CN115201450B - Prototype time and deformation calculation method for geotechnical centrifugal model test - Google Patents
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Abstract
The invention provides a prototype time and deformation calculation method for a geotechnical centrifugal model test, which comprises the following steps: preparing a reduced-scale geotechnical model, and carrying out centrifugal test on the reduced-scale geotechnical model to obtain test data; and according to the test data, considering the centrifugal acceleration stage, and calculating by using a test prototype corresponding relation model to obtain prototype time and prototype deformation data. The prototype time and deformation calculation method for the geotechnical centrifugal model test can obtain more accurate prototype time and deformation.
Description
Technical Field
The invention belongs to the technical field of geotechnical centrifugal model tests, and particularly relates to a prototype time and deformation calculation method for geotechnical centrifugal model tests.
Background
The geotechnical centrifugal model test is the most effective physical model test technology recognized in the field of geotechnical engineering. The principle is that a scale geotechnical engineering model is placed in a geotechnical centrifuge, the deadweight stress of prototype engineering is applied to the model by utilizing an ultragravity field, the engineering characteristics of geotechnical materials can be reproduced, wherein the most important is the analysis of stress, deformation and time, and the direct action of the geotechnical materials caused by stress is mainly reflected in the deformation, so that the analysis of the test result of the geotechnical centrifuge model is mainly reflected in the aspects of time and deformation.
However, in long-term centrifugal model test practices at home and abroad, it is also found that the acceleration and shutdown deceleration stages of the centrifugal machine cannot well correspond to the prototype engineering, and in the acceleration stage of the centrifugal machine, the soil body can generate larger deformation because the stress borne by the soil body is gradually reduced to the prototype self-weight stress. In the shutdown deceleration stage, the deformation of the soil body can generate resilience because the stress borne by the soil body is reduced. The command to shutdown is typically issued with the test objectives completed, and therefore researchers are often not concerned with the shutdown deceleration phase. To reach the design acceleration, the centrifuge model must go through an acceleration phase. For the experimental data in the acceleration stage, because the theoretical basis is insufficient and the analysis is not good, the general method is to take the moment when the centrifuge runs to reach the designed acceleration as the starting point of the analysis. Researchers also use an acceleration process to simulate the filling process of a prototype dam-dam project (chapter min, xu Guangming. Centrifugal simulation method of the filling process of an earth and rockdam. Hydronics, 1997), and analysis thereof shows that the deformation in the acceleration stage is divided by 4 to be converted into the dam crest settlement in the prototype filling process. And time uses the conventional quadratic similarity relationship. It can be seen that the data of the acceleration stage cannot be directly analyzed according to the existing centrifugal model similarity law. Therefore, conventional analysis is generally not considered for the test data of the acceleration phase.
However, the data of the acceleration phase is also valuable, and there is currently no way to accurately convert it to a prototype.
Disclosure of Invention
Aiming at the defects, the invention provides a prototype time and deformation calculation method for a geotechnical centrifugal model test, which can obtain more accurate prototype time and deformation.
In order to solve the technical problem, the embodiment of the invention adopts the following technical scheme:
the embodiment of the invention provides a prototype time and deformation calculation method for a geotechnical centrifugal model test, which comprises the following steps:
step 10), preparing a reduced-scale geotechnical model, and carrying out centrifugal test on the reduced-scale geotechnical model to obtain test data; the test data comprises model time and model deformation in a centrifugal acceleration stage and model time and model deformation in a centrifugal speed stabilization stage;
step 20) calculating by utilizing a test prototype corresponding relation model according to the test data to obtain prototype time and prototype deformation;
the expression form of the test prototype corresponding relation model is shown as formula (1) and formula (2):
wherein T represents the prototype time, T 0 The time of the centrifugal acceleration stage is shown, N represents the geometric similarity reduction multiple of the scaled geotechnical model, N (t) represents the acceleration scale,
s represents the prototype deformation, and S (t) represents the model deformation at time t.
As a further improvement of the embodiment of the present invention, the model deformation amount includes a model vertical settlement amount, a model horizontal displacement amount, or a vector sum of the model vertical settlement and the model horizontal displacement.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects: the prototype time and deformation calculation method for the geotechnical centrifugal model test effectively establishes a corresponding relation model between the prototype time and deformation and the model time and deformation in all stages (including an acceleration stage and a steady speed operation stage) of the geotechnical centrifugal model test, and calculates and obtains the prototype time and the deformation by using the prototype corresponding relation model according to test data obtained by the centrifugal test. The established test prototype corresponding relation model considers all test stages including a centrifugal acceleration stage and a centrifugal speed stabilization stage, and the acceleration stage and the speed stabilization operation stage of the centrifugal model test are generally used for simulating the construction period and the operation period of the prototype engineering respectively, so that all time of the prototype engineering is simulated, and the prototype time and deformation obtained by calculation in the acceleration stage are considered to be more complete and accurate. Meanwhile, the test prototype corresponding relation model also conforms to the geotechnical centrifugal model similarity law, and more accurate prototype time and deformation can be obtained according to the centrifugal test data of the geotechnical model and used for analysis of prototype engineering.
