Allowable Bearing Research Articles

Challenging choice of safety factor for design of strip footings on gypsum-rich soils

A fine-grained gypsum-rich clayey soil having a gypsum content of 33% is subjected, in CBR moulds, to modified American association of state highway and transportation officials compaction at optimum moisture content. Two sets of samples were prepared. The first set remained unsoaked, while the second was soaked in fresh water for 120 days. From each CBR sample, three specimens were extracted for unconsolidated undrained triaxial test and the Mohr–Coloumb failure envelopes were obtained for soaked and unsoaked conditions. Soaked samples suffered a significant drop in both cohesion and angle of internal friction. The ultimate bearing capacity of a strip footing was calculated for each of soaked and unsoaked conditions revealing the critical region. For important structures on gypsum-rich soil, the paper shows that the allowable bearing capacity should be based on soaked condition. Based on unsoaked conditions, a safety factor of 8 is required to assure a safety factor of 3 based on soaked condition. For less important structures in regions of hot dry climate with low probability of soaking, safety factors of 4 and 3, based on unsoaked conditions, are required to give safety factors of 1.5 and 1.1 based on soaked conditions, respectively.

Subsoil Engineering Characterization and Foundation Design in Derived Geological Coastal Sands of Ilaje Area of Ondo State, Nigeria

Engineering subsoil evaluation and foundation design have been undertaken at Ilaje area of Ondo State, Nigeria. The aim of this study was to examine the geo-electrical and geotechnical parameters of the subsoil to sustain building structures and also provide appropriate foundation design alternatives. A total of six VES stations were occupied and complemented with geotechnical analysis of seven soil samples collected at two cone penetration test locations. The result showed that all the determined geotechnical parameters of the subsoil fall within the specification recommended for foundation material by federal ministry of works and housing of Nigeria. The VES showed a predominant (66.67%) HKQ curve type. The upper 5 m is characterized by moderate thickness and high resistivity (average of 450ohm-m) values to sustain structural load. An average allowable bearing capacity of 150 KN/m2 was recommended for design of bases/footings for shallow foundation at a depth not less than 1.0 m. The obtained settlement values are less than 50 mm and within tolerable limit, for foundation width ranging from 0.5 to 3.0 m. However there was drastic reduction in settlement values (below 25mm) when the foundation width was increased to 2 and 3m. The allowable capacity of the driven pile ranges from 64 – 115 KN, 206 – 347 KN, and 418 – 677 KN at 5m, 10 m and 15 m respectively. The allowable bearing capacity for bored piles ranges from 34 – 69 KN, 85 – 165 KN, and 146 – 268 at depth levels of 5 m, 10 m, and 15 m respectively.

A Comparison Study on the Effect of Various Layered Sandy Soil Deposited on Final Settlement under Dynamic Loading

The foundation is expansion in base of column, wall or other structure in order to transmit the loads from the structure to under footing with a suitable pressure with soil property. There are two conditions to design foundation: 1. The stress is applied by footing on soil is not exceeded allowable bearing capacity ( ). 2. The foundation settlement and differential settlement are due to applied loads are not exceeding the allowable settlement that based on the type and size of structure, the nature of soil. Rigid square machine footing with dimension 200*200 mm with two types of relative density (50 and 85)% medium and dense density respectively are using in this study in different 28 models to show the effect of layered sandy soil in two configuration, medium-dense MD and dense-medium DM on the final settlement in magnitudes and behaviors under dynamics loads applying with different amplitude of loads (0.25 and 2) tons at surface with amplitude-frequency 0.5 Hz with explain the effect of reinforcements material on reduction the magnitude of settlement. The final results appeared with respect to the specified continuous pressure and the number of loading cycles, the resulting settlement from the dynamic loading increases with the increase in the dynamic pressure magnitude, the variation on densities of layered soil effect on the amount of settlement due to different loads applied...

