## 1 Introduction  
The dynamics of pile groups are important due to their applications in machine foundations and structures exposed to cyclic loads such as wind or earthquakes. The response of structures supported by pile groups depends upon the cyclic stiffness and damping generated by geomaterial-pile interaction. Due to complex geomaterial-pile interaction, the dynamics of pile groups are not well understood. There are no readily available methods that could evaluate the response of geomaterial-pile interaction hence the geomaterial stiffness is ignored and only the pile stiffness is considered. The omission of geomaterial-pile interaction makes the analysis of pile groups quite unrealistic ([PERSON] [1] and [PERSON] [2, 3]). Several analytical and numerical studies on the piles subjected to static lateral and torsional load ([PERSON] [4, 5]; [PERSON] [6, 7]; [PERSON] [8]; [PERSON] [9]; [PERSON] and [PERSON] [10]; [PERSON] and [PERSON] [11]; [PERSON] [12]; [PERSON] and [PERSON] [13, 14]; [PERSON], [PERSON] and [PERSON] [15]; [PERSON], [PERSON] and [PERSON] [16]) are extended to the pile groups in the present work. A series of experiments was reported on single piles and pile groups subjected to torsional loads ([PERSON] and [PERSON] [17, 18, 19, 20, 21]). The numerical model was developed for the combined axial and torsional loads in flow-controlled geomaterial for the pile groups ([PERSON] and [PERSON] [20]). The progressive twist, displacements and torsional energy around the pile groups have been presented ([PERSON] and [PERSON] [21]). The settlements of sand due to the cyclic twisting of the tube were investigated by [PERSON] and [PERSON] [22]. The solutions for dynamic analysis of piles ([PERSON] and [PERSON] [23]; [PERSON] and [PERSON] [3]; [PERSON] and [PERSON] [24]; [PERSON] and [PERSON] [25]; [PERSON] and [PERSON] [26]) including the literature reported mainly focused on the generic behavior of pile groups subjected to torsion while the cyclic torsion effect have not been considered. The investigators [PERSON] and [PERSON] [27] have used the finite element -finite difference method to evaluate the safety against the liquefaction of a reservoir subjected to cyclic loading.  
The design of offshore pile groups requires consideration of the effects of cyclic torsional loading. Therefore, the present paper considers a numerical scheme that provides a framework for the estimation of the behavior of a pile group in the sand under cyclic torsional loading. Based on a numerical scheme, the three-dimensional finite element analysis has been used to clarify the mechanism of load transfer from the pile to the surrounding geomaterial for the pile groups. The cyclic analysis of the torsionally loaded pile group in the sand is carried out by idealizing the individual pile as beam elements and the geomaterial as nonlinear spring elements. An iterative procedure is adopted and the effect of lateral and torsional load on deflection and twist, respectively, for the pile groups are investigated. Based on the lateral deflection and twist at the end of the first cycle, the degradation factor is evaluated and p-y and \(\tau\)-\(\theta\) curves are modified. The results from the numerical analysis work well with the published experimental results on the pile group subjected to two-way cyclic loading. Therefore, regarding the effect of torsional loads on the pile group, the following mechanisms have been investigated, namely, (a) cyclic twist behavior of the pile group (2,2) in the flow-controlled geomaterial as a result of the torsional loading and (b) the plastic strain and peak shear stress in a flow-controlled geomaterial captured for cyclic torsional loads, which, in turn, is a function of the number of cycles and dilation.