Drawings
FIG. 1 is a graph showing the change in centrifugal acceleration and deformation with time, which are obtained after a centrifugal test in an example of the present invention;
FIG. 2 is a graph comparing time and distortion obtained using the method of the present embodiment, time and distortion obtained using the conventional centrifugal model semblance law, and time and distortion obtained from an actual monitoring prototype.
Detailed Description
The technical solution of the present invention will be explained in detail below.
The embodiment of the invention provides a prototype time and deformation calculation method for a geotechnical centrifugal model test, which comprises the following steps:
and step 10), preparing a reduced-size geotechnical model, and carrying out centrifugal test on the reduced-size geotechnical model to obtain test data. The test data includes test time and model deformation in the centrifugal acceleration phase, and test time and model deformation in the centrifugal steady speed phase.
Specifically, a prototype engineering site soil body is collected, impurities are removed, the prototype engineering site soil body is added into a model box, then the soil body is prepared into a reduced scale geotechnical model according to characteristics (parameters such as density, water content and gradation) of the prototype soil body, and the geometric scale of the reduced scale geotechnical model and the prototype is 1/N.
Placing the scaled geotechnical model in a centrifuge, starting the centrifuge, increasing centrifugal acceleration Ng of the centrifuge, wherein the centrifugal acceleration is in direct proportion to the square of time, the test is in a centrifugal acceleration stage, and after the centrifugal acceleration Ng reaches Ng, the centrifuge runs at a stable speed, and the test is in a centrifugal stable speed stage, as shown in figure 1. Wherein g represents the gravitational acceleration, n represents the acceleration scale, which varies with the test time t,
t 0 indicating the end of the centrifugal acceleration phaseTime, f (t), is related to centrifuge speed control performance and test process design.
And collecting the time and the deformation in the centrifugal test process, wherein the time and the deformation comprise a centrifugal acceleration stage and a centrifugal speed stabilization stage.
If the foundation soil settlement process is researched, the deformation amount is the vertical settlement amount. If the landslide process of the slope body is researched, the deformation amount is the vector sum of vertical settlement and horizontal displacement.
And step 20) calculating to obtain prototype time by using the formula (1) according to the test data:
wherein T represents the prototype time, T represents the test time, T 0 The time of the centrifugal acceleration stage is shown, N represents the geometric similarity reduction multiple of the scaled geotechnical model, N (t) represents the acceleration scale,
according to the test data, the prototype deformation is calculated by using the formula (2):
wherein S represents the deformation of the prototype, t represents the test time, and t 0 The time of the centrifugal acceleration stage is shown, N represents the geometric similarity reduction multiple of the scaled geotechnical model, N (t) represents the acceleration scale,
s (t) represents the amount of model deformation at time t.
Wherein the prototype correspondence model expressed in the form of the equations (1) and (2) is derived by the following method:
at any time t in the test process, according to the general centrifugal model similarity law (table 1),dT＝[n(t)] 2 dt, dS = n (t) dS (t) = n (t) s' (t) dt. From the integration at 0 time at the beginning of the test, the arbitrary time t during the test can be obtained
And &>
In the centrifugal acceleration stage, 0 < t 0 Is provided with
And &>
T is more than or equal to t in the stable speed operation stage 0 Has a->
And &>
According to the embodiment of the invention, the prototype time is calculated by using the formula (1) according to the test time, and the prototype deformation is calculated by using the formula (2) according to the test time and the model deformation. If the acceleration phase is not considered, then t 0 =0,n (t) = N, there are
And &>
The model of the experimental prototype corresponding relation for calculating prototype time and deformation in the embodiment of the invention returns to the general centrifugal model similarity law, as shown in table 1. Therefore, the accuracy of the prototype time calculation and the accuracy of the deformation method in the embodiment of the invention can be verified.
TABLE 1
The following provides a specific example and comparative example to analyze the consolidation process of a project under the action of dead weight stress and stacking load.