Engineering Subsoil Characterization for Shallow Foundation Design in Ode Irele Area of Ondo State, Southwestern Nigeria

Integrated geophysical and geotechnical investigations for foundation design have proved to be good veritable tools in effective foundation design and construction. Geophysical and geotechnical methods involving electrical resistivity and cone penetration test have been carried out to investigate the foundation soil conditions of Ode Irele, southwestern Nigeria. Six vertical electrical sounding (VES) were carried out along two traverses; which is complemented by two cone penetration tests with seven trial tests at different subsurface depths. The geotechnical results showed that the soils are sand and silt dominated. All the tested parameters fall within the Nigeria federal ministry of works and housing specification with liquid limit (< 50%), plastic limit (< 30%), plasticity index (< 20%). The geoelectric sections identified maximum of six geoelectric/geologic subsurface layers comprising the topsoil (red sand), weathered layer (made up of coastal sand/white sand), clayey sand (which is the major aquitard in the area), intermediate sand aquifer unit. However the coastal sand layer has moderately high resistivity at shallow depth to sustain foundation load with thickness greater than 2 m. The groundwater level measured from existing borehole records 17.5 m which may not or seriously affect the bases of the foundation footing. Consequently an average allowable bearing capacity of 150 KN/m2 (ultimate bearing capacity of 450 KN/m2) would be appropriate for design of shallow foundation in the area, at a depth not less than 1.6 m in Ode Irele and 0.8 m at Ajagba. The foundation width of 0.6 m would produce minimum bearing settlement less than 25 mm. The appropriate (recommended) ultimate bearing and allowable bearing capacity for strip and square footings at depth levels of 0.6 – 1.2 m vary from 1486 – 1842 KN/m2 and 495 - 614 KN/m2; and 2056 – 2489 KN/m2 and 685 - 830 KN/m2 respectively.

Geotechnical assessment of near-surface sediments and their hazardous impact: Case study of Jizan city, southwestern Saudi Arabia

The geotechnical parameters of near-surface sediments in Jizan city have been assessed through shear wave velocity (Vs) from twenty-two profiles of multi-channel analysis of surface waves (MASW) through Jizan city. The Vs varies between 106 and 560 m/s indicating wide range of soil stiffness properties. While the allowable bearing capacity, qa varies from less than 1 kg/cm2 at sites till depth 21 m indicating very soft/loose materials; these are considered by building codes as special cases and increased into 2.5 kg/cm2 suggesting stiff or medium dense materials Moreover, qa reaches 6.5 kg/cm2 indicating dense materials, while reaches 8.5 kg/cm2 suggesting the presence of very dense materials. Accordingly, the allowable bearing capacity at a depth of 13 m is less than the recommended values for foundation materials by building codes. Jizan city differentiated into two zones; Jizan salt dome to the west and sabkha deposits to the east. Several weakness zones in the Jizan salt dome zone have been detected with significant variations in the topography of salt rock. While sabkha deposits have low shear strength which requires engineering treatment before construction. Furthermore, shear modulus varies both vertically and laterally through Jizan city where values of shear strength of the near-surface sediments overlying salt rocks are greater than those of sabkha zone. Therefore, deep foundation and ground improvement are highly recommended.

Engineering Site Investigation and Shallow Foundation Design in Ore Area of Ondo State, Nigeria

Abstract The study integrates geophysical and geotechnical methods for subsoil evaluation and shallow foundation design. The study involved six vertical electrical sounding and geotechnical investigation involving cone penetration test and laboratory soil analysis. Three major geologic units were delineated; the topsoil, weathered layer and partly weathered/fractured/fresh bedrock. The overburden thickness is in between 15.2–32.9 m. Based on resistivity (16–890 ohm-m) and thickness (12.7–32 m) the weathered layer is competent to distribute structural load to underlying soil/rock. The groundwater level varies from 4.5 to 12.3 m. Therefore an average allowable bearing capacity of 200 kPa is recommended and would be appropriate for design of shallow foundation in the area, at a depth not less than 1.0 m with an expected settlement ranging from 9.03–48.20 mm. The ultimate bearing and allowable bearing capacity for depth levels of 1–3 m vary from 1403–2666 kPa and 468–889 kPa for strip footing while square footing varies in between 1956–3489 kPa and 652–1163 kPa respectively.

