Soil-structure pile foundation interaction model due to lateral loading

. Experimental research on piles, by models and physical tests on a laboratory scale, using materials and sizes that are different from the prototypes. The model is designed, treated, and interpreted the results of observing the response based on similarity using Model theory, but the soil sample cannot be modeled with model theory, giving rise to doubts similarity of the research. This study was conducted to examine the effect of pile-soil interaction on several views of the elastic modulus of the soil due to lateral loads. Laboratory model pile foundations are laterally loaded, on soil samples in a test box. The deflection of the pile foundation is analyzed based on the use of linear, layered, and non-linear modulus of elasticity. A non-linear simulation of the Winkler model with a spring along the depth of the pile was carried out to calibrate the horizontal deflection of the laboratory experimental model. The results showed that the Winkler model's modulus of elasticity was approximately 40% of the pile length, and the non-linear difference between the Winkler and laboratory models was 10.77%, comparisons can be conclusive about the need for similar research on lateral loading of laboratory model piles. The analysis also noted that the surface deflection was determined by winkler’s model elastic modulus analysis with an excess of about 12% to 14% in the first 10% of the pile length.


Introduction
Pile foundations with considerable lateral loads, for example, tall buildings, basement walls, and transmission towers, in general, the pile response due to lateral loads is obtained from lateral loading tests in the field, ASTM D3966 [1], and mathematical model simulations, Sumiyati Gunawan et al [2][3][4].Pile response due to lateral loads depends on the strength of the pile and the soil around the pile which is represented by the elastic modulus of the soil which is expressed by the stiffness value ks.
Research on pile foundations that receive loads from superstructures requires a field test model to obtain results in research and design.Model tests are very helpful in developing new theories and developing simple formulations for design and analysis purposes.The field test model has a very large size and workload and requires high costs so in research it is necessary to have a test model made in a laboratory with a certain geometric scale (smaller than the prototype), which is of course cheaper.
Suhendro [5], states 2 important things that must be known before we make experimental work, namely the theory of structural models and experimental techniques.Structural models in the laboratory use materials and sizes that are different from the prototype.Careful planning is required to obtain good results, including accuracy, similitude requirements (for geometry, materials, loading, and interpretation of results), model selection, and others.This research will be conducted in the laboratory to analyze the response of the soil around acoustically loaded laterally, Suhendro [5], Yosafat [6] using theory Winkler [7] modeling as a spring system with non-linear ks stiffness, and using theory Reese Matlock [8] modeling linear ks stiffness along the depth of the pile with the help program Mathlab R2013a.
Soil samples in the laboratory cannot be modeled using theoretical models, because soil samples are taken directly in the field with certain physical and mechanical properties according to the original conditions in the field, giving rise to doubts about the need for similar research.Comparison of the difference in mean results can be used to ensure the need for similarity of research on pile foundation loading with laboratory models.
The structural model uses the True Model, that is, all similitude requirements are met by the model so that it has complete similarity with the prototype.There are 10 (ten) types of physical variables involved in modeling calculations including horizontal load (H) and lateral load (V), horizontal deflection and lateral settlement (δy and δx), pile length (L), pile width/diameter (D), box height (Z), box width/diameter (B), pile elastic modulus (E), the moment of inertia (I), as independent variables.Loading the piles in the test box and recording the horizontal deflection and lateral settlement of the pile foundation with the simultaneously combined load, the variables involved include Table 1.With model theory Suhendro [5] by involving 10 (ten) types of physical variables involved in calculating the modeling of pile foundations that receive lateral loads, Equations 1-7.
Equations 1-7 are used to model the test pile foundations, loads, and test boxes in the laboratory as shown in Table 2. Soil sample modeling uses soil property values (soil specific gravity, soil volume weight, and density) because the soil samples are taken directly in the field and cannot be modeled with Structural Model Theory.Yosafat [6], the finite element method is a calculation procedure used to get an approach to mathematical problems that often arise in engineering.The core of the method is to make mathematical equations with various approaches and a series of algebraic equations involving values at points.discrete on the part being evaluated.Finite element method equations are made, and solutions are sought as best as possible to avoid errors in the result.The net (mesh) consists of elements connected by nodes.Nodes are the points on the net where the value of the primary variable is calculated.In displacement analysis, the value of the primary variable is the value of the displacement.The nodal displacement values are interpolated to the elements to obtain algebraic equations for displacement and strain through the formed nets.
The purpose of this study is to analyze and compare the results of lateral deflection on single-pile foundations subjected to lateral loads, on a full scale using the Winkler foundation concept and on a laboratory scale, a comparison of the average differences is expected to be used to ensure that the need for similarities in research on pile foundation loading with laboratory models, even though the soil samples used cannot be modeled with theoretical models.

