Dynamic characteristics of soils subject to impact loadings

Acta Mechanica Solida Sinica, Vol. 21, No. 4, August, 2008 Published by AMSS Press, Wuhan, China. DOI: 10.1007/s10338-008-0841-2

ISSN 0894-9166

DYNAMIC CHARACTERISTICS OF SOILS SUBJECT TO IMPACT LOADINGS Zhirong Niu1

Guoyun Lu2

Dongzuo Cheng3

(1 College of Civil Engineering and Architecture, Jiaxing University, Jiaxing, Zhejiang, 314001, China) (2 Institute of Application Mechanics, Taiyuan University of Technology, Shanxi, Taiyuan, 030024, China) (3 Taiyuan University, Shanxi, Taiyuan, 030026, China)

Received 24 June 2008; revision received 14 July 2008

ABSTRACT The dynamic properties of soil under impact loads are studied experimentally and numerically. By analyzing the microstructural photos of soils with and without impact, it is shown that impact loads can destroy the original structures in the compact area, where the soil grains are rearranged regularly and form the compact whirlpool structure. Simultaneously, the dynamic impact process of soil is simulated by using the software of Ls-dyna. The time-dependent distribution of the dynamic stress and density is obtained in the soil. Furthermore, the simulation results are consistent with the experimental results. The reinforcement mechanism and the rule of dynamic compaction of soils due to impact load are also elucidated.

KEY WORDS dynamic destruction, impact, soil, dynamic consolidation

I. INTRODUCTION Dynamic consolidation (DC) is a ground improvement technique. The process involves dropping heavy weights on to the surface of the soil from a considerable height. These high-energy impacts produce sufficient compaction effort to reduce void space, increase density and reduce long-term settlement of the soil. By increasing the density, it increases the bearing capacity and reduces the long-term settlement. For evaluating the effects of the improvement of bearing capacity by DC, much attention has been paid to the virtual reinforcement depth and affecting area of dynamic consolidation. Usually the change of reinforcement depth of DC is tested in-situ and laboratory. Some researchers have put forward several models of reinforcement pattern to evaluate the effect of DC[1–3] . But the dynamic stress, density change, and other dynamic characteristics in the dynamic destruction area subject to the impact loading have been in quest phase. In the existing theoretical analysis and numerical simulations, the muzzle velocity of soil unit contacting with hammer and the different characteristics of soil[2, 4] during the process of loading and unloading have not been considered for analyzing the stress state of soils in DC. Usually the contacting stress is calculated based on the one-dimensional line elastic model. It is unreasonable to use this kind of postulation in three-dimensional non-elastic or elasto-plastic analysis[5, 6]. The movement characteristics of the hammer and soils cannot be considered as a whole in these analyses. The boundary element method can give a satisfactory result of boundary stress but the self-weight of the hammer is ignored. In this paper, we carry out numerical analysis on the problem of dynamic consolidation of soil of Shanxi fertilizer factory (China), in which the muzzle velocities of soil unit contacting with hammer and the different characteristics of soil during the process of loading and unloading have been taken into account. The dynamic stress distributing law, density field, dynamic stress yield, and other factors

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of the dynamic destruction area of the soil subjected the impact loading. were discussed and compared with the results of in-situ tests. The simulation results are consistent with the data recorded in tests. In addition, the soils microstructure test has also been done to investigate the process of dynamic compact. The varying processes of soils’ microstructures of soil in the area of dynamic destruction were given: undisturbed soils, soils fracture, accelerated consolidation, soils consolidated again (thixotropy recovering) and new compact soils structure formed (compact whirlpool soils structure).

II. NUMERICAL ANALYSIS OF SOILS DYNAMIC CONSOLIDATION SUBJECT TO IMPACT LOADING 2.1. Foundation of Calculation Model The numerical mode considered multi-layer medium with assuming each layer as homogeneous and isotropic. The hammer is a short cylinder so that the DC problem can be taken as axially symmetric. Half of the soils section in the hammer axis is analyzed and the horizontal displacement of the soil in the middle axis is defined as zero. The surface to surface contact was defined between the soils and the drop hammer. One manpower boundary is confirmed in a certain depth. Taking an engineering example of Shanxi fertile factory, the numerical model includes two parts. One part is the hammer with 3 m height and 1 m diameter. It is simplified as a rigid body and divided to 90 count units. Its mass results from the equivalent density. The other part is the soil simulated with the elastoplastic constitutive model of Drucker-Prager. The numerical model of the hammer and soil is simplified as 5 m wide from the middle axis and 7.5 m deep according to the axis symmetry. The model is with 60 thousand count units and the non reflecting boundary is adopted. 2.2. Dynamic Balance Equation and Numerical Integral When the finite element method is applied to solve the dynamic equations, the equation of motion of the system is expressed in a matrix-form as follows: ¨ + [C]{Z} ˙ + [K]{Z} = [R] [M ]{Z}

