating forces on the coastal structure surface [18,19]. Unfortunately, the plunging wave-breaking mechanism had not been fully understood. The maximum slamming pressure due to breaking waves acting on the sea dike slope is a stochastic variable even for regular waves because the instabilities at the breaking point are influenced by the highly turbulent water–air mixture produced by the preceding breakers. This leads to the difficulty of reliable estimation of breaking wave loads, which is necessary for the effective design of coastal structures like sea dikes.

Most predictions of breaker loads are based on empirical or semi-empirical formulas calibrated from laboratory data because wave breaking mechanism is complex and filed data available are remarkably slight [20,21]. Since the last century, some breaker load formulas had been suggested and adopted in the coastal structure design, such as improved Morison’s formula [22,23,24], Soviet CHиПII57-75 formula widely used in China, the Ikeno–Tanaka formula of Japan [25], Führböter–Sparboom formula of Germany [26,27], and Stanczak formula derived from the Führböter–Sparboom formula [28]. The comparison of these formulas with the measurements was done by Yang [29], which showed that the difference with the measurements was primarily because of some important shortcomings in these formulas.

These formulas mentioned above do not take into account the comprehensive influence of the wave steepness, slope angle, and breaker height and depth on breaker loads. To eliminate this drawback, Yang [29] reviewed some of the recent literature and gave a derivation of a formula for wave impacts, based on an analysis of the impulse in the breaking wave tongue and the kinetic and potential energy in the wave tongue. This is a rather simple method, which does not include important aspects, like air entrainment in the impacting water. Nevertheless, the resulting formula is interesting because the comparison of the formula with some measurements was performed well. But Yang [29] believes that further analysis is still required for the accuracy improvement in predicting wave slamming pressures.

Yang formula’s validity is limited according to the experimental data from Führböter [26] and Stagonas et al. [32]. In practice, the calculated result may be larger than the true value in some breaker conditions. Moreover, the formula only works for small slope angles. So, this article aims to revise the Yang formula to improve its performance and make it suitable for a range of hydraulic conditions and bottom slope conditions. The improved Yang formula will be compared with some formulas, of which Soviet CHиПII57-75 formula has been adopted in the Chinese design guidelines of coastal structures for many years. The selected breaker data used in this comparative analysis include some laboratory data and field data. The article is divided into four main sections:

  1. Section 1 briefly reviews the existing breaker load formulas.

  2. Section 2 is the improvement of the existing Yang formula.

  3. Section 3 presents the results and discussion.

  4. Section 4 details the main conclusions.

2 Breaker load formulas including the Yang formula

The comparison of the revised formula with those of Soviet CHиПII57-75, Führböter–Sparboom, Stanczak formulas, and Yang formula will be done in this study. The Ikeno–Tanaka formula is usually suitable for vertical structures. The Führböter–Sparboom formula does not take into account the influence of the wave steepness on the maximum slamming pressure, and the Stanczak formula eliminates the drawback. The Yang formula gives the influence of the wave steepness, slope angle, and breaker height and depth. These formulas suitable for slope structures are as follows:

  1. In Soviet CHиПII57-75 formula, the maximum slamming pressure p max [Pa] on the slope is described by

(1) p max = k 1 k 2 p ¯ ρ g H , k 1 = 0.85 + 44.8 H L + n 0.028 − 1.15 H L ,

where ρ is the density of the water (kg/m3); g is the acceleration due to gravity (m/s2); n is the dike bottom slope ratio denoted by 1:n; H is the wave height at the dike toe (m); L is the deep water wave length (m); k 2 is the constant coefficient as listed in Table 1; p ¯ is the relative wave pressure as listed in Table 2. The formula was suggested to be used for the range of 1.5 ≤ n ≤ 5.0 and 10 ≤ L/H ≤ 35.

  1. The complexity of wave breaking makes the breaker load a highly random process, even in a regular wave train. So, in the Führböter–Sparboom formula and the Stanczak formula, the notation p max,i [Pa] is used to indicate the maximum pressure with no more than i% probability. The p max,99 can be used as the highest maximum slamming pressure in practice [28]. The two formulas were suggested to be used for the range of surf similarity parameter ξ < 2.6 for plunging breaker, with ξ = tan α H / L where the deep wave length L = gT 2/(2π).

