ANALYSIS OF STATIC AND DYNAMIC DEFORMATION MODULUS

Mindaugas MIKOLAINISa, Marijus USTINOVIČIUSb, Danutė SLIŽYTĖc, Tatyana ZHILKINAd aSP „Baltijos inžineriniai sprendimai“, Laisvės 3-16, LT-97147 Kretinga, Lithuania bAB „Markuciai Sverige“ Box 37 SE-125 21 Älvsjö, Stockholm Sweden cVilniaus Gedimino technikos universitetas, Statybos fakultetas, Geotechnikos katedra, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania dMoscow State University of Civil Engineering (National Research University), Yaroslavskoye shosse 26, 129337 Moscow, Russia


Introduction
Dynamic plate load (DPL) tests in road construction are not used very often, since dynamic plate load test is not accepted as an official compaction method in Lithuania (Bertulienė 2011;Lietuvos automobilių... 2004). Thus aforementioned test is rarely used as an official compaction test and is used in sites where minor compaction is permissible (for example: sidewalk zones, trenches, etc.) where static plate load (SPL) test would be difficult to execute, or where loads are light. e.g., pedestrian sidewalks or residential floors. In order to use dynamic plate load tests for road base compaction tests it is needed to have a reliable comparison between dynamic deformation modulus and second load static plate deformation modulus. New dynamic plate load test values and their comparison with static plate load test values would help to evaluate compaction quality in both methods, thus helping to gain credibility of DPL tests (Tompai 2008;Bertulienė 2014). It is worth to mention that different countries had done these experiments and the analyses of results gave a mutual result showing that there is a relation between DPL and SPL tests, but they differ when applying them on different soil layers (Tompai 2008;Bertulienė et al. 2010). When the compaction quality of soil is tested as usualy the correlation relationship between E vd and E V2 is indicated, but these cases are often mentioned in literature with postscript: 'for information purposes only, no guarantee of information correctness' (Zorn instruments 2004). Herefore, the study was to verify whether relationships between E vd and E v2 which are found in literature can be applied to uniform (poorly graded) fine sand and how E vd depends on surcharges near the plate during the DPL test.

Dynamic deformation modulus evaluation according to dynamic plate load test
Theoretically if one wants to evaluate compressibility it is considered that a soil deforms as an ideally homogenical, isotropical material (Smoltczyk 2002;Zorn instruments 2004). Concentrated force P is loading load plate, and cause of this load plates' settlement is s. This elasticity modulus is taken from theory of elasticity and can be evaluated as follows: Here E -modulus of elasticity, MPa, ν -Poisson's ratio, r -radius of plate, m, P -force at plate workplane, MN. It is assumed that contact stresses under load plate are even and equal: If assuming that soil Poisson's ratio is ν = 0.212 and that soil is elastic, formula can be represented as a differential equation: It is important that this equation is derrivative out of formula (1) where soil is elastic and this is true only when density ratio (actual density versus Proctor optimal density -D pr , %) is large.
When analysing dynamic deformation modulus it is assumed that inertial forces and scale factor is not evaluated. Maximal stress to base is equal, i.e. not dependant from soil type, properties σ 0 max = 0.1 MPa, plate radius 150 mm. When these entered to (3), we get: Here s max -plate settlement (average of three tests) from dynamic load.

Soil static plate load test according0 to LST 1360.5:1995
Load to soil is increased incrementally by 0.02 MPa. This incrementation is around 10. When maximum value is reached, load plate is unloaded to 50% of maximal loading, then to 25% of maximal loading, then it is totally unloaded. When load plate is fully unloaded an additional secondary loading is executed, but it is loaded up to 9 th load incrementation value from the previous load. Two deformation modules E v1 and E v2 are evaluated, respectivelly for first load curve and for second load curve (Fig. 1).
In order to evaluate modulus of deformation, a regression curve has to be solved, which is defined as follows Here σ 0 -soil stress under load plate, s -load plate settlement, mm; a 0 , a 1 , a 2 -second degree constants, which can be found from the following equations: The first and the secondary load curves from which deformation modulus is calculated connecting tangent values of curve values 0,3σ 0j max and 0,7σ 0j max are analysed: Here Δσ 0 -load plate contact stress difference, MPa; a 1 , a 2 -constants found from equation 6; σ 0j max -j maximum stresses under load plate, MPa. Recommended values applicable for Lithuania see in Figure 2.
Ustinovičius (2015) has done subgrade deformation modulus tests in Vilnius Intermodal terminal. Subgrade was prepared and densified with uniform fine sand strata (LST EN ISO 14688-2, LST EN 933-1:2002). 30 static plate load and dynamic plate load tests were done by using statical beam "Frowag" and dynamic plate load "Zorn ZSG -02". Results with recommended correlation values in Lithuania are presented in Figure 3.
A comparison of the experimental data ( Fig. 4) indicated that in Lithuania the E VD to E V2 conversion values (Zorn instruments 2004; Lietuvos automobilių ... 1995) used for uniform (poorly graded) fine sand is too high. To such soils the dependencies of "Baksay formula" and Tompa 2008 for the coarse and fine soils suit better. In a very important objects formation of dependence according the results of tests in Situ is recommended.