(1)

where [M ] is the mass matrix of the system, [C] is the damp matrix of the  system, [C] = a[M ] + b[K], a, b are constants, [K] is the whole rigidity matrix of the system [K] =

[B]T [Dep ][B]dV , {R} is the

¨ {Z}, ˙ {Z} is the acceleration, velocity and displacement of node external dynamic load vector, {Z}, respectively, and [B] is the geometry matrix. The acceleration Z¨ and the velocity Z˙ of a node at time t can be expressed as: ¨ t= {Z} where

1 {Z}t − {A}t−θΔt , bθ2 Δt2

˙ t= {Z}

1 {Z}t − {B}t−θΔt bθΔt

    1 1 2 2 ¨ ˙ − b θ Δt {Z}t−θΔt {A}t−θΔt = 2 2 {Z}t−θΔt + θΔt{Z}t−θΔt + bθ Δt 2    r b 1 b 2 2 ¨ ˙ {Z}t−θΔt + 1 − θΔt{Z}t−θΔt + ( − )θ Δt {Z}t−θΔt {B}t−θΔt = bθΔt r 2 r

(2)

(3)

Substituting Eq.(2) into Eq.(1) yields [K] {Z}t = [R]

(4)

where 1 r [C] [M ] + bθ2 Δt2 bθΔt 1 r [R] = [R] + 2 2 [M ] {A}t−θΔt + [C] {B}t−θΔt bθ Δt bθΔt [K] = [K] +

(5) (6)

In Eqs.(2)-(6), r, b, θ are integral constants. With the Newmark constant acceleration method, these parameters are r=0.5, b=0.25, and θ=1. ¨ {Z}, ˙ {Z}, the corresponding stress, strain, and displacement can also be After calculating {Z}, gained.

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2.3. Soil Constitutive Model DC results in the permanent displacement of soils, so the elastoplastic constitutive model of DruckerPrager is applied: {dσ} = [Dep ] {dε} (7) where dσ is the stress increment, dε is the strain increment, and [Dep ] is the elastoplastic matrix   T ∂f ∂g [D] [D] ∂σ ∂σ [Dep ] = [D] −  T   ∂f ∂g +A [D] ∂σ ∂σ 

(8)

where [D] is the elastic matrix, f the yield function, g the plastic potential function, and A the process rigidification modulus. During the unloading process, the slope of the curve of stress and strain is equal to the slope of elastic phase. 2.4. Boundary Condition and Initial Condition Boundary conditionMulti-times transmission boundary[7] is adopted. Its finite element equation in an incremental form is: N (−1)j+1 CjN S j ΔV (9) ΔZ(t + Δt, r1 ) ≈ j=1

where ΔZ(t + Δt, r1 ) is the displacement of boundary node r1 , CjN is the binomial coefficient, ⎡ j−1 ⎤ S 0 0 N ! , S j = S 1 ⎣ 0 S j−1 0 ⎦, and N is the number of the transmission steps, CjN = (N − 1)!j! 0 0 S j−1 1 S = {T1,1 T1,2 T1,3 }, and T1,1 = (2 − ω)(1 − ω)/2, T1,2 = ω(2 − ω), T1,3 = ω(ω − 1)/2, ω = cA Δt/Δr, with cA being the common manual transmission wave rate, between the maximum rate and minimum rate, Δt the time steps, Δr the space between grids, ΔVjT = {ΔZ1,j ΔZ2,j · · · ΔZ2j+1,j }, and ΔZi,j = ΔZ[t − (j − 1)Δt, r1 ] the displacement increment in node r1 before t + Δt. Displacement initial condition: initial displacement and initial √ acceleration are equal to zero with initial rate 2gh (h: drop height of the hammer). Loading initial condition: interface dynamic Fig. 1 Impact loading model of dynamic consolidation. stress is initial condition of the external load (see Fig.1) 2.5. Impact Load of DC Qiu and Guo[1] Carried out the in-situ tests about the DC hammer impacting ground course in Shanxi fertilizer factory, whose site belongs to II-class self-weight collapse loess area. Test’s results show that the boundary stress wave has a pinnacle without a clear second stress wave. Duration of the action is about 0.04-0.2 seconds. Kong and Yuan[8, 9] , Thilakasiri, et al.[3] studied the surface touch dynamic stress. These results indicate that dynamic touch stress of the surface turns out to be a pulse stress wave, while the second stress wave is not clear. Therefore, the instantaneous load of DC is simplified as a triangulate loading model (see Fig.1).