  1. The Führböter–Sparboom formula is described by

    (2) p max , i = const i ρ g H tan α ,

    where const i is the coefficient depending on the characteristic maximum value considered, const50 = 12, const90 = 16, const99 = 20, and const24 = 24; α is the outer dike slope (deg).

  2. The Stanczak formula is described by

    (3) p max , i = k i ρ g H tan α , k 50 = − 289 H g T 2 + 11.2 , k 90 = 1.33 k 50 , k 99 = 1.67 k 50 , k 99.9 = 2.5 k 50 ,

    where T is the wave period (s).

    1. The Yang formula is as follows:

(4) p y = 2 ρ g 1 + 1.6 γ γ K K G H 2 π H g T 2 − 0.2 , K KG = 10.02 ( tan α ) 3 − 7.46 ( tan α ) 2 + 1.32 tan α + 0.55 , γ = 1.1 ξ 1 / 6 = 1.1 tan α H / L 1 / 6 , with L = g T 2 2 π ,

where K KG is the slope effect coefficient [30]; γ depends on both the wave steepness and the out dike slope angle α [31]. The Yang formula was suggested to be used for the range of 0.5 ≤ ξ ≤ 3.3 and 0.01 ≤ tan α ≤ 0.44.

Table 1

Constant coefficient k 2

L/H 10 15 20 25 35
k 2 1.00 1.15 1.30 1.35 1.48
Table 2

Relative wave pressure p ¯

H 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ≥4.0
p ¯ 3.7 2.8 2.3 2.1 1.9 1.8 1.75 1.7

3 Revised Yang formula

The limited range of the Yang formula is 0.5 ≤ ξ ≤ 3.3 and 0.01 ≤ tan α ≤ 0.44; otherwise, the formula’s prediction error will greatly increase, especially when tanα increases. In addition, the results from Yang [29] show that the calculated results using the formula are larger compared with some experimental data. The main aim of this section is to modify the formula so that it can better predict a wider range of breaker conditions. The wave-breaking process is very complex, so some assumptions and simplifications are necessary in order to be able to calculate the breaker loads. Following Yang [29], some construction derivation steps of the Yang formula under some hypotheses are listed in Figure 1.

Figure 1 Main steps in the derivation of Yang formula [29].
Figure 1

Main steps in the derivation of Yang formula [29].

As shown in Figure 1, the most important assumptions implied in the derivation of the Yang formula are as follows:

  1. Conservation of cross sections 1 – 1, 2 – 2, and 3 – 3 momentum in control volume.

  2. A homogeneous velocity distribution across the cross Sections 1 – 1, 2 – 2 and 3 – 3.

  3. Ignoring the incidence angle α 1 and reflection angle α 2 of the breaking wave plunging on the dike slope.

Under assumption (iii), “p y = ρu 2 A(sin α 1 + sin α 2) where A is section area” is modified to “p y ≤ 2ρu 2,” where constant 2 is also a constant term in the Yang formula (equation (4)). The larger constant term should be one of the main reasons that the calculated results by the Yang formula are obviously larger in some breaker conditions. This drawback can be weakened by replacing the constant value 2 in equation (4) with an empirical function that depends on the incidence angle α 1° and reflection angle α 2°.

Let tanα 1 ≈ 1.8ƞ b /(u b t) empirically, where u b is the water particle velocity at the breaking wave crest; ƞ b is the maximum free surface height from the mean water level (MWL) at the breaking location, ƞ b ≈ 0.8H b [29]; t is the time that the water particles on the breaking wave crest travel to MWL. The derivation of t is as follows:

(5) η b ≈ 1 2 g t 2 ⇒ t = 2 η b g ⇒ t = 1 .6 H b g .

Let u b be proportional to the square root of water depth, u b = g d b with d b = H b /γ [29], where d b is the water depth at the breaking location; H b is the breaking wave height at the breaking location. Then

(6) tan α 1 = 1 .8 η b u b t = 1 .8 × 0 .8 H b g H b / γ 1.6 H b / g = 1 .296 γ ⇒ α 1 = arctan 1 .296 γ .