In a certain homogeneous silt soil layer, the thickness of the prototype engineering silt soil layer is 20m, the upper surface is drained, and the surcharge preloading is 14 m. The natural density of the sludge is 1.6g/cm 3 The natural water content is 100 percent, and the density of the heaped soil body is 1.8g/cm 3 。
Reference example
And (3) actually monitoring the prototype project, recording to obtain actual time and actual settlement, and corresponding the actual time and the actual settlement to obtain the change trend of the actual settlement along with time, as shown by a curve A in figure 2.
Example 1
(1) Collecting engineering site soil samples, transporting the engineering site soil samples back to a laboratory for paving, airing, grinding, sieving and other treatments, then preparing a silt soil layer in a model box according to natural density and water content, and arranging a laser displacement meter on the upper surface of the soil layer for measuring the consolidation settlement amount of the model soil body in the test process.
The geometric scale of the model is 1/100, the design acceleration is 100g, the thickness of the soil layer of the model is 200mm, the sludge is taken from an engineering site, and the density and the water content are consistent with those of prototype soil.
(2) The model was placed in a centrifuge and the centrifuge was started. The centrifugal machine adopts a direct current speed regulation control mode, and the rotating speed of the centrifugal machine is linearly increased, so that the centrifugal acceleration is in direct proportion to the square of time, and the centrifugal machine runs at a stable speed after the centrifugal acceleration reaches 100 g. The test time and model settling volume were recorded throughout the test.
(3) And (3) calculating by using a formula (1) to obtain prototype time according to the recorded test time and model settlement amount, and obtaining the prototype settlement amount by using a formula (2). The prototype time and the prototype settlement amount are corresponded to obtain the time-dependent change trend of the prototype settlement, as shown by a curve B in FIG. 2.
Comparative example 1
(1) Collecting engineering site soil samples, transporting the engineering site soil samples back to a laboratory for paving, airing, grinding, sieving and other treatment, preparing a silt soil layer in a model box according to natural density and water content, and arranging a laser displacement meter on the upper surface of the soil layer for measuring the consolidation settlement amount of the model soil body in the test process.
The geometric scale of the model is 1/100, the design acceleration is 100g, the thickness of the soil layer of the model is 200mm, the sludge is taken from an engineering site, and the density and the water content are consistent with those of prototype soil.
(2) The model was placed in a centrifuge and the centrifuge was started. The centrifugal machine adopts a direct current speed regulation control mode, and the rotating speed of the centrifugal machine is linearly increased, so that the centrifugal acceleration is in direct proportion to the square of time, and the centrifugal machine runs at a stable speed after the centrifugal acceleration reaches 100 g. And recording the test time and the model settlement amount in the centrifugal speed stabilizing process.
(3) And (4) according to the recorded test time and model sedimentation amount, calculating to obtain prototype time and prototype sedimentation amount by adopting a conventional method and taking the time when the centrifuge runs to reach the designed acceleration as the starting point of analysis without considering the acceleration stage. The prototype time and the prototype settlement amount are corresponded to obtain the time-dependent change trend of the prototype settlement, as shown by a curve C in FIG. 2.
As can be seen from fig. 2, the method of the embodiment of the present invention is closer to the actual measurement variation trend, which can show that the method of the embodiment of the present invention can obtain more accurate prototype time and deformation.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are intended to further illustrate the principles of the invention, and that various changes and modifications may be made without departing from the spirit and scope of the invention, which is also intended to be covered by the appended claims. The scope of the invention is defined by the claims and their equivalents.
Claims (2)
1. A prototype time and deformation calculation method for a geotechnical centrifugal model test is characterized by comprising the following steps:
step 10), preparing a reduced-scale geotechnical model, and carrying out centrifugal test on the reduced-scale geotechnical model to obtain test data; the test data comprises model time and model deformation in a centrifugal acceleration stage and model time and model deformation in a centrifugal speed stabilization stage;
step 20) calculating by utilizing a test prototype corresponding relation model according to the test data to obtain prototype time and prototype deformation;
the expression form of the test prototype corresponding relation model is shown as formula (1) and formula (2):
wherein T represents the prototype time, T 0 The time of the centrifugal acceleration stage is shown, N represents the geometric similarity reduction multiple of the scaled geotechnical model, N (t) represents the acceleration scale,
s represents the prototype deformation, and S (t) represents the model deformation at time t.
2. The prototype time and deformation calculation method for geotechnical centrifugal model test according to claim 1, wherein said model deformation comprises model vertical sedimentation, model horizontal displacement, or vector sum of model vertical sedimentation and model horizontal displacement.
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