III. RESULTS ANALYSIS 3.1. Project General Situation Taking the example of Shanxi fertilizer factory ground with II-class self-weight collapse loess, the tests were performed as followsexplore well, dynamic penetration, standard penetrationstatic cone penetration, pressurementer test, ground surface displacement, ash mark side displacement, pore water

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pressure, dynamic stress beneath hammer and in deep soils, density change of ground, vibration of surface of ground, consolidation time after DC etc. A lot of test data are obtained. The soils characteristics of the dynamic destruction area subject to the impact load are numerically analyzed and boundary dynamic touch stress is used as the stress boundary condition. The dynamic stress, soil density, pore water pressure in soils, displacement and acceleration etc change clearly, when Ansys-Ls-dyna software is used. The simulated results are consistent with test results. Main input parameters are in the Table 1. Table 1. Main input parameters

Unit weight (kN/m3 ) 16.5 Increase load time tR (s) 0.0383

Elastic modulus E(MPa) 60 Decrease load time tN − tR (s) 0.033

Cohesion C (kPa) 86 Δt (s) 0.0003

Angel of internal friction ϕ(◦ ) 32 Space between grid vertical (m) 1.5

Poisson’s ratio ν 0.3 Space between grid horizontal (m) 1.0

Maximum action load P max (MPa) 3.25

3.2. Change Law of Dynamic Stress with Depth The analytical result of dynamic stress of soil after DC is shown in Fig.2. The curve indicates that the dynamic stress of soil attenuates with the depth and the effective depth is 6 m. Compared with Fig.3, the change law of the curve is the same. Niu Z.R. and Yang G.T.[10, 11] have illustrated the character of vertical dynamic stress curve at the different depth: if the layer gradually moved from shallow to deep, the frequency varies from high to low, and the stress wave curve becomes simpler and more smooth.

Fig. 2. Calculated results of dynamic stress vs. depth.

Fig. 3. Test results of dynamic stress vs. depth.

3.3. Change Process of Dynamic Stress in Soils

Fig. 4. Developing course of the isograms of soil dynamic stress.

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The change process of dynamic stress with time is shown in Fig.5. In the initial phase of the impact loading, the area affected by the load is small. With time’s increasing, the disturbed area diffuses from the centre of the hammer pit forth. The shape of the curves looks like an ellipse. Fig.4 and Fig.5 indicate that the change of the dynamic stress diffuses from the centre of the hammer pit forth. Its effective area is similar to an ellipse. As time goes on, the pull stress approaches the border of the hammer pit gradually. This is why the ground raises in the border of the hammer pit.

Fig. 5. Isograms of soil dynamic stress (unit:time:ms, stress: Pa).

3.4. Compacted Area and Swelled Area of Soils after Impact Loading Both of the simulated results and the test data show that the displacement becomes permanent in the soils when the impact load is applied, which results in the variation of the volume of soil unit. Therefore, the soil density changes, and the simulation results indicate that the density of soil beneath the hammer pit reaches the maximum. The natural dry density of soil is 1.4 g/cm3 . The area of dry density >1.4 g/cm3 is named as ‘compacted area’, whose vertical section shape is ellipse. The dry density of soils reduces the external surface of the hammer pit (Fig.6) that follows the upheaval of external surface of the hammer pit. This is similar to the experimental curves in Fig.7 (the shape of compacted area).

Fig. 6. Compacted and swelled areas.

Fig. 7. Test dry density isograms of soil subjected to impact loading (ρd : soil dry density, unit: kg/m3 ).

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3.5. Change Law of Compacted Area and Swelled Area of Soils after Impact Loading Figure 6 shows that the compacted area and swelled area occur at different zones after the impact. There are swelled areas in both sides of the hammer pit. The area changes with soil compact modulus. The ground in the area is not suitable to up heave and moves forward hammer pit when soil is strong, and vice versa. Figure 6 is similar to Fig.7. In addition, there is a loose layer under the compacted area beneath the hammer that is explained by Chen[12] using microstructure experimental data. The loose layer is under the compacted depth and the characteristic is reflected in the isograms of vertical displacement. That is why the soil beyond the effectual reinforced depth (that is, the dynamic destruction area) of DC turned looser for its initial structure is stirred by little energy, and its density decreases for the energy attenuation of DC.

IV. MICROSTRUCTURE ANALYSIS The microstructure of soils is analyzed by electron microscope DC fore-and-aft as follows (for example of soil in 3∼5 m deep). In Fig.8(a), the undisturbed soil is point-point, point-border and point-plane touch, and the big pore and fly-over structure of soil formed with different shapes and different pore diameters. Under the action of DC impact load, the undisturbed structure is destroyed, a great deal of pore decreases and soil density increases (see Fig.8(b)). The soil grains are rearranged regularly and the compacted whirlpool structure forms (Fig.8(c)). The pore change of soils is provided in Table 2 DC fore-and-aft.