Let K KG = 0.56 if tan α > 0.44 [30]. Assume that α 1 = α 2 in the symmetric case and replace the constant value 2 in equation (4) with equation (6). Then, the revised Yang formula is as follows:

(7) p y = 2 sin ( α 1 ) ρ g 1 + 1.6 γ γ K K G H 2 π H g T 2 − 0.2 ,

with

α 1 = arctan 1 .296 γ , if 0 .01 ≤ tan α ≤ 0.44 , K K G = 10.02 ( tan α ) 3 − 7.46 ( tan α ) 2 + 1.32 tan α + 0.55 , else if tan α > 0.44 , K KG = 0.56 γ = 1.1 ξ 1 / 6 = 1.1 tan α H / L 1 / 6 , with L = g T 2 2 π .

4 Results and discussion

4.1 Predictive performance of revised Yang formula in experimental conditions

We will verify the revised Yang formula with the laboratory breaker data from the studies of Führböter [26] and Stagonas et al. [32]. In the experimental work of Führböter [26], eight breaking wave cases (H = 0.09–1.3 m; T = 1.3–4.6 s) with the bottom slope ratio of 1:4 were selected. In the experimental condition of Stagonas et al. [32], two breaking wave cases (H = 0.09 m, 0.13 m; T = 1.3 s, 1.43 s) with the bottom slope ratio of 1:3 were selected. The purpose of Figure 2 is to investigate the predictive performance of the revised Yang formula in the above cases. The calibration of the formula indicates that

  1. The calculated result using the revised Yang formula is about 25% smaller than that of the original formula.

  2. The calculated result using the revised Yang formula is generally between P max,99 by the Führböter–Sparboom formula and P max,99 by the Stanczak formula.

  3. The relative errors between the calculated results from the revised formula and the measured values are 0.96% (case H = 0.92 m, T = 3.37 s) ∼ 32.7% (case H = 0.45 m, T = 2.38 s), and the average relative error is 12.6%, which is better than other formulas in most of the cases.

Figure 2 Calibration of revised Yang Formula in experimental conditions: (a) conditions from Führböter [26] and (b) conditions from Stagonas et al. [32].
Figure 2

Calibration of revised Yang Formula in experimental conditions: (a) conditions from Führböter [26] and (b) conditions from Stagonas et al. [32].

4.2 Predictive performance of revised Yang formula in field conditions

An earlier field investigation completed in 2004 provides some breaker data. The primary goal of this investigation was to evaluate the safety of the Dongpuxintang sea dike located at Wenling City, Zhejiang Province, China. Figure 3 shows the field investigation site (28°19′52″ N, 121°30′34″ E) and the cross-section of the investigated sea dike. The crest elevation of the dike is 6.95 m (vertical datum: 1985 National Height Datum), and the crest is 5.0 m wide.

Figure 3 Schematic diagram of field investigation.
Figure 3

Schematic diagram of field investigation.

The incident wave height was measured using a capacitance-wire wave recorder at a distance of 100 m toward offshore. The sensor has a wave elevation metering range of 0–7 m. The maximum slamming pressure on the dike slope was measured using six pressure transducers at elevations ranging from 3.46 to 6.23 m. Due to the presence of comparatively large noise, field measuring equipment commonly suffers from poor signal quality [20]. Compared with the sampling of wave loads at 680 Hz [32] and 2,000 Hz [26] in laboratory, and at 200 Hz in field [20], the sampling frequency of this field investigation is only 100 Hz.

The calibration of the formula in Figure 4(a) indicates that

  1. The calculated results using formulas are commonly larger than field data, which may be because that the low sampling frequency makes it difficult for us to capture the real breaker load peak.

  2. The calculated results using the revised Yang formula and Soviet CHиПII57-75 are closer to field data. The relative errors between calculation and measurement are 24.9% (case H = 1.37 m, T = 4 s)–44.2% (case H = 1.18 m, T = 5 s).

Figure 4 Calibration of revised Yang formula in filed data: (a) from the author and (b) from Bird et al. [20].
Figure 4

Calibration of revised Yang formula in filed data: (a) from the author and (b) from Bird et al. [20].

Figure 4(b) describes the performance of the revised Yang formula on the vertical wall under the field condition by Bird et al. [20]. The results show that the relative error between the revised Yang formula and the field data is 20.2% and that of the Ikeno–Tanaka formula suitable for vertical structures is 38.4%. However, it is still not possible to judge which formula is better or worse, because the field data are affected by sampling frequency as well as possible noise interference.