Near-surface foundation level assessment from seismic measurements: a case study of north Jeddah City, Saudi Arabia

Near-surface seismic measurements, along with relevant geotechnical methods, have become important techniques for delineating the elastic coefficients and geotechnical parameters of shallow foundations. In the north Jeddah expansion zone, shallow seismic measurements at 76 sites have been carried out to estimate both the P- and S-wave velocities for near-surface sediments. These data have been processed where the results revealed a three-layered ground model that reaches to 30 m depth with varying velocities and thicknesses. Then, the elastic coefficients such as Young’s modulus, bulk modulus, shear modulus, ultimate bearing capacity, and allowable bearing capacity have been assessed based on the estimated seismic wave velocities. It can be concluded that bearing capacity is closely related to shear wave velocity and shear modulus. Comparing our results with the published safe ranges of allowable bearing capacities, it is recommended that the first layer in the western zone as well as the second layer is the most suitable areas for constructing safe engineering foundations in the area of interest. Additionally, the best locations of these foundations can be easily identified from contouring maps.

Study the behavior of square footing in clayey soil subjected to vertical loading

Foundation is a part of the structure that transmits the load applied from the super structure to the soil below. Estimation of the bearing capacity of foundation is one of the most complicated problems in geotechnical engineering, therefore it provides a number of theories to estimate the bearing capacity. The purpose of this paper to study the behavior of model square footing in clayey soil subjected to vertical axial loading. The tests are conducted at three grades of undrained shear strength (Cu) of clayey soil which are (20 or 40 or 60 kPa). It is found that, in general, the load settlement curves of raft tests are non-linear hyperbolic shape without a well-defined peak load and the mode of failure is local shear failure in this type of soil, i.e. the behavior of this type of soil is strain hardening. Moreover, the bearing capacity factor (Nc) is equal to (2.8) where this value is not within the acceptable range of the bearing capacity factor (Nc) which ranges from (4 to 6.18) for saturated clay at (φ = 0). The ultimate load may occur at settlement more than (10%) of the width of the foundation which leads to make the settlement criterion control the allowable bearing capacity in design of shallow foundation in this type of soils.

Subsoil Foundation Support Assessment in Owo Area of Ondo State, Southwestern Nigeria

Subsoil foundation study was carried out in Owo Local Government of Ondo State, Southwestern Nigeria with an aim to assess the soil geophysical and geotechnical properties for design of shallow foundation structural support. The geophysical method which consists electrical resistivity [involving vertical electrical sounding (VES) and combined profiling field techniques] and very low frequency electromagnetic. The geotechnical method involved field cone penetrometer test and laboratory analysis of eight soil samples, collected at a depth between 1 and 3 m. These were complimented by hydrogeological measurements (static water level and hydraulic head determinations) and borehole drilling. The result showed that the upper 3 m is competent to support structural foundation elements with an allowable bearing capacity ranging from 291 to 293 kN/m2 (resistivity values of 59–569 Ω-m) with low settlement values of 0.72–0.75 mm. These bearing pressures are considered appropriate for use in design of bases, strip or raft foundations. The AASHTO classification of A-2-4/A-5 constitutes about 62.9%. The average static water level (5.6 m) will not or seriously affect footing structures even in wet season. However, the result of the borehole drilling and VES/Resistivity structures revealed the presence of clayey weathered layer at shallow depth less than 5 m in some places, therefore relatively high consolidation settlement is expected in those places upon loading. The depth to basement is 35 m, this overburden thickness would assist in evenly distribution of the foundation/structural load to the basement rock. All the determined geotechnical parameters of the subsoil fall within the specification recommended for foundation material by Federal Ministry Works and Housing of Nigeria. The quartz-schist and schistose quartzite are the most prominent rocks observed in the field. The Schist tends to slide/split along their planes of schistocity while the quartzite show significant fractures and joints which might require grouting/backfilling during construction activity.

Sustainable Decommission of Mining Lands: Landform Design for Eaton Tuner Shaft (ETS) Area, Obuasi, Ghana

