The engineering method for determining the settlement of point due adjacent constantly distributed circular load

Abstract

The article considers linear half space subjected to the circular load of constant intensity. Point settlement is determined by integrating relation to an infinitesimally small area, as per the Bussinesque solution, for concentrated load. The authors propose to replace an integration technique with a summation technique aiming to reduce computational efforts. The application of the summation techniques developed by the authors and their subsequent employment to develop an engineering method ensures sufficient accuracy for engineering purposes for point settlement evaluation. An attractive feature of the proposed engineering method is its implementation via nomograms ready for fast usage. It is especially convenient for a design process that requires obtaining relatively rapid results for multi-variant geotechnical design situations. A calculation algorithm and computational program have been developed to perform the summation techniques. Thanks to the extensive numerical simulations of settlement evaluations under the developed method, variation in the loading surface radius has also been limited. When applying the engineering method, relative error does not exceed 2% for cases when the ratio of radii from the settlement point being investigated to the centre point of circular loading varies within the interval of 1.5 to 7 times. This degree of accuracy is sufficient for engineering design needs. In practice, this engineering method can be applied in case it is assumed that the circular load of constant intensity is the load that acts on the base at the point of contact between the foundation and the base. The point the settlement of which is calculated is the point of the base or the point at the centre of the foundation. It is recommended to apply the engineering method presented in the article when the distance between adjacent foundations is 10 times less than the diameter of the foundation. When the distance is 10 times more than the diameter, foundations almost do not affect each other. The engineering method is especially useful when differential settlements are being calculated, e.g. the impact of deformation seams on the foundations or the effects of a projected building that will be attached to an existing one. This method can be used for calculating both shallow and deep foundations. When deep foundations are calculated, it is necessary to evaluate the enlargement of the pile base occurring due to friction between the ground and the pile material.

Article in Lithuanian.

Inžinerinis metodas taško nuosėdžiui skaičiuoti nuo gretutinės apskritiminės tolygiai išskirstytos apkrovos

Santrauka. Tiesiškai deformuojamo puserdvio, apkrauto apskritimine tolygiai išskirstyta apkrova, vertikalieji poslinkiai apskaičiuojami integruojant Businesko sprendinio vertikaliojo poslinkio išraišką apkrautame plote. Šis integralas apskaičiuojamas sumavimo metodu. Darbe pateiktas tiesiškai deformuojamo pagrindo, apkrauto apskritimine tolygiai išskirstyta apkrova, nuosėdžių skaičiavimo metodas yra gana tikslus. Šiuo metodu galima įvertinti puserdvio paviršiaus nuosėdį ne tik nuo apskritiminės tolygiai išskirstytos apkrovos, bet ir nuo kitų, greta esančių apskritiminių tolygiai išskirstytų apkrovų. Inžineriniam metodui realizuoti taikytas sumavimo principas, pakeičiantis tiesioginį integravimą reikiamu tikslumu. Tuo tikslu sukurtas sumavimo algoritmas, jį realizuojanti kompiuterinė programa. Inžinerinis poslinkio skaičiavimo metodas realizuotas laipsnine lygtimi ir jam taikyti patogia naudoti nomogramų forma. Taikant sukurtą inžinerinį metodą atliktas nuosėdžių apskaičiavimo skaitinis modeliavimas. Atlikus skaitinio eksperimento rezultatų analizę, identifikuoti nuosėdžių kitimo dėsningumai. Pasiūlyta analizinė išraiška nuosėdžiams skaičiuoti. Nuosėdžių, apskaičiuotų inžineriniu metodu, santykinė paklaida neviršija 2 %, kai apskritiminės tolygiai išskirstytos apkrovos centro taško atstumo iki taško, kurio skaičiuojamas nuosėdis, santykis su apskritiminės tolygiai išskirstytos apkrovos spinduliu kinta nuo 1,5 iki 7.

Reikšminiai žodžiai: apkritiminė išskirstytoji apkrova, Bussinesque sprendiniai, sumavimo algoritmas, inžinerinis metodas taško nuosėdžiui skaičiuoti.

First Published Online: 16 May 2013

Keyword : circular distributed loading, Bussinesque solutions, summation algorithm, engineering method for point settlement evaluation