4.3 Comparative analysis of empirical formulas for given breaker data

The computations of the formulas (i.e. revised Yang, Yang, Führböter–Sparboom, Stanczak, and CHиПII57-75) are carried out with 90 cases from nine sets of data (Figure 5), with H = 0.1–3.0 m, T = 2–5 s, and n = 1–5. For cases beyond the applicable scope of these formulas, such as ξ > 2.6 for the Stanczak formula, tan α > 0.44 for Yang formula, k 2 is out of scope in Table 1 for CHиПII57-75 formula and so on, the calculation results are not presented in Figure 5. It is shown that

  1. For all formulas, the maximum slamming pressure generally increases as the wave period increases. With the decrease in slope ratio, the calculation result of the revised Yang formula (including Yang formula) increases, but Führböter–Sparboom and Stanczak formulas show the opposite trend.

  2. The calculation result of the Führböter–Sparboom formula is larger than that of other formulas, and it increases rapidly with the increase in slope ratio. In the case of slope ratio 1:1, its calculation result is about six times that of the revised Yang formula.

  3. The calculation result of CHиПII57-75 formula is generally smaller than that of other formulas. The calculated result using the revised Yang formula is closer to p max,90 using the Stanczak formula under the case condition that both are suitable.

Figure 5 Comparative analysis of formulas for given data: (a) n = 5, T = 2 s, (b) n = 5, T = 3 s, (c) n = 5, T = 5 s, (d) n = 3, T = 2 s, (e) n = 3, T = 3 s, (f) n = 3, T = 5 s, (g) n = 1, T = 2 s, (h) n = 1, T = 3 s, and (i) n = 1, T = 5 s.
Figure 5

Comparative analysis of formulas for given data: (a) n = 5, T = 2 s, (b) n = 5, T = 3 s, (c) n = 5, T = 5 s, (d) n = 3, T = 2 s, (e) n = 3, T = 3 s, (f) n = 3, T = 5 s, (g) n = 1, T = 2 s, (h) n = 1, T = 3 s, and (i) n = 1, T = 5 s.

4.4 Future directions for further improvement of the proposed formula

Three main aspects in the improvement of the proposed formula are worthy of further discussion: First, the “sub-atmosphere pressure” phenomenon induced by entrapped air in breaking waves and the instabilities of the breaking point lead to the slamming pressure acting on the sea dike slope is a stochastic variable even for regular waves [26,27]. Führböter’s findings showed that low air contents may produce a short and large slamming pressure, while high air contents may produce a long and weak one [26]. None of the above formulas take into account the water–air mixture mechanism. This may affect the performance of the formulas. Therefore, it is meaningful to study the probability form of the revised Yang formula since the slamming pressure is stochastic. The p y in the revised Yang formula can be expressed by p y(i%), where i% (e.g., 80, 90, and 99%) is non-exceedance probability and p y(i%) denotes the slamming pressure at i% probability. Second, coastal marsh vegetation and artificial materials are widely used in the protection of sea dikes. Kamil et al. [33] reviewed the mangrove performance in wave attenuation. Yamini et al. [34] investigated the revetment effect of the artificial concrete block mattress against destructive wave action. It will be of interest to further revise the proposed Yang formula by considering the effect of different revetments on wave breaking. In addition, numerical modeling has become more attractive because of its high efficiency and low cost in studies related to wave phenomena. Truong et al. [35] used Mike 21 hydrodynamic model to analyze the impact of waves on the sediment transport at the seaport. It is also worthy of further discussion on whether numerical models can be used to calibrate the proposed Yang formula. Some optimization algorithms, such as fashionable nature-inspired algorithms [36,37], seem to be able to be used to further optimize the Young formula, which is also worthy of further investigation.

5 Conclusion

Plunging breaker impinging is one of the main causes of sea dike failure. The main aim of this study is to find a reliable empirical formula to better predict the slamming pressure on the dike slope for a wider range of breaker conditions. Compared with other widely used empirical formulas, the Yang formula takes into account more comprehensive factors and shows good performance under some wave breaking conditions. However, the prediction error of the Yang formula will increase with the increase in dike slope. The unreasonable constant term also causes the calculation result of Yang formula to be larger in some cases. For this, the Yang formula was revised in this study. The major conclusions of this study are obtained as follows:

  1. Yang formula does not take into account the incidence angle α 1 and reflection angle α 2 of the breaking wave plunging on the dike slope. The revised Yang formula eliminates this drawback. Moreover, the Yang formula is only applicable under the condition of 0.01 ≤ tan α ≤ 0.44. By modifying the slope effect coefficient K KG , the revised formula can be applied for a range of tan α > 0.44. The revised formula may be applicable to vertical walls under some breaker conditions. By replacing the constant term in the Yang formula with a function related to α 1° and α 2°, the accuracy of the formula is also improved.