Ghana is the first country in the Sub-Sahara African region to reform its mining sector and has become the poster child for such change in the developing world. Obuasi is the hub of gold mining in Ghana. The Obuasi mine is currently operated by AngloGold Ashanti (AGA), and contributes immensely to the Gross Domestic Product (GDP) of Ghana. Mining is however, an activity that causes disturbance to the natural habitat and threatens biodiversity. Mining of mineral resources results in extensive soil damage, altering microbial communities and affecting vegetation leading to destruction of vast amounts of land which needs to be reclaimed and restored. Reclamation is the process to restore the ecological integrity of these disturbed mine land areas. Mining at the Eaton Tuner Shaft (ETS) area has been decommissioned and this paper seeks to explain processes leading to the sustainable design of a safe and suitable landform for the ETS as part of closure plan by reclaiming the vast land currently in the heart of Obuasi town. This is an exploratory study employing survey methods, geotechnical profiling and topographical survey to obtain data for the landform design and ultimate land reclamation. The study revealed that the soils at the ETS area have an upper stratum of sandy Gravels underlain by strata of silts or sands with average plasticity index of 14.46% and can be used as fill material with mean allowable bearing capacity between 781KPa and 1,413KPa. For a sustainable landform design, the study recommends a gentle slope transitions of about 2.5% and 1:2 for embankments. Keywords: Reclamation, Mining lands, Sustainable decommissioning, Landform design, Obuasi DOI : 10.7176/JEES/9-12-07 Publication date: December 31 st 2019

Bearing Capacity Analysis of Bridge Foundation Based on Cone Penetration Test Data and Soil Parameters Data

One that deserves the attention of planners in designing a bridge structure is the design of the substructure. This is due to the fact that the structure below determines the quality and service life of a bridge and at present many cases of bridge structure failures are caused by failures of the substructure in holding the load acting on the bridge The aim of this research to test the characteristics of the soil and calculate bearing capacity of the foundation based cone penetration testing data and soil parameters at the Aifa bridge construction field in Fafurwar District, Teluk Bintuni Regency, West Papua Province. From the results of testing the soil characteristics in the laboratory, the type of soil at point 1 is the type of good to bad graded sand soil (SW-SP) with a water content of 17.72%, specific gravity 2.98, liquid limit (LL) = 16,746% included in the non-plastic category. While the location of point 2 is obtained from good to bad graded sand soil type (SW-SP) with a water content of 28.52%, specific gravity 2.73, liquid limit (LL) = 16.746% including the non-plastic category. To analysis of the calculation of the bearing capacity of the foundation Aifa bridge using data from the sondir test results for point 1 was obtained allowable bearing capacity (Qall) is 4.610,44 kN and for point 2 was obtained allowable bearing capacity (Qall) is 3.598,43 kN. For calculating bearing capacity of the foundation using soil parameter data for point 1 was obtained bearing capacity allowable (Qall) is 2.209,93 kN and for point 2 was obtained allowable bearing capacity (Qall) is 655,41 kN

Determination of the Geotechnical Parameters of Soils Behavior for Safe Future Urban Development, Najran Area, Saudi Arabia: Implications for Settlements Mitigation

This paper deals with the geotechnical characterization of Sultana soils (Najran region, Saudi Arabia) by in situ and laboratory tests, for a project proposal for the construction of commercial and government buildings. Geotechnical parameters of the subsoil were analyzed with a view to using the soil as an earth construction material and as a foundation for buildings constructed on the grounds tested. The site was investigated by means of boreholes, trial pits, standard penetration tests, plate load tests, Seismological data, particle size analyses, modified Proctor Tests, Oedometer and direct shear tests. The study contains full description to the subsurface soil conditions and provides recommendations for collapse potential, foundation type, foundation depth, allowable net bearing capacity, estimation for the expected settlement. In this paper a review of the principal results of the in situ and laboratory investigations is described. Results of the study revealed that within the maximum depth of 10.0 m of boring, the soil was found to be composed of brown soil mixture of sand and clayey silt with little gravel, classified as (SM) and (SC) according to USCS classification and as (A-2-4) and A-2-6 according to AASHTO classification. The area was found to consist in general of collapsible soils, classified as collapsible alluvial soils. The results show that the collapse potential of the majority of semi-arid soils tested were classified as severe trouble soils and natural moisture content is an important factor influencing the collapse potential of the soil. In addition, the results of this study provide the parameters to evaluate the soil behavior and the geotechnical model for the foundation bearing capacity and soil settlements evaluation.