Dynamic deformation modulus dependence on surcharge
Dynamic plate load test can be used also in trench. It is known that during static plate load test static deformation module E V2 of 2 nd loading obtained in trench is larger than E V2 , then the test is executable with the same conditions from the ground surface (Paulmich 2004). Ascertaining whether the dynamic plate load test results for surcharge of soil are affected by the results of the tests the experiment was carried out. Surcharge around to the plate simulates the soil prism of trench. Test scheduled equivalent trench depth is equal to 1.5 m (30 kPa assuming that the soil volumetric weight of 20 kN / m3).
An area in which the natural soil is homogeneous and of natural density was selected, and the tests were carried out in three rows, separated from each other by 2 m (Fig. 5).  Dynamic load plate test in the above place for determination of soil dynamic deformation modulus (E VD ) was carried out. Close distance (15-30 cm), but not in the same place load blocks (5 kPa) on two floors (10 kPa) were fixed on four sides around the plate (symmetric surcharge). The plate during the test is left between the load blocks (Fig. 6). The test objective was to distract the testing locations so that one test soil compaction should not affect other test results.
The test plan is shown in Figure 5. The load is therefore increased up to 20 kPa and then to 30 kPa, by the same procedure. For a maximum of 24 bricks at 6 in the floor should be used in total. The tests' results are shown in Table 2.
Experimental data show, that the soil is very loose. According the graphic (Fig. 7) can be seen that when the increase surcharge values with equal intervals (intervals of 10 kPa) dynamic deformation modulus increases more rapidly, in other words, the curve slope increases. From the experimental data can be determined curve function.
Acceptance curve function b successive power curve. This polynomial is represented by Levenberg-Marquard minimization method (Marquardt 1979 According the said method of calculation, we get the polynomial constants a, b, c. Then the expression of prediction of dynamic deformation modulus (MPa) is: There the relative depth: Here p -surcharge, kPa, γ -soil unit weight, taken 20 kN/m 3 , because soil above tested surface must be compacted.
The experimental data and theoretical relationship between the E VD and the excavation depth (or surcharge) presented in Figure 8.

Conclusions
For uniform (poorly graded) fine sand used E VD to E V2 conversion values according Zorn instruments (2004) and (Lietuvos automobilių ... 1995) are too high, making it unusable. For uniform (poorly graded) fine sand E VD to E V2 conversion values are better suited from the dependencies of "Baksay formula" (Measurement of load) and Tompa (2008) for the coarse and fine soils. In a very responsible objects recommended formation of dependence according the results of in Situ tests.
It was found that an E VD value depends on surchage around plate during test, its rises with surcharge (or increased of depth).
The proposed empirical regression equation evaluates deformation module size at surcharge. It applies to the measurement of the compaction of trenches. However, the suggested relationship for only a very loose sand. In order to evaluate the deformation of the module dependency surcharge, should be performed with a variety of different parameters (granulometry and state of compaction). Marquardt, D. 1979  Mindaugas MIKOLAINIS. Freelance geotechnical engineer of Baltijos Inžineriniai sprendimai. Fields of research and work: heavy construction, foundation design, construction on weak soils, highway engineering, engineering with geosynthetics. He have been in the field not only in Lithuania but also abroad practicing geotechnical engineering on major Austrian geotechnical consulting firm -3P Geotechnik as well as using his knowledge on field in drilled shaft foundations, deep excavations, highway engineering, undergound construction, and offshore engineering in Boston and New York, USA at SKANSKA USA Civil.