  2. Some laboratory data and field data were employed in the verification of the revised Yang formula. The performance of the formula was also compared with that of CHиПII57-75 formula, the Ikeno–Tanaka formula, the Führböter–Sparboom formula, and the Stanczak formula. It is found that the revised formula predicts well. The average relative error between the calculated results from the revised Yang formula and the measured values from Führböter [26] and Stagonas et al. [32] was 12.6%, which was better than other formulas in most of the cases. Validation based on field data also showed that the Yang formula performed best.

  3. The analysis results of empirical formulas for given breaker data showed that the Yang formula could adapt to more wave-breaking conditions compared with other empirical formulas. As Stanczak [28] pointed out that the complex characteristics of wave breaking made the breaker loads highly random. Even in a regular wave train, the maximum slamming pressure of each wave was quite different [28]. In addition, no matter whether in the laboratory or field, noise interference is inevitable in wave load measurement. All of this can undermine the authenticity of the wave load data. An important solution is to conduct more reliable laboratory tests or field observations used for validation.

This study would significantly contribute to the sea dike design against wave. However, Yang formula’s validity may be limited due to the limited breaker data for verification. The subject is important but has not been solved sufficiently yet. Addressing this subject is still relevant. In addition, some important aspects of this study are worthy of further discussion, including the probability form of the revised Yang formula since the slamming pressure is stochastic, the improvement of the proposed Yang formula by considering the effect of different revetments on wave breaking, and the further improvement of the proposed formula by using some numerical models and optimization algorithms.

Acknowledgement

This work was supported by the Science and Technology Project of Jiangsu Province (Grant No. BM2018028) and the Water Resources Science and Technology Project of Jiangsu Province (Grant No. 2019022).

  1. Author contributions: XY: conceptualization, methodology, validation, formal analysis, investigation, writing – original draft, writing – review and editing, funding acquisition. KC: investigation, formal analysis, data curation, writing – original draft. The authors applied the SDC approach for the sequence of authors.

  2. Conflict of interest: The authors state no conflict of interest in this article.

  3. Data availability statement: Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.

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Received: 2022-06-22
Revised: 2022-10-31
Accepted: 2022-11-23
Published Online: 2022-12-22