Fig. 8. Soils micrwstructure (undisturbed and disturbed).

Table 2. The bores change of soils DC fore-and-aft

``` SS

SL

``` BC ``

SLN

D 1 1 2 Q24 3 4 2 5 6 1 7 Q4 8 3 9 10 4 11 Q3 12 13 5 14 Q2 15 6 16 Note: BC: bore class, A: after DC

BD>500 μm

BD=500∼50 μm

Level B A

Vertical B A

Level B A

Vertical B A

3

6

80

90

0 3

0 3

0 2

0

0 0

15

0

3

5

1

60 45

2 0

80 35

40 25

45 20

10000

8000 6000

6000

400

5000 5000

4500 6500

300 250

9000 5000

8000

400 450

350

8000

300

350

10000 2100

5500

300

300

3300

7000 250

300

Vertical B A

11000

200

300

300

A

2600

400 300

13 35

B 1300

470

350

Level

50

300

13

25

800

450

25

40

1

10

BD=<5 μm

Vertical B A

100 475

30

50

2

2

10

0

625 0

60

40

0

1

2

75

1

2

0

BD=500∼5 μm Level B A

6500 6000

4700 3000

6300 3300

2 0 20 12 400 250 5000 3000 2 20 200 3500 SS: soil section, SL: soil layer, SLN: soil layer number, BD: bore diameter, D: depth, B: before DC,

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V. CONCLUSIONS The dynamic stress is greater in the surface of ground and shallow ground, and attenuates with the depth, and is almost zero far from the hammer pit. As time goes by, the dynamic stress diffuses forth in the center of the hammer pit. The area of dynamic stress appears gradually in the border of the hammer pit and the area is an ellipse, and the stress attenuates from the hammer pit gradually. The ground beneath the hammer is reinforced by DC, and the elliptical compacted area forms in a certain depth scope. The ground becomes loose from the bottom of the drop hammer to the top surface of ground. The ground out of the hammer pit becomes looser and should be treated using engineering techniques. We observe that the destruction area subject to the impact load is an elliptical sphere from the dynamic stress isograms, compact area and swelled area. According to this, the reinforcement depth can be estimated and the plan layout of DC hammer dot. That can be applied as the theoretical basis of design and construction of DC. There is a little loose layer under the compacted area. The scope of loose layer changes with the depth of compacted area. The undisturbed structure of soils in the compact area is destroyed subject to impact loading. The soil grains is forced to rearrange directionally and the compacted whirlpool structure forms. The pore of the soil decreases greatly and the density increases.

References [1] Qiu.Y.H., Guo,Y.L., The in-site measurement of dynamic stress in soil mass during heavy taping by dynamic consolidation method in ground improvement. Journal of the Taiyuan University of Technology, 1984, 1: 49-56, [2] Brandel,H., et al., Dynamic stresses in soil caused by falling weights. In: Proc. 9th Int. Conf. Soil Mech. Found. Engng., 1977, 187-194, [3] Thilakasiri,S., Millins,G., Stinnette,P., Gunaratne,M. and Jory,B., Analytical and experimental investigation of dynamic compaction induced stresses. Geotech 1993, 11. [4] Shang,S.Z., Some aspects about the treatment on saturated soft clay by dynamic consolidation. Journal of Building Structures, 1983, 2: 57-71. [5] Qian,J.H., Qian,X.D., Zhao,W.B. and Shuai,F.S., Theory and Practice of Dynamic Consolidation. Chinese Jounal of Geotechnical Engineering, 1986, 18: 3-19. [6] Wu,M.B. and Wang,Z.Q., Numerical analysis of dynamic compaction caused by the impacting vibration. Geotechnical Investigation & Surveying, 1989, 3: 1-5. [7] Liao,Z.P., Accuracies of local transmitting boundaries. Earthquake Engineering and Engineering Vibration, 1993, 13: 1-6. [8] Kong,L.W. and Yuan,J.X., Study on surface contact stress distribution properties for multi-layered foundation during dynamic consolidation. Acta Mechanica Sinica, 1999, 31: 250-256 [9] Kong,L.W. and Yuan,J.X., Study on surface contact stress and settlement properties during dynamic consolidation. Chinese of journal Geotechnical Engineering, 1998, 21: 86-92. [10] Yang,G.T., Soil Dynamic. China Building Material Industry Publishing House, China, 2000. [11] Niu,Z.R. and Yang,G.T., Dynamic characteristics of soils during and after dynamic consolidation. Engineering Mechanics (supp.) 2006, 3: 118-125. [12] Chen,D.Z., Study on microstructure of collapsible loess before and after dynamic consolidation. Master’s Degree Dissertation of Taiyuan University of Technology, China, 1983.