Methodology
Tools and Materials used in the laboratory: 1. Test box of reinforced steel (1.5m x 1.5m x 1.2m) as shown in Fig. 1. 2. Soil samples from Kalitirto, Berbah, Sleman, Special Region of Yogyakarta, with soil parameters as shown in Table 3,

Load test in the laboratory
The following loading steps are carried out in the laboratory: 1. Prepare a soil sample in a test box, try to make it so that the conditions following Table 3, 2. The pile model is installed laterally and covered with a steel plate as a poer, fastened with bolts as shown in Fig. 4 no.1, 3. The load is installed with the load layout frame shown in Fig. 4 No.9, for the proper load position, 4. Vertical hydraulic jack installed, to provide an axial load on a single pole, according to Fig. 4 no.3, 5. Dial gauge is installed to read the movement of the lateral decline due to the given load, 6.The addition of axial load (single pile) with a load interval of 2500 gr, is carried out gradually increasing until it collapses if the rate of lateral settlement is less than 0.05 mm / 10 minutes or 0.0125 mm / 2.5 minutes, otherwise it is considered to have collapsed and loading is stopped.[1] Note the decrease.

Spring modeling with the winkler formula
The elastic modulus values of the soil in the field are layered and non-linear, but physical modeling in the laboratory uses the assumption that the average length of the pile is used to simplify the analysis.
From the Winkler's foundation concept [7], the soil reaction is idealized as spring points acting along the pile column as shown in Fig. 5.

Fig. 5. Model spring along the pile, Winkler [7]
The soil reaction along the pile beam at the finite difference node is as follows Equations 8-9.The solution of this equation uses the matrix method as follows Equation 17.Based on the Winkler concept, the horizontal deflection along the pile at 16 modeled points is obtained, with the help of Matlab R13a as shown in Fig. 6.

Modeling with reese& matlock
Reese-Matlock [8], for calculating moments and horizontal loads, soil reactions and deflections along the piles, based on the analogy of beams on elastic supports as shown in Fig. 7, mathematically it can be written Equation 18.
In each case, there are six terms with two dimensions, namely: force and length, Equation 19.
So that the following Equation 20 is the total displacement that occurs due to the moment and lateral force.
Modeling is done with the average modulus of elasticity along the pile, the average elastic modulus of the lining, and the non-linear modulus of elasticity along the pile, shown in Table 4 and Fig. 8, that the deflection which has a very significant effect is around 40% of the top pile length.

Research result
The research results predicted a significant difference in the influence of soil elastic modulus occurs in about 40% of the top pile length, and the remaining 60% is no longer significant, between the non-linear soil spring model and the laboratory test model in the case of a single pile under loading.laterally.The results showed that the difference in horizontal deflection between the finite element model and the laboratory model was an average of 6.35%, and the Winkler model and the laboratory model were an average of 10.77%.A comparison of the average difference can be used to ensure the need for similarity in pile foundation loading studies with laboratory models.

Conclusion
1.The conclusion showed that the average comparison of   /  and   /  at laboratory model was 6.35% and 10.77%.A comparison of the difference in results can be used to consider the assumption of using the average soil elastic modulus along the pile in modeling to simplify the analysis.2. The results of the analysis show that the effect of horizontal deflection occurs at around 40% of the pile length from the pile head.3. The analysis results note that the surface deflection is determined by nonlinear elastic modulus analysis with an excess of about 12% to 14% over the average horizontal deflection in the first 10% of the pile length.These results need to be considered in the subsequent analysis of the linear elastic modulus.

3 .
Closed steel pile foundation with a thickness of 0.001m, length L = 0.6 m, and diameter D = 0.02 m, shown in Fig. 2., 4. 0.001m thickness steel plate as poer, 5. Load control frames and lateral & horizontal hydraulic jacks, proving rings for lateral and horizontal loads, sketches shown in Fig. 3-4.

Table 1 .
Variables involved in pile foundation deflection.

Table 3 .
Laboratory experimental soil sample parameters.