© 2022 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/geo-2022-0445
Keywords for this article
plunging breaker; sea dike; slamming pressure; empirical formula; prediction error
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Articles
  2. Study on observation system of seismic forward prospecting in tunnel: A case on tailrace tunnel of Wudongde hydropower station
  3. The behaviour of stress variation in sandy soil
  4. Research on the current situation of rural tourism in southern Fujian in China after the COVID-19 epidemic
  5. Late Triassic–Early Jurassic paleogeomorphic characteristics and hydrocarbon potential of the Ordos Basin, China, a case of study of the Jiyuan area
  6. Application of X-ray fluorescence mapping in turbiditic sandstones, Huai Bo Khong Formation of Nam Pat Group, Thailand
  7. Fractal expression of soil particle-size distribution at the basin scale
  8. Study on the changes in vegetation structural coverage and its response mechanism to hydrology
  9. Spatial distribution analysis of seismic activity based on GMI, LMI, and LISA in China
  10. Rock mass structural surface trace extraction based on transfer learning
  11. Hydrochemical characteristics and D–O–Sr isotopes of groundwater and surface water in the northern Longzi county of southern Tibet (southwestern China)
  12. Insights into origins of the natural gas in the Lower Paleozoic of Ordos basin, China
  13. Research on comprehensive benefits and reasonable selection of marine resources development types
  14. Embedded deformation of the rubble-mound foundation of gravity-type quay walls and influence factors
  15. Activation of Ad Damm shear zone, western Saudi Arabian margin, and its relation to the Red Sea rift system
  16. A mathematical conjecture associates Martian TARs with sand ripples
  17. Study on spatio-temporal characteristics of earthquakes in southwest China based on z-value
  18. Sedimentary facies characterization of forced regression in the Pearl River Mouth basin
  19. High-precision remote sensing mapping of aeolian sand landforms based on deep learning algorithms
  20. Experimental study on reservoir characteristics and oil-bearing properties of Chang 7 lacustrine oil shale in Yan’an area, China
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  23. Curve number estimation using rainfall and runoff data from five catchments in Sudan
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  28. A comprehensive evaluation method for topographic correction model of remote sensing image based on entropy weight method
  29. Quantitative discrimination of the influences of climate change and human activity on rocky desertification based on a novel feature space model
  30. Assessment of climatic conditions for tourism in Xinjiang, China
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  32. Effect of brackish water irrigation on the movement of water and salt in salinized soil
  33. Mapping paddy rice and rice phenology with Sentinel-1 SAR time series using a unified dynamic programming framework
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  36. Influence of Three Gorges Dam on earthquakes based on GRACE gravity field
  37. Comparative study of estimating the Curie point depth and heat flow using potential magnetic data
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  39. Major, trace and platinum-group element geochemistry of harzburgites and chromitites from Fuchuan, China, and its geological significance
  40. Vertical distribution of STN and STP in watershed of loess hilly region
  41. Hyperspectral denoising based on the principal component low-rank tensor decomposition
  42. Evaluation of fractures using conventional and FMI logs, and 3D seismic interpretation in continental tight sandstone reservoir
  43. U–Pb zircon dating of the Paleoproterozoic khondalite series in the northeastern Helanshan region and its geological significance
  44. Quantitatively determine the dominant driving factors of the spatial-temporal changes of vegetation-impacts of global change and human activity
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  47. Attribution identification of terrestrial ecosystem evolution in the Yellow River Basin
  48. An intelligent approach for reservoir quality evaluation in tight sandstone reservoir using gradient boosting decision tree algorithm
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  50. Influence of heterogeneity on fluid property variations in carbonate reservoirs with multistage hydrocarbon accumulation: A case study of the Khasib formation, Cretaceous, AB oilfield, southern Iraq
  51. Designing teaching materials with disaster maps and evaluating its effectiveness for primary students
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  53. Appropriated protection time and region for Qinghai–Tibet Plateau grassland
  54. Identification of high-temperature targets in remote sensing based on correspondence analysis
  55. Influence of differential diagenesis on pore evolution of the sandy conglomerate reservoir in different structural units: A case study of the Upper Permian Wutonggou Formation in eastern Junggar Basin, NW China
  56. Planting in ecologically solidified soil and its use
  57. National and regional-scale landslide indicators and indexes: Applications in Italy
  58. Occurrence of yttrium in the Zhijin phosphorus deposit in Guizhou Province, China
  59. The response of Chudao’s beach to typhoon “Lekima” (No. 1909)
  60. Soil wind erosion resistance analysis for soft rock and sand compound soil: A case study for the Mu Us Sandy Land, China
  61. Investigation into the pore structures and CH4 adsorption capacities of clay minerals in coal reservoirs in the Yangquan Mining District, North China
  62. Overview of eco-environmental impact of Xiaolangdi Water Conservancy Hub on the Yellow River
  63. Response of extreme precipitation to climatic warming in the Weihe river basin, China and its mechanism
  64. Analysis of land use change on urban landscape patterns in Northwest China: A case study of Xi’an city
  65. Optimization of interpolation parameters based on statistical experiment