Rock Mass Characterization for Assessment of Safe Cut Slope and Rock Bearing Capacity at Gondang Dam Site, Karanganyar, Indonesia

This paper presents results of surface rock mass characterization for assessment of safe cut slopes and allowable bearing capacity of foundation rocks at the construction area of Gondang Dam. The rock mass characterization involved determination of intact rock engineering properties and rock mass quality based on the Geological Strength Index. The rock mass characterization results showed that the research area consisted of moderately to highly weathered and very weak to weak andesite breccia and andesite tuff breccia. The andesite breccia had very poor to fair rock mass quality, while the andesite tuff breccia had poor to fair rock mass quality. The research area was divided into three zones of safe cut slope and allowable bearing capacity. Landslides occurred at natural slopes having poor to very poor rock mass quality and inclinations greater than the determined safe cut slopes.The foundation rock of the embankment dam had fair rock massquality and 135–280 T/m2 allowable bearing capacity

Experimental investigation for the behavior of concrete slab rests on sandy soil contains cavities

Cavities formation into soil media is a very common problem that occurs in the gypseous soils (in which the gypsum content equals 2% and more). The gypsum dissolves by water flow leaching and leaves cavities in different shapes and sizes. In slab on grade system, the American concrete institute (ACI 360) recommends, the concrete slab transforms the load to the ground by about less than 50% of the allowable bearing capacity thereof, but when the soil contains cavities and excavation, the concrete slab behavior will change. In order to investigate the changing in behavior, twelve concrete slabs were prepared and tested on a soil media contains cavities. The investigated parameters were: cavity depth, steel wire reinforcement existence, bearing load plate shapes, and the load distributed parallel or perpendicular to the cavity. From the experimental results, it has been concluded that, the plain and reinforced concrete slab capacity decreases by (30.7%) and (7.4%) when a cylindrical continuous cavity forms at (30% mm) depth from the soil surface. However, when the cavity forms at a distance equal to (15%) from the soil surface, the plain and reinforced concrete slab capacity reduced by (70%) and (61%) respectively.

Nomographs for predicting allowable bearing capacity and elastic settlement of shallow foundation on granular soil

Prediction of allowable bearing capacity of granular soil requires an intensive field investigation program. This research proposes empirical correlations to predict the allowable bearing capacity and elastic settlement of shallow foundation on granular soils. The current correlation using only standard penetration blow count number and soil unit weight an estimation of the bearing capacity can be attained. Such correlations can be used at the preliminary stage of estimating the allowable bearing capacity and elastic settlement of shallow foundation on granular soils and can help site engineers make immediate decisions in cases of field variations given in soil reports. Moreover, it can be used to create a map for the country in basis of the allowable bearing capacity based on few soil parameters. In this study, database of granular soil properties obtained from 650 boreholes collected from various locations in Sharjah, United Arab Emirates, were used to develop the governing predictive equations. Multiple regression analyses were conducted to develop mathematical models and nomographic solutions to predict the allowable bearing capacity and elastic settlement of shallow foundation. Following development of predictive equations, a set of data collected from 40 boreholes and 20 zone load tests was used to verify validity of the predictive model. The results indicated that the nomographs could effectively predict allowable bearing capacity within ± 15% confidence interval and the elastic settlement within ± 10%.

Development of allowable bearing capacity for strip foundations in unsaturated soils

An allowable bearing capacity formulation of strip foundations is developed for unsaturated soils under the non–hydrostatic in–situ stress. Four cases are analyzed according to both in–situ stress states and suction distributions. The proposed closed–form formulation is easy to use along with non–negative factors as an application condition. Furthermore, the obtained results are compared against three published results reported in the literature, and good agreements between these results are observed. Finally, a parametric study is performed to present how unsaturated strength characteristics and in–situ stress states affect the allowable bearing capacity.

Reliability analysis of shallow foundation in the vicinity of the existing buried conduit

ABSTRACTThe present study proposes reliability-based approach for assessing the performance of shallow foundation placed in the vicinity of an existing buried flexible pipe or utility tunnel. Performance function for the reliability analysis is defined in terms of % bearing capacity loss in the load carrying capacity of the shallow foundation due to the presence of buried flexible pipe or utility tunnel, and, allowable bearing capacity loss in load carrying capacity that can be tolerated. For the reliability analysis, an explicit functional relationship between input variables, such as geotechnical parameters of in situ soil as well as material properties of pipe, and, output response, i.e. % bearing capacity loss in load carrying capacity of foundation soil is needed. Using concept of response surface methodology (RSM) combined with the results of the numerical analysis; such an explicit functional relationship is easily established. Thereafter, reliability analysis can be performed, conveniently, using standard First Order Second Moment (FOSM) approach and performance of the foundation soil system with buried flexible pipe, present in the vicinity, can be assessed in terms of an index, popularly known as ‘reliability index (β)’.

Determination of Engineering Geological Conditions of A Plant-Site: A Case Study in an Open Pit Mine in Çine, Aydın

A plant will be constructed between the Alipasa and Sarıkısık feldspar open-pit mines in Karpuzlu-Çine (Aydın) to conduct the works of crushing-grinding and flotation. An investigation was carried out to determine engineering geological conditions at and below the plant-site using scan-lines, geophysical measurements, and three inclined borehole data. Geological structure and ground conditions including geotechnical data such as discontinuity frequency and spacing, RQD% and CR% acquired from the drill hole exploration and geophysical survey are determined. Along the inclined drill holes, true discontinuity spacing values computed for each core run represent the most intersected discontinuities. In these calculations, determination of the acute angles between the axes of drill holes and strikes of the discontinuity sets are important as much as the investigation of fracture distributions in the subsurface. For this reason, the stereographic projection techniques were used to determine the true acute angle in this work. The purpose of the investigation is to identify and mitigate difficulties caused by ground conditions. The rock conditions comprise heavily jointed and weathered metamorphic rocks and the ability of these to support the foundations is considered. It was determined that the bearing capacity values obtained from the geotechnical computations considering RQD values agree with the ones acquired from the geophysical measurements, except the weakness zones (sheared zones). It was also determined that the values of allowable bearing pressure based on the geotechnical works are more conservative than the ones from the geophysical measurements. When all results are considered, the ratio between the allowable bearing capacity (qa) values acquired from geotechnical and geophysical measurements is close to 0.65.

Impact of climate change on allowable bearing capacity on the Qinghai-Tibetan Plateau

Climate change has a substantial impact on infrastructures in the permafrost on the Qinghai-Tibetan Plateau (QTP). In this study, the mean annual ground temperature (MAGT) and permafrost evolution were investigated in both the historical (1950–2005) and projected (2006–2099) periods. Then, an allowable bearing capacity model was used to discuss the allowable bearing capacity change on the QTP. Results show that the MAGT increased by 0.36 °C during 1950–2005. The MAGT will increase by 0.40 (RCP2.6), 0.79 (RCP4.5), 1.07 (RCP6.0), and 1.75 (RCP8.5) °C during 2006–2099. In addition, the permafrost area has decreased by 0.195 × 106 km2 in 1950–2005. The permafrost area will decrease by 0.232 × 106 (RCP2.6), 0.468 × 106 (RCP4.5), 0.564 × 106 (RCP6.0), and 0.803 × 106 (RCP8.5) km2 during 2006–2099. With the degradation of permafrost, the allowable bearing capacity in permafrost zones would decrease accordingly. The decreasing trend is 6 kPa per 10 years in 1950–2005, and will be 0.6 (RCP2.6), 5 (RCP4.5), 7 (RCP6.0), and 11 (RCP8.5) kPa per 10 years during 2006–2099. The most remarkable trend would be observed under RCP8.5. Meanwhile, some scientific advices for the design, construction, operation and maintenance of permafrost engineering in the context of climate change were provided.

Evaluation of allowable bearing capacity of Ayila Soil, south-west Nigeria

Accurate determination of allowable bearing capacity of soil is key to geotechnical foundations design so as to prevent collapse of structures built on them. Allowable bearing capacity of the study location has been determined by shear wave velocity approach. The seismic data used in this study are the in-situ shear and compressional wave velocities values measured by a 12-channel signal enhancement seismograph. Three layers were detected by the method. Empirical formulations and mathematical relationship between seismic velocities and elastic parameters were used to evaluate the allowable bearing capacity and other parameters presented in Table 1. Results show that allowable bearing capacity for layer 1 ranges from 123.56 to 173.54kN/m2. Layer 2 ranges from 233.24 to 377.62kN/m2, while layer 3 ranges from 437.62 – 616kN/m2. It was observed that allowable bearing capacity increases with depth – a 13% difference between layers 1 and 2 while between layer 2 and 3 there is a 22% difference. By comparison, the allowable bearing capacities evaluated in this study are in agreement with empirical values of allowable bearing capacity of soils proposed by other scholars. Findings show the study location is suitable for geotechnical foundation designs.Keywords: Ayila, Shear wave velocity, Allowable bearing capacity, Coefficient of subgrade reaction