  66. Late Cretaceous adakitic intrusive rocks in the Laimailang area, Gangdese batholith: Implications for the Neo-Tethyan Ocean subduction
  67. Tectonic evolution of the Eocene–Oligocene Lushi Basin in the eastern Qinling belt, Central China: Insights from paleomagnetic constraints
  68. Geographic and cartographic inconsistency factors among different cropland classification datasets: A field validation case in Cambodia
  69. Distribution of large- and medium-scale loess landslides induced by the Haiyuan Earthquake in 1920 based on field investigation and interpretation of satellite images
  70. Numerical simulation of impact and entrainment behaviors of debris flow by using SPH–DEM–FEM coupling method
  71. Study on the evaluation method and application of logging irreducible water saturation in tight sandstone reservoirs
  72. Geochemical characteristics and genesis of natural gas in the Upper Triassic Xujiahe Formation in the Sichuan Basin
  73. Wehrlite xenoliths and petrogenetic implications, Hosséré Do Guessa volcano, Adamawa plateau, Cameroon
  74. Changes in landscape pattern and ecological service value as land use evolves in the Manas River Basin
  75. Spatial structure-preserving and conflict-avoiding methods for point settlement selection
  76. Fission characteristics of heavy metal intrusion into rocks based on hydrolysis
  77. Sequence stratigraphic filling model of the Cretaceous in the western Tabei Uplift, Tarim Basin, NW China
  78. Fractal analysis of structural characteristics and prospecting of the Luanchuan polymetallic mining district, China
  79. Spatial and temporal variations of vegetation coverage and their driving factors following gully control and land consolidation in Loess Plateau, China
  80. Assessing the tourist potential of cultural–historical spatial units of Serbia using comparative application of AHP and mathematical method
  81. Urban black and odorous water body mapping from Gaofen-2 images
  82. Geochronology and geochemistry of Early Cretaceous granitic plutons in northern Great Xing’an Range, NE China, and implications for geodynamic setting
  83. Spatial planning concept for flood prevention in the Kedurus River watershed
  84. Geophysical exploration and geological appraisal of the Siah Diq porphyry Cu–Au prospect: A recent discovery in the Chagai volcano magmatic arc, SW Pakistan
  85. Possibility of using the DInSAR method in the development of vertical crustal movements with Sentinel-1 data
  86. Using modified inverse distance weight and principal component analysis for spatial interpolation of foundation settlement based on geodetic observations
  87. Geochemical properties and heavy metal contents of carbonaceous rocks in the Pliocene siliciclastic rock sequence from southeastern Denizli-Turkey
  88. Study on water regime assessment and prediction of stream flow based on an improved RVA
  89. A new method to explore the abnormal space of urban hidden dangers under epidemic outbreak and its prevention and control: A case study of Jinan City
  90. Milankovitch cycles and the astronomical time scale of the Zhujiang Formation in the Baiyun Sag, Pearl River Mouth Basin, China
  91. Shear strength and meso-pore characteristic of saturated compacted loess
  92. Key point extraction method for spatial objects in high-resolution remote sensing images based on multi-hot cross-entropy loss
  93. Identifying driving factors of the runoff coefficient based on the geographic detector model in the upper reaches of Huaihe River Basin
  94. Study on rainfall early warning model for Xiangmi Lake slope based on unsaturated soil mechanics
  95. Extraction of mineralized indicator minerals using ensemble learning model optimized by SSA based on hyperspectral image
  96. Lithofacies discrimination using seismic anisotropic attributes from logging data in Muglad Basin, South Sudan
  97. Three-dimensional modeling of loose layers based on stratum development law
  98. Occurrence, sources, and potential risk of polycyclic aromatic hydrocarbons in southern Xinjiang, China
  99. Attribution analysis of different driving forces on vegetation and streamflow variation in the Jialing River Basin, China
  100. Slope characteristics of urban construction land and its correlation with ground slope in China
  101. Limitations of the Yang’s breaking wave force formula and its improvement under a wider range of breaker conditions
  102. The spatial-temporal pattern evolution and influencing factors of county-scale tourism efficiency in Xinjiang, China
  103. Evaluation and analysis of observed soil temperature data over Northwest China
  104. Agriculture and aquaculture land-use change prediction in five central coastal provinces of Vietnam using ANN, SVR, and SARIMA models
  105. Leaf color attributes of urban colored-leaf plants
  106. Application of statistical and machine learning techniques for landslide susceptibility mapping in the Himalayan road corridors
  107. Sediment provenance in the Northern South China Sea since the Late Miocene
  108. Drones applications for smart cities: Monitoring palm trees and street lights
  109. Double rupture event in the Tianshan Mountains: A case study of the 2021 Mw 5.3 Baicheng earthquake, NW China
  110. Review Article
  111. Mobile phone indoor scene features recognition localization method based on semantic constraint of building map location anchor
  112. Technical Note
  113. Experimental analysis on creep mechanics of unsaturated soil based on empirical model
  114. Rapid Communications
  115. A protocol for canopy cover monitoring on forest restoration projects using low-cost drones
  116. Landscape tree species recognition using RedEdge-MX: Suitability analysis of two different texture extraction forms under MLC and RF supervision
  117. Special Issue: Geoethics 2022 - Part I
  118. Geomorphological and hydrological heritage of Mt. Stara Planina in SE Serbia: From river protection initiative to potential geotouristic destination
  119. Geotourism and geoethics as support for rural development in the Knjaževac municipality, Serbia
  120. Modeling spa destination choice for leveraging hydrogeothermal potentials